Keywords:Network analysis and control, Agents-based systems, Cooperative control Abstract: In the present paper, we provide results on the control of sam{general} opinion dynamics systems. The control is applied to one agent only, called the leader. Explicit control laws ensure three complementary desired behaviours of the system: i) drag all agents arbitrarily close to the leader, then ii) make all agents follow the leader toward a targeted value, iii) make all agents converge to a targeted consensus value. Unlike the existing literature, the control is carried out under weak assumptions on the leader influence. In particular, the leader may only have a bounded influence range (this for instance includes the Hegselmann-Krause bounded confidence model). Finally our results are illustrated by numerical examples.

Keywords:Network analysis and control, Agents-based systems, Large-scale systems Abstract: The paper considers the consensus problem in large networks represented by time-varying directed graphs. A practical way of dealing with large-scale networks is to reduce their dimension by collapsing the states of nodes belonging to densely and intensively connected clusters into aggregate variables. It will be shown that under suitable conditions, the states of the agents in each cluster converge fast toward a local agreement. Local agreements correspond to aggregate variables which slowly converge to consensus. Existing results concerning the time-scale separation in large networks focus on fixed and undirected graphs. The aim of this work is to extend these results to the more general case of time-varying directed topologies. It is noteworthy that in the fixed and undirected graph case the average of the states in each cluster is time-invariant when neglecting the interactions between clusters. Therefore, they are good candidates for the aggregate variables. This is no longer possible here. Instead, we find suitable time-varying weights to compute the aggregate variables as time-invariant weighted averages of the states in each cluster. This allows to deal with the more challenging time-varying directed graph case. We end up with a singularly perturbed system which is analyzed by using the tools of two time-scales averaging which seem appropriate to this system.

Keywords:Network analysis and control, Communication networks, Sensor networks Abstract: We consider the network reliability problem in wireless sensor networks secured by the heterogeneous random key predistribution scheme. This scheme generalizes Eschenauer-Gligor scheme by considering the cases when the network comprises sensor nodes with varying level of resources; e.g., regular nodes vs. cluster heads. The scheme induces the inhomogeneous random key graph, denoted G(n;mu,K,P). We analyze the reliability of G(n;mu,K,P) against random link failures. Namely, we consider G(n;mu,K,P,alpha) formed by deleting each edge of G(n;mu,K,P) independently with probability 1-alpha, and study the probability that the resulting graph i) has no isolated node; and ii) is connected. We present scaling conditions on K, P, and alpha such that both events take place with probability zero or one, respectively, as the number of nodes gets large. We present numerical results to support these in the finite-node regime.

Keywords:Network analysis and control, Distributed control, Algebraic/geometric methods Abstract: This paper studies an extension of Euclidean consensus dynamics to unit spheres. The use of invariant manifolds techniques enables us not only to prove exponential asymptotic stability of the synchronization manifold, but also to show persistence of the synchronization manifold under perturbations. We also consider the case that the agents are subject to a common drift term and show the extension of the stability and persistence results to this case.

Keywords:Large-scale systems, Network analysis and control, Control applications Abstract: We propose a distributed coordination mechanism which enables nodes in a directed graph to accurately estimate their eigenvector centrality (eigencentrality) even if they update their values at times determined by their own clocks. The clocks need neither be synchronized nor have the same speed. The main idea is to let nodes adjust the weights on outgoing links to compensate for their update speed: the higher the update frequency, the smaller the link weights. Our mechanism is used to develop a distributed algorithm for computing the PageRank vector, commonly used to assign importance to web pages and rank search results. Although several distributed approaches in the literature can deal with asynchronism, they cannot handle the different update speeds that occur when servers have heterogeneous computational capabilities. When existing algorithms are executed using heterogeneous update speeds, they compute incorrect PageRank values. The advantages of our algorithm over existing approaches are verified through illustrative examples.

Keywords:Large-scale systems, Network analysis and control, Switched systems Abstract: This paper considers the problem of detecting topology variations in networks of linear dynamical systems interconnected via static coupling. The problem of interest is that of finding conditions under which it is possible to detect node or link disconnections from prior knowledge of the nominal network behavior and on-line measurements from all or a fraction of network nodes. Necessary and sufficient conditions for detectability are given. The considered approach makes use of analysis tools from switching system theory.

Keywords:Agents-based systems, Automata, Cooperative control Abstract: We consider in this paper a discrete-time deterministic m-ary diffusion model over a strongly connected directed graph. The update rule is easy to state: let the vertices of the graph represent the agents and the edges represent the information flow; at every time step, each vertex updates its value to the maximum value held by its incoming neighbors at the last time step. The resulting system, defined over the graph, is a finite state machine, and hence, enters a periodic motion in finite time from any initial condition. We compute in this paper all possible periods of periodic motions of the system. In particular, by relating the periodic motions to directed cycles in the graph, we show that periods are common divisors of the lengths of the cycles, and vice versa.

Keywords:Agents-based systems, Autonomous robots Abstract: This paper proposes a novel algorithm for performing multi-robot coverage on networks with dendritic topology where the communication topology is location dependent and where the motion of each robot is constrained by the presence of the other robots in the network. The algorithm provides complete network coverage by the minimum number of robots, maintenance of communication constraints and robot collision avoidance. The minimum number of robots required for coverage is a by-product of the proposed algorithm.

The efficiency of the algorithm is demonstrated through simulation studies.

Keywords:Agents-based systems, Autonomous systems Abstract: We propose a distributed control scheme for cyclic formations of multi-agent systems using relative position measurements in local coordinate frames. It is assumed that agents cannot communicate with each other and do not have access to global position information. For the case of three and four agents with desired formation defined as a regular polygon, we prove that under the proposed control, starting from almost any initial condition, agents converge to the desired configuration. Moreover, it is shown that the control is robust to the failure of any single agent. From Monte Carlo analysis, a conjecture is proposed to extend the results to any number of agents.

Keywords:Agents-based systems, Cooperative control, Stability of nonlinear systems Abstract: Consider a formation control problem in which agents in Euclidean space are tasked with stabilizing their positions at prescribed target distances from each other, and for which these distances are described by a rigid graph. There is a mismatch in target distances if, say, agent i aims to stabilize from agent j at a distance d_{ij}, but agent j from agent i at a distance overline d_{ij} . It was shown in a recent paper that when there is a small mismatch in the target distances, the formation undergoes a constant rigid motion. In this paper, we build on this observation to establish a controllability result. We assume that a subset of agents linked by an edge can control the corresponding mismatch in target distances. We show that if this subset of agents form a triangle (or, in the case of formations in n-dimensional space, a simplex), they can control the global position of the formation in Euclidean space within an arbitrarily small tolerance.

Department of Shanghai Municipal Monitoring Centre of Water Supp

Keywords:Agents-based systems, Cooperative control, Fault tolerant systems Abstract: This paper investigates the leader-follower problem in the presence of potential actuator faults. We focus on continuous-time multi-agent uncertain systems with a directed network topology. Time-varying fault parameters are considered, which relax the assumption in the prior work that the fault parameters of all followers must be fixed. We assume that these parameters can be sampled in an intermittent manner. Based on these samples, the cooperative control law is updated according to the proposed fault tolerant control strategy. It is shown that if the sampling condition, in terms of LMIs, is satisfied, the resulting closed-loop system will achieve consensus. Simulation results are provided to verify the theoretical finding.

Keywords:Agents-based systems, Cooperative control, Variable-structure/sliding-mode control Abstract: This paper aims to introduce a new framework for the distributed control of multi-agent systems with adjustable swarm control objectives. Our goal is twofold: 1) to provide an overview to how time-varying objectives in the control of autonomous systems may be applied to the distributed control of multi-agent systems with variable autonomy level, and 2) to introduce a framework to incorporate the proposed concept to fundamental swarm behaviors such as aggregation and leader tracking. Leader-follower multi-agent systems are considered in this study, and a general form of time-dependent artificial potential function is proposed to describe the varying objectives of the system. Using Lyapunov methods, the stability and boundedness of the agents' trajectories under single order and higher order dynamics are analyzed. Illustrative numerical simulations are presented to demonstrate the validity of our results.

Keywords:Cooperative control, Adaptive control, Distributed control Abstract: We consider a dynamic average consensus problem, where a group of agents is required to track the average of their time-varying inputs. We assume that the inputs are sinusoidal with a single unknown frequency. We develop a distributed two-time-scale estimator that estimates the unknown frequency and achieves average consensus of the inputs. We establish input-to-state (ISS) properties of the estimator using two-time-scale averaging theory. We also explore benefits of fusing the agents' individual frequency estimates. Using a simulation example, we demonstrate that the average consensus performance is significantly improved by incorporating the fused frequency estimates into the estimator.

Keywords:Hybrid systems, Cooperative control, Formal verification/synthesis Abstract: In this paper, we aim at the development of a decentralized abstraction framework for multi-agent systems under coupled constraints, with the possibility for a varying degree of decentralization. The methodology is based on the analysis employed in our recent work, where decentralized abstractions based exclusively on the information of each agent's neighbors were derived. In the first part of this paper, we define the notion each agent's m-neighbor set, which constitutes a measure for the employed degree of decentralization. Then, sufficient conditions are provided on the space and time discretization that provides the abstract system's model, which guarantee the extraction of a meaningful transition system with quantifiable transition possibilities.

Keywords:Cooperative control, Autonomous robots, Stability of nonlinear systems Abstract: This paper presents a solution to the rendezvous control problem for a network of unicycles on the plane. A smooth, time-invariant control law is presented that drives the unicycles to a common position from arbitrary initial conditions. Each unicycle is equipped with an onboard camera and can measure its relative displacement to its neighbors in body frame. The feedback is a function only of these onboard measurements and no global positioning system is required, nor any information about the unicycles' orientations.

Keywords:Cooperative control, Autonomous robots, Uncertain systems Abstract: Most of the proposed methods in literature on multi-target interception and related problems such as pursuit-evasion still suffer from a major drawback: They do not account for the uncertainties inherited in the environment in many applications. In the authors' previous work, multi-target interception problem was investigated where uncertainties in the environment stem from the fact that targets were assumed to be moving objects with a priori unknown arrival times, positions and trajectories. In this paper, in addition to these uncertainties, the mission space is also assumed to contain obstacles. The problem is formulated as a reward collection mission, and subsequently, a cooperative receding horizon controller is utilized toward maximizing the total collected reward. Inspired by the urban areas, the cases with polygonal obstacles are discussed. The introduced scheme is then adapted to improve the computational efficacy of algorithm. Analytical aspects of problem are discussed. The effectiveness and advantages of the proposed algorithm are demonstrated via numerical simulations.

Keywords:Cooperative control, Autonomous robots Abstract: The network connectivity in a group of cooperative robots can be easily broken if one of them loses its connectivity with the rest of the group. In case of having robustness with respect to one-robot failure, the communication network is termed biconnected. In simple words, to have a biconnected network graph, we need to prove that no articulation point exists. We propose a decentralized approach that provides sufficient conditions for biconnectivity of the network, and we prove that these conditions are related to the third smallest eigenvalue of the Laplacian matrix. Data exchange among the robots is supposed to be neighbor-to-neighbor.

Keywords:Cooperative control, Estimation, Linear systems Abstract: The distributed framework has been considered as one promising framework for the control of large-scale systems. In this work, we propose a coordination algorithm for distributed moving horizon state estimators (MHEs) for discrete-time linear systems composed of subsystems. In the proposed coordinated distributed MHE (CDMHE) scheme, each subsystem is associated with a local MHE. In the design of a local MHE, a coordinating term is incorporated into its cost function which is determined by an upper-layer coordinator. At each sampling time, a local MHE estimates its local state and system noise, then sends them to the coordinator. The coordinator calculates a price vector based on information received from all the local MHEs and sends the price vector together with the calculated interaction estimates to each local MHE. The above steps are performed iteratively every sampling time. It is shown that the CDMHE scheme is able to achieve the estimation performance of the corresponding centralized design if convergence at each sampling time is ensured. A simulation study based on a chemical process is used to illustrate the applicability and effectiveness of the proposed scheme.

Keywords:Network analysis and control, Distributed control, Transportation networks Abstract: In this paper, we are concerned with the resilience of locally routed network flows with finite link capacities. In this setting, an external inflow is injected to the so-called origin nodes. The total inflow arriving at each node is routed locally such that none of the outgoing links are overloaded unless the node receives an inflow greater than its total outgoing capacity. A link irreversibly fails if it is overloaded or if there is no operational link in its immediate downstream to carry its flow. For such systems, resilience is defined as the minimum amount of reduction in the link capacities that would result in the failure of all the outgoing links of an origin node. We show that such networks do not necessarily become more resilient as additional capacity is built in the network. Moreover, when the external inflow does not exceed the network capacity, selective reductions of capacity at certain links can actually help averting the cascading failures, without requiring any change in the local routing policies. This is an attractive feature as it is often easier in practice to reduce the available capacity of some critical links than to add physical capacity or to alter routing policies, e.g., when such policies are determined by social behavior, as in the case of road traffic networks. The results can thus be used for real-time monitoring of distance-to-failure in such networks and devising a feasible course of actions to avert systemic failures.

Keywords:Network analysis and control, Autonomous systems, Agents-based systems Abstract: This paper builds upon the Koopman spectral analysis tools to develop a method for assessment of the performance of a class of first-order nonlinear consensus networks. This class of networks is defined over an interconnected graph with state-dependent weights that are nonlinear functions of the state of the network. The mean energy of the output of the system with respect to random initial conditions is utilized as the performance measure. We quantify this performance measure in terms of the Koopman eigenfunctions of the nonlinear dynamics, and the eigenvalues of the corresponding linearized system at the equilibrium of the network, where the eigenvalues of the linearized system are indeed Laplacian eigenvalues of the underlying graph with opposite sign. Our results reveal that the performance measure of the nonlinear network depends on the interconnection topology of the underlying graph. We illustrate effectiveness of our results using several examples, including a Cucker-Smale type consensus network and first-order network of identical Kuramoto oscillators

Keywords:Optimal control, Distributed control, Robust control Abstract: We consider the problem of output feedback controller sparsification for systems with parametric uncertainties. We develop an optimization scheme that minimizes the performance deterioration from that of a well-performing pre-designed centralized controller, while enhancing sparsity pattern of the feedback gain. In order to improve temporal proximity of the pre-designed control system and its sparsified counterpart, we also incorporate an additional constraint into the problem formulation such that the output of the controlled system is enforced to stay in the vicinity of the output of the pre-designed system. It is shown that the resulting non-convex optimization problem can be equivalently reformulated into a rank-constrained problem. We then formulate a bi-linear minimization problem to obtain a sub-optimal solution which satisfies the rank constraint with arbitrary tolerance. Finally, a sub-optimal sparse controller synthesis for IEEE 39-bus New England power network is used to showcase the effectiveness of our proposed method.

Keywords:Control over communications, Optimization algorithms, Stochastic systems Abstract: We examine the problem of a sensor communicating over a wireless channel to an actuator in order to control a plant that is perturbed by a random disturbance. By allowing the sensor to adapt online to the stochastic system state, we develop transmission policies with guarantees on average control performance and required average communication resources. More specifically we design policies with guarantees either on a linear combination of these two objectives, or with guarantees with respect to a hard constraint on the average communication resources. Based on approximate dynamic programming we prove, as well as illustrate in simulations, that our policies outperform policies that do not adapt online to the stochastic system state.

Keywords:Network analysis and control, Optimization algorithms, Control of networks Abstract: We introduce an online network formation game: starting with a base graph and a set of candidate edges, at each round, player one picks an edge and reveals it to player two, then player two decides whether to accept it; player two can accept a limited number of edges and makes online decisions aiming to achieve optimal properties (e.g., the number of spanning trees, algebraic connectivity, and total effective resistance) in the synthesized network. Online network formation arises in cooperative multiagent systems, such as robots establishing a secure network in a changing uncertain environment, or individuals forming teams in social networks.

We propose a primal-dual algorithm framework for this problem. At each round the algorithm updates the dual solution using all information from previous rounds, and decides the weight on the new edge based on the complementary slackness conditions. We give interpretations of the algorithm for different graph objectives, and derive a bound on the competitive ratio of the algorithm for the log-determinant problem.

Keywords:Network analysis and control, Optimal control Abstract: In this paper, the optimal control problem for information diffusion over heterogeneous networks is inspected. First, the node-based susceptible-infected-susceptible (SIS) is introduced considering the heterogeneity of both network structure and diverse transition rates. Second, taking the scenario of campaigning and marketing as examples, an optimal control scheme is proposed aiming at information diffusion by a given final time with limited resources. The solution of the optimal control problem is proved to be existed and obtained by using Pontryagin Maximum Principle. Considering the computation problem of the analytical solution, a modified forward-backward sweep algorithm is provided to obtain a numerical solution. At last, the effectiveness of the proposed method is examined with several simulations.

Keywords:Machine learning, Pattern recognition and classification, Markov processes Abstract: In this paper, we propose a new spectral clustering algorithm relying on a simulated mixing process over a graph. In contrast to existing spectral clustering algorithms, our algorithm does not necessitate the computation of eigenvectors. Alternatively, our algorithm determines the equivalent of a linear combination of eigenvectors of the normalized similarity matrix, which are weighted by the corresponding eigenvalues obtained by the mixing process on the graph. We use the information gained from this linear combination of eigenvectors directly to partition the dataset into meaningful clusters. Simulations on real datasets show that our algorithm achieves better accuracy than standard spectral clustering methods as the number of clusters increase.

Keywords:Optimization algorithms, Large-scale systems, Randomized algorithms Abstract: In this paper we consider a distributed optimization scenario in which the aggregate objective function to minimize is partitioned, big-data and possibly non-convex. Specifically, we focus on a set-up in which the dimension of the decision variable depends on the network size as well as the number of local functions, but each local function handled by a node depends only on a (small) portion of the entire optimization variable. This problem set-up has been shown to appear in many interesting network application scenarios. As main paper contribution, we develop a simple, primal distributed algorithm to solve the optimization problem, based on a randomized descent approach, which works under asynchronous gossip communication. We prove that the proposed asynchronous algorithm is a proper, ad-hoc version of a coordinate descent method and thus converges to a stationary point. To show the effectiveness of the proposed algorithm, we also present numerical simulations on a non-convex quadratic program, which confirm the theoretical results.

Keywords:Distributed control, Control of networks, Optimization algorithms Abstract: There has been a growing effort in studying the distributed optimization problem over a network. The objective is to optimize a global function formed by a sum of local functions, using only local computation and communication. Literature has developed consensus-based distributed (sub)gradient descent (DGD) methods and has shown that they have the same convergence rate O(frac{log t}{sqrt{t}}) as the centralized (sub)gradient methods (CGD) when the function is convex but possibly nonsmooth. However, when the function is convex and smooth, under the framework of DGD, it is unclear how to harness the smoothness to obtain a faster convergence rate comparable to CGD's convergence rate. In this paper, we propose a distributed algorithm that, despite using the same amount of communication per iteration as DGD, can effectively harnesses the function smoothness and converge to the optimum with a rate of O(frac{1}{t}). If the objective function is further strongly convex, our algorithm has a linear convergence rate. Both rates match the convergence rate of CGD. The key step in our algorithm is a novel gradient estimation scheme that uses history information to achieve fast and accurate estimation of the average gradient. To motivate the necessity of history information, we also show that it is impossible for a class of distributed algorithms like DGD to achieve a linear convergence rate without using history information even if the objective function is strongly convex and smooth.

Keywords:Network analysis and control, Distributed control, Communication networks Abstract: We study distributed cooperative decision-making under the explore-exploit tradeoff in the multiarmed bandit (MAB) problem. We extend state-of-the-art frequentist and Bayesian algorithms for single-agent MAB problems to cooperative distributed algorithms for multi-agent MAB problems in which agents communicate according to a fixed network graph. We rely on a running consensus algorithm for each agent's estimation of mean rewards from its own rewards and the estimated rewards of its neighbors. We prove the performance of these algorithms and show that they asymptotically recover the performance of a centralized agent. Further, we rigorously characterize the influence of the communication graph structure on the decision-making performance of the group.

Keywords:Optimization, Optimization algorithms Abstract: We analyze the proximal incremental aggregated gradient (PIAG) method for minimizing the sum of a large number of smooth component functions f(x) = sum_{i=1}^m f_i(x) and a convex function r(x). Such composite optimization problems arise in a number of machine learning applications including regularized regression problems and constrained distributed optimization problems over sensor networks. Our method computes an approximate gradient for the function f(x) by aggregating the component gradients evaluated at outdated iterates over a finite window K and uses a proximal operator with respect to the regularization function r(x) at the intermediate iterate obtained by moving along the approximate gradient. Under the assumptions that f(x) is strongly convex and each f_i(x) is smooth with Lipschitz gradients, we show the first {linear convergence rate} result for the PIAG method and provide explicit convergence rate estimates that highlight the dependence on the condition number of the problem and the size of the window K over which outdated component gradients are evaluated.

Keywords:Cooperative control, Decentralized control, Distributed control Abstract: We study the performance of linear consensus protocols based on repeated averaging in the presence of additive noise. When the consensus dynamics corresponds to a reversible Markov chain, we give an exact expression for the weighted steady-state disagreement in terms of the stationary distribution and hitting times in an underlying graph. This expression unifies and extends several results in the existing literature. We show how this result can be used to characterize the scalability of protocols for formation control.

Keywords:Optimal control, Algebraic/geometric methods, Nonholonomic systems Abstract: We consider a left-invariant optimal control problem on the six-dimensional special Euclidean group. Helical trajectories are extremals of the optimal control problem, and we derive an explicit parameterization of these helices. Using this parameterization of the helical extremals, we compute the relative equilibria of the Hamiltonian system associated with the optimal control problem. For a particular choice of system parameters, we use Jacobi's sufficient condition to determine which of the relative equilibria correspond to local optima of the optimal control problem. We show that the optimality of a relative equilibrium is completely determined by the curvature and torsion of the helix that the trajectory traces.

Keywords:Optimal control, Computational methods, Model/Controller reduction Abstract: With the recent surge of interest in using robotics and automation for civil purposes, providing safety and performance guarantees has become extremely important. In the past, differential games have been successfully used for the analysis of safety-critical systems. In particular, the Hamilton-Jacobi (HJ) formulation of differential games provides a flexible way to compute the reachable set, which can characterize the set of states which lead to either desirable or undesirable configurations, depending on the application. While HJ reachability is applicable to many small practical systems, the curse of dimensionality prevents the direct application of HJ reachability to many larger systems. To address computation complexity issues, various efficient computation methods in the literature have been developed for approximating or exactly computing the solution to HJ partial differential equations, but only when the system dynamics are of specific forms. In this paper, we propose a flexible method to trade off optimality with computation complexity in HJ reachability analysis. To achieve this, we propose to simplify system dynamics by treating state variables as disturbances. We prove that the resulting approximation is conservative in the desired direction, and demonstrate our method using a four-dimensional plane model.

Keywords:Optimal control, Algebraic/geometric methods, Stochastic systems Abstract: Using a parametrically-controlled stochastic oscillator (a model of a heat engine) as illustration, we bring geometric control theory to non-equilibrium thermodynamics. A problem of optimal control is to find finite-time protocols maximizing efficiency of the heat engine. In the approximation of linear response theory, working cycles of the engine are constrained minimizers of energy dissipation, determined through the Pontryagin maximum principle.

Keywords:Optimal control, Automotive control, Autonomous robots Abstract: We consider the problem of trajectory planning with geometric constraints for a car--like vehicle. The vehicle is described by its dynamic model, considering such effects as lateral slipping and aerodynamic drag. We propose a modular solution, where three different problems are identified and solved by specific modules. The execution of the three modules can be orchestrated in different ways in order to produce efficient solutions to a variety of trajectory planning problems (e.g., obstacle avoidance, or overtake). As a specific example, we show how to generate the optimal lap on a specified racing track. The numeric examples provided in the paper are good witnesses of the effectiveness of our strategy.

Keywords:Optimal control, Autonomous robots, Simulation Abstract: Here we propose a simplified model for the path planning of an Autonomous Underwater Vehicle (AUV) in an horizontal plane when ocean currents are considered. The model includes kinetimac equations and a simple dynamic equation. Our problem of interest is a minimum time problem with state constraints where the control appears linearly. This problem is solved numerically using the direct method. We extract various tests from the Maximum Principle that are then used to validate the numerical solution. In contrast to many other literature we apply the Maximum Principle as defined in the book Optimal Control (2000) by Richard Vinter.

Keywords:Behavioural systems, Optimal control Abstract: The aim of this paper is to compare and discuss some old and new results on the discrete-time finite-horizon linear quadratic (LQ) optimal control problem in the case where the quadratic forms in the performance index are not assumed to be positive semidefinite, but only symmetric. We show in particular that the necessary and sufficient conditions presented in most contributions in the literature for the existence of a solution to this problem are in fact only sufficient. Our aim is to investigate this issue further, by addressing some of the most delicate and counterintuitive issues that arise in this context.

Keywords:Optimization algorithms, Networked control systems, Optimization Abstract: This paper investigates resource allocation algorithms that use limited communication - where the supplier of a resource broadcasts a coordinating signal using one bit of information to users per iteration. Rather than relay anticipated consumption to the supplier, the users locally compute their allocation, while the supplier measures the total resource consumption. Since the users do not compare their local consumption against the supplier's capacity at each iteration, they can easily overload the system and cause an outage (for example blackout in power networks). To address this challenge, this paper investigates pragmatic coding schemes, called PF-codes (Primal-Feasible codes), that not only allow the restriction of communication to a single bit of information, but also avoid system overload due to users' heavy consumption. We derive a worst case lower bound on the number of bits needed to achieve any desired accuracy using PF-codes. In addition, we demonstrate how to construct time-invariant and time-varying PF-codes. We provide an upper bound on the number of bits needed to achieve any desired solution accuracy using time-invariant PF-codes. Remarkably, the difference between the upper and lower bound is only 2 bits. It is proved that the time-varying PF-codes asymptotically converge to the true primal/dual optimal solution. Simulations demonstrating accuracy of our theoretical analyses are presented.

Keywords:Optimization algorithms, Automotive control, Control applications Abstract: In this paper, we present a framework for connected cruise control (CCC) design utilizing wireless vehicle-to-vehicle (V2V) communication. We propose a sequential optimization approach to select the control parameters for the available communication links that allows graceful degradation of performance when certain links become unavailable. We apply the theoretical results to improve the fuel economy of a heavy duty vehicle while requiring head-to-tail string stability of the vehicle string. Simulation results are presented to demonstrate the effectiveness of the proposed controller in improving fuel economy.

Keywords:Optimization algorithms, Optimal control, Predictive control for linear systems Abstract: We establish necessary and sufficient conditions for linear convergence of operator splitting methods for a general class of convex optimization problems where the associated fixed-point operator is averaged. Most existing results establishing linear convergence in such methods require restrictive assumptions regarding strong convexity and smoothness of the constituent functions in the optimization problem. However, there are several examples in the literature showing that linear convergence is possible even when these properties do not hold. We provide a unifying analysis method for establishing linear convergence based on linear regularity and show that many existing results are special cases of our approach. Moreover, we propose a novel linearly convergent splitting method for linear programming.

Keywords:Optimization algorithms, Flight control, Optimal control Abstract: In this paper we present a novel strategy to compute minimum-time trajectories for quadrotors. In particular, we consider the motion in constrained environments, taking into account the physical limitations of the vehicle. Instead of approaching the optimization problem in its standard time-parameterized formulation, the proposed strategy is based on an appealing re-formulation. Transverse coordinates, expressing the distance from a "reference" path, are used to parameterize the vehicle position and a spatial parameter is used as independent variable. This re-formulation allows us to (i) obtain a fixed horizon problem and (ii) easily formulate (even complex) position constraints. The effectiveness of the proposed strategy is proven by numerical computations on two different illustrative scenarios.

Keywords:Optimization algorithms, Network analysis and control, Estimation Abstract: This paper considers distributed convex optimization problems over a multi-agent network, with each agent possessing a dynamic objective function. The agents aim to collectively track the minimum of the sum of locally known time-varying convex functions by exchanging information between the neighbors. We focus on scenarios when the communication among the agents is described by a emph{directed} network. We devise an algorithm with a discrete time-sampling scheme such that the distance between any agent estimate and time-varying optimal solutions converges to a steady state error bound whose size is related to the constant step-size and the sampling interval. The convergence rate is shown to be linear given that the objective function is strongly-convex. Numerical simulations demonstrate the practical utility of the proposed approach.

Keywords:Optimization algorithms, Networked control systems, Autonomous systems Abstract: This paper deals with the problem of assigning tasks to a set of nodes communicating in a connected graph topology to satisfy the following requirements: assigning all the tasks to the agents; assigning to each agent no more than M tasks; minimizing the maximum total load of each agent. A gossip-based algorithm is presented: starting from an unfeasible solution, at each iteration a node solves a Local-Integer Linear Programming problem with its neighbors (i.e., the connected nodes in the communication graph). The convergence of the algorithm is proved and the expected convergence time is evaluated. A simulation campaign shows experimental results on the performance of the proposed approach.

Keywords:Constrained control, Stochastic systems, Randomized algorithms Abstract: This paper deals with the problem of steering an aircraft along a reference trajectory while counteracting the wind disturbance. We develop a control strategy where the aircraft nonlinear dynamics, physical limitations on the aircraft maneuverability, and passengers comfort are accounted for by feedback linearization and a suitable convex relaxation of constraints. A probabilistic constraint is introduced to account for the tracking error introduced by the stochastic wind disturbance. Since wind is represented by a Gaussian random field and its characteristics depend on both time and space, we identify on-the-fly a local autoregressive model via recursive least squares with forgetting factor. The probabilistic constraint formulation, the wind model update, and the re-computation of the control action jointly allow to account for the spatial variability of the random field and to obtain recursive feasibility in the receding horizon solution. A randomized method is adopted to obtain a convex relaxation of the resulting chance-constrained optimization problem, which can then be solved on-line, at low computational effort.

Keywords:Identification, Estimation, Randomized algorithms Abstract: Sign-Perturbed Sums (SPS) is a recently developed finite sample system identification method that can build exact confidence regions for linear regression problems under mild statistical assumptions. The regions are well-shaped, e.g., they are centred around the least-squares (LS) estimate, star-convex and strongly consistent. One of the main assumptions of SPS is that the distribution of the noise terms are symmetric about zero. This paper analyses how robust SPS is with respect to the violation of this assumption and how it could be robustified with respect to non-symmetric noises. First, some alternative solutions are overviewed, then a robustness analysis is performed resulting in a robustified version of SPS. We also suggest a modification of SPS, called LAD-SPS, which builds exact confidence regions around the least-absolute deviation (LAD) estimate instead of the LS estimate. LAD-SPS requires less assumptions as the noise needs only to have a conditionally zero median (w.r.t. the past). Furthermore, that approach can also be robustified using similar ideas as in the LS-SPS case. Finally, some numerical experiments are presented.

Keywords:Finance, Estimation, Mean field games Abstract: Partially observed Mean Field Game (PO MFG) theory was introduced and developed in (Caines and Kizilkale, 2013, 2014, Sen and Caines 2014, 2015), where it is assumed the major agent's state is partially observed by each minor agent, and the major agent completely observes its own state. Accordingly, each minor agent can recursively estimate the major agent's state, compute the system's mean field and thence generate the feedback control which yields the epsilon-Nash property. This PO MM LQG MFG theory was further extended in recent work (Firoozi and Caines, 2015) to major-minor LQG systems in which both the major agent and the minor agents partially observe the major agent's state. The existence of epsilon-Nash equilibria, together with the individual agents' control laws yielding the equilibria, were established wherein each minor agent recursively generates (i) an estimate of the major agent's state, and (ii) an estimate of the major agent's estimate of its own state (in order to estimate the major agent's control feedback), and hence generates a version of the system's mean field. In the current work, PO MM LQG MFG theory is applied to the optimal execution problem in the financial sector where an institutional investor, interpreted as a major agent, has partial observations of its own inventories, and high frequency traders (HFTs), interpreted as minor agents, have partial observations of the major agent's inventories. The objective for each agent is to maximize its own wealth and to avoid the occurrence of asset price bubbles which are appropriately weighted in the agent's performance function. PO LQG MFG theory is utilized to establish the existence of epsilon-Nash equilibria and a simulation example is provided.

Keywords:Game theory, Stochastic optimal control, Stochastic systems Abstract: A two players stochastic differential game is considered with a given cost function. The players engage in a non-cooperative game where one tries to minimize and the other tries to maximize the cost. The players are given a dynamical system and their actions serve as the control inputs to the dynamical system. Their job is to control the state of this dynamical system to optimize the given objective function. We use the term "state of the game" to describe the state of this dynamical system. The challenge is that none of the players has access to the state of the game for all time, rather they can access the state intermittently and only after paying some information cost. Thus the cost structure is non-classical for a linear-quadratic game and it incorporates the value of information. We provide the Nash equilibrium strategy for the players under full state information access at no cost, as well as under costly state information access. The optimal instances for accessing the state information are also explicitly computed for the players.

Keywords:Networked control systems, Stochastic systems Abstract: For networked cyberphysical systems to proliferate, it is important to ensure that the resulting control system is secure. We consider a physical plant, abstracted as a single-input-single-output stochastic linear dynamical system, in which a sensor node can exhibit malicious behavior. A malicious sensor may report false or distorted sensor measurements. For such compromised systems, we propose a technique which ensures that malicious nodes cannot introduce any significant distortion without being detected. The crux of our technique consists of the actuator node superimposing a random signal, whose realization is unknown to the sensor, on the control law-specified input. We show that in spite of a background of process noise, the above method can detect the presence of malicious nodes. Specifically, we establish that by injecting an arbitrarily small amount of such random excitation into the system, one can ensure that either the malicious sensor is detected, or it is restricted to introduce distortion that is only of zero-power to the noise entering the system. The proposed technique is potentially usable in applications such as smart grids, intelligent transportation, and process control.

Keywords:Networked control systems, Control of networks, Network analysis and control Abstract: This paper studies a distributed continuous-time bi-virus model for a system of groups of individuals. An in-depth stability analysis is performed for the healthy and epidemic equilibria. Sensitivity properties of some nontrivial equilibria are also investigated.

Keywords:Estimation, Filtering, Mechanical systems/robotics Abstract: A nonlinear deterministic attitude estimator is developed. The estimator evolves directly on the special orthogonal group of rigid-body rotations. Similar estimators in the literature are characterized by constant estimator gains that amplify noise across all frequencies. The proposed method accounts for undesirable noise in exteroceptive measurements by incorporating a strictly positive real (SPR) filter in the estimator structure. By tuning the ''embedded'' SPR filter over a frequency bandwidth undesirable noise corrupting exteroceptive measurements may be rejected. Rate-gyro bias estimation is also considered. The proposed attitude estimator is shown to asymptotically converge to the desired equilibrium point (i.e., when the estimated attitude and bias are equal to their true counterparts), provided a restriction on the set of initial conditions is satisfied. Moreover, exponential convergence is shown in a certain region about the desired equilibrium point. The proposed method is demonstrated in simulation.

Keywords:Estimation, Filtering, Randomized algorithms Abstract: Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the state is approximated using a randomized method. The method relies on that the Laplace noise can be rewritten as Gaussian noise scaled by Rayleigh random variable. The probability of the event that the distance between the approximation and the best estimate is smaller than a constant is determined as function of the number of parallel Kalman filters that is used in the randomized method. This estimator is then compared with the optimal linear estimator, the maximum a posteriori (MAP) estimate of the state, and the particle filter.

Keywords:Aerospace, Estimation, Stability of hybrid systems Abstract: We propose a hybrid attitude and gyro-bias observer designed directly on the Special Orthogonal group SO(3). The proposed hybrid observer guarantees global exponential stability using biased angular velocity measurements and inertial vector observations. Simulation results are provided to illustrate the effectiveness of the proposed observer.

Keywords:Automotive systems, Hybrid systems, Estimation Abstract: This paper considers the vehicle positioning problem of an automobile on-board navigation system which is mainly supported by Global Positioning System (GPS). To complement GPS, the existing navigation techniques incorporate additional vehicle sensors, together with the map data to match the positioning solution with the road map. We propose an advanced map-matching algorithm that integrates the additional map data with GPS and vehicle sensor measurements. Specifically, the detailed road map data, where individual road segments are subdivided into lanes, can impose further restriction on the vehicle as it is likely to move along the center of each lane and is rarely at boundary. Such a tendency can be mathematically interpreted as a statistical constraint in our map-matching algorithm. In addition, the lane change behavior of the vehicle can be accounted for by the discrete modes assigned to the individual road lanes. Then, the overall positioning process can be posed as a constrained stochastic hybrid system framework. The proposed map-matching algorithm provides more reliable vehicle positioning (continuous state estimate) and lane discrimination (discrete mode estimate) without needing costly sensor resources.

Keywords:Estimation, Decentralized control, Networked control systems Abstract: We consider a remote estimation system formed by two sensors that access dependent observations and a remote estimator. Each sensor observes a private and a common random variable and must decide whether to attempt to transmit them to the estimator, which seeks to produce estimates of the private measurements of both sensors and the common observation. Information is transmitted from the sensors to the estimator over a collision channel that outputs a collision when both sensors attempt a transmission. The goal is to design decentralized transmission policies at the sensors that jointly minimize a mean squared error criterion. We show that there exists a team-optimal solution that, for each realization of the common random variable, is a threshold policy on the private random variable.

Keywords:Estimation, Discrete event systems, Networked control systems Abstract: We investigate the design of a remote state estimation system for a self-propelled particle (SPP). Our framework consists of a sensing unit that accesses the full state of the SPP and an estimator that is remotely located from the sensing unit. The sensing unit must pay a cost when it decides to transmit information on the state of the SPP to the estimator; and the estimator computes the best estimate of the state of the SPP based on received information. In this paper, we provide methods to design transmission policies and estimation rules for the sensing unit and estimator, respectively, that are optimal for a given cost functional combining state estimation distortion and communication costs. We consider two notions of optimality: joint optimality and person-by-person optimality. Our main results establish the existence of a jointly optimal solution and describe an iterative procedure to find a person-by-person optimal solution. In addition, we explain how the remote estimation scheme can be applied to tracking of animal movements over a costly communication link. We also provide experimental results to show the effectiveness of the scheme.

Keywords:Adaptive control, Identification, Process Control Abstract: Internal model control (IMC), which explicitly incorporates a plant model and a plant inverse as its components, has an intuitive control structure and simple tuning philosophy, making it appealing to industrial applications. Combining the IMC structure with adaptation through the certainty equivalence principle leads to adaptive IMC (AIMC), where the plant model is identified and the plant inverse is derived by inverting the estimated model. In [1], [2], we proposed the composite adaptive IMC (CAIMC) for a first-order plant and successfully applied it to the boost-pressure control problem of a turbocharged gasoline engine system. Within the IMC control structure, the plant model and the plant inverse are simultaneously identified to minimize modeling errors and further reduce the tracking error. Through theoretical analysis, simulations, and experimental validation, CAIMC was shown to demonstrate better performance compared to AIMC. In this paper the design procedure of CAIMC is generalized to a n-th order plant, and stability and asymptotic performance are established and analyzed under proper conditions.

Keywords:Closed-loop identification, Identification Abstract: Estimating unstable systems typically requires additional system identification techniques. In this paper, we consider the weighted null-space fitting method, a three step method that is asymptotically efficient for stable systems. This method first estimates a high order ARX model and then reduces it to a structured model with lower variance using weighted least squares. However, with unstable systems, the method cannot be used to simultaneously estimate the stable and unstable poles. To solve this, we observe that the unstable poles can be estimated from the high order ARX model with relative high accuracy, and use this as an estimate for the unstable poles of the model of interest. Then, the remaining parameters in this model can be estimated by weighted least squares. Because the complete set of parameters is not estimated jointly, asymptotic efficiency is lost. Nevertheless, a simulation study shows good performance.

Keywords:Control applications, Identification, Adaptive control Abstract: This paper summarizes our research results on local active noise reduction. Our aim is to create a small quiet zone for astronauts in noisy spacecraft environments. A novel approach is proposed. Extensive simulations and preliminary real-time experiments demonstrate the efficacy of the proposed system.

Keywords:Identification, Hybrid systems, Automata Abstract: Hybrid dynamical models are a powerful tool for describing the behaviour of many industrial processes and physical phenomena in which logical (discrete) and analog (continuous) dynamics exist and interact. Black-box identification of hybrid models from input/output observations and no information on the operating mode of the system is a challenging problem, as both the logical and the continuous dynamics must be retrieved. In this work, we consider the identification of discrete hybrid automata (DHA), which represent a mathematical abstraction of hybrid models whose logical dynamics are described by a finite state machine (FSM) and the continuous dynamics are represented through affine discrete-time dynamical models. We propose a two stage estimation algorithm based on the joint use of clustering, multi-model recursive least-squares and linear multicategory discrimination techniques, which allows us to estimate both the affine models describing the continuous dynamics and the FSM governing the logical dynamics of the system.

Keywords:Estimation, Identification, Time-varying systems Abstract: Many important problems in signal processing and control engineering concern the reconstitution of a noisy biased signal. For this issue, in this paper, we consider the signal written as an orthogonal polynomial series expansion and we provide an algebraic estimation of its coefficients. We specialize in Hermite polynomials. On the other hand, the dynamical system described by the noisy biased signal may be given by an ordinary differential equation associated with classical orthogonal polynomials. The signal may be recovered through the coefficients identification. As an example, we illustrate our algebraic method on the parameter estimation in the case of Hermite polynomials.

Keywords:Identification, Estimation, Time-varying systems Abstract: The paper deals with the estimation of the noise covariance matrices of a linear time-varying system described by the state-space model. In particular, the stress is laid on the correlation methods and a novel method, the measurement difference autocovariance method, is proposed. The proposed method is based on the statistical analysis of differenced linearly transformed and shifted measurements resulting in a system of linear matrix equations. Compared to other correlation methods, the proposed method provides unbiased estimates even for a finite number of measurements. The theoretical results are discussed and illustrated in numerical examples.

Keywords:Adaptive control, Adaptive systems, Closed-loop identification Abstract: We consider retrospective cost adaptive control (RCAC) of a plant whose NMP zeros are time-dependent. The goal is to estimate the NMP zeros and replicate the estimated NMP zeros in the target model used by RCAC. This problem is challenging due to the fact that the estimates of the locations of the NMP zeros must be sufficiently accurate at each instant of time so that the target model can correctly influence the controller adaptation. We use closed-loop identification to estimate the location of the NMP zeros. In order to enhance the accuracy of the estimation, we inject an additional noise term in order to improve persistency of the control signal. Numerical examples show the feasibility and performance of the overall approach.

Keywords:Adaptive control, Adaptive systems, Direct adaptive control Abstract: On model reference adaptive control for uncertain dynamical systems, it is well know that there exists a fundamental stability limit, where the closed-loop dynamical system subject to this class of control laws remains stable either if there does not exist significant unmodeled dynamics or the effect of system uncertainties is negligible. Specifically, this implies that model reference adaptive controllers cannot tolerate large system uncertainties even when unmodeled dynamics satisfy a set of conditions. Motivated from this standpoint, this paper proposes a model reference adaptive control approach to relax this fundamental stability limit, where an adaptive control signal is augmented with an adaptive robustifying term. The key feature of our framework allows the closed-loop dynamical system to remain stable in the presence of large system uncertainties when the unmodeled dynamics satisfy a set of conditions. An illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.

Keywords:Adaptive control, Direct adaptive control, Robust adaptive control Abstract: Some LTI plants are nearly impossible to control due to extremely small gain and phase margins. These plants tend to be either unstable or nonminimum phase or both. Since practical control of these plants using fixed-gain controllers is not feasible, it is of interest to determine whether adaptive control can overcome these difficulties. To investigate this question, we apply retrospective cost adaptive control (RCAC) to a collection of plants that are nearly impossible to control from an LTI perspective. For each plant, we introduce a destabilizing perturbation in order to determine whether or not RCAC can re-adapt in such a way as to compensate for the loss of margin and restabilize the closed-loop system without manual retuning. Since these plants are inherently difficult to control, it is of interest to determine whether or not restabilization is possible and, if so, assess the severity of the transient response.

Keywords:Adaptive control, Mechanical systems/robotics, Maritime control Abstract: Abstract--- A controller is developed for a three degrees-of-freedom surface marine craft where both the rigid body and hydrodynamic parameters are unknown. A Lyapunov-based analysis is presented to show the closed loop system is globally exponentially stable and the uncertain parameters are identified exponentially without the requirement of persistence of excitation. Simulation results are provided to validate the theory and demonstrate performance.

Keywords:Adaptive control, Spacecraft control, Autonomous systems Abstract: This work is concerned with the design of adaptive learning controllers for rendezvous maneuvers of two spacecraft. Unlike earlier efforts using linearized dynamics, the current work considers the nonlinear equations of relative motion. The main idea behind the Lyapunov-based controller design is to allow a flexibility in the time-varying gains to adapt in proportion to the relative distance of the two spacecraft. By augmenting an adaptive controller, one opts to improve controller performance. The adaptation schemes of the controller gains are derived via Lyapunov redesign methods. In order to gain some insights on the choice of the optimal gains, a scheme that penalizes a combination of the relative position error and of the relative velocity error is considered. Extensive numerical studies are provided to further support the theoretical predictions on the choice of controller gains.

Keywords:Adaptive control, Hybrid systems, Distributed control Abstract: This paper presents a stochastic distributed algorithm for robust learning in networks of asynchronous sampled-data systems characterized by strongly connected directed graphs, where the steady-state input-to-output mapping of each sampled-data system has a quadratic structure, and each system can decide online whether or not to be in an “on/off” mode. Specifically, we consider sampled-data systems, also called agents, with individual resetting clocks, and plant dynamics modeled by a differential inclusion. The goal of the agents is to individually maximize their own response map by making use of measurements of their output, clock signal, and control states, and by sharing information only with their neighboring agents. To achieve this goal we propose a class of robust distributed stochastic hybrid dynamics that guarantee convergence of the inputs of the players (in a mean-square sense) to a neighborhood of the unique Nash equilibrium of the networked system. Numerical examples illustrate the results.

Keywords:Formal verification/synthesis, Automotive systems, Hybrid systems Abstract: Motivated by driver-assist systems that warn the driver before taking control action, we study the safety problem for a class of bounded hybrid automata. We show that for this class there exists a least restrictive safe feedback controller that has a simple structure and can be computed efficiently online. The theoretical results are then used to design driver-assist systems for rear-end and merging collision scenarios.

Keywords:Discrete event systems, Supervisory control, Automata Abstract: We consider a reliable decentralized supervisory control problem for discrete event systems in the conditional architecture. This reliable decentralized control problem requires synthesizing local supervisors such that a given specification can be achieved without blocking even if local control decisions of some local supervisors are not available for making the global control decision. We introduce a notion of reliable conditional-coobservability and show that reliable conditional-coobservability together with reliable controllability and Lm(G)-closedness is a necessary and sufficient condition for the existence of a solution to the reliable decentralized control problem. In addition, we develop a method for verifying reliable conditional-coobservability.

Keywords:Automata, Estimation, Discrete event systems Abstract: This paper studies observability in discrete event systems (DES), and introduces and analyzes the property of K-detectability. In particular, a given DES is strongly K-detectable if eventually (after a finite number of observations) all corresponding sets of possible states (current state estimates following any given sequence of observations) are guaranteed to have cardinality less than or equal to K, where K is a positive integer. Note that for K=1, strong K-detectability reduces to the standard notion of strong detectability. The paper briefly discusses ways to verify K-detectability using the standard observer construction (with exponential complexity) and also proposes a new construction (called the K-detector) that can be used to verify K-detectability with polynomial complexity.

Keywords:Formal verification/synthesis, Stochastic optimal control, Automata Abstract: Many control problems in environments that can be modeled as Markov decision processes (MDPs) concern infinite-time horizon specifications. The classical aim in this context is to compute a control policy that maximizes the probability of satisfying the specification. In many scenarios, there is however a non-zero probability of failure in every step of the system's execution. For infinite-time horizon specifications, this implies that the specification is violated with probability 1 in the long run no matter what policy is chosen, which prevents previous policy computation methods from being useful in these scenarios.

In this paper, we introduce a new optimization criterion for MDP policies that captures the task of working towards the satisfaction of some infinite-time horizon omega-regular specification. The new criterion is applicable to MDPs in which the violation of the specification cannot be avoided in the long run. We give an algorithm to compute policies that are optimal in this criterion and show that it captures the ideas of optimism and risk-averseness in MDP control: while the computed policies are optimistic in that a MDP run enters a failure state relatively late, they are risk-averse by always maximizing the probability to reach their respective next goal state. We give results on two robot control scenarios to validate the usability of risk-averse MDP policies.

Keywords:Automata, Hybrid systems, Switched systems Abstract: We investigate the synthesis of optimal controllers for continuous-time and continuous-state systems under temporal logic specifications. The specification is expressed as a deterministic, finite automaton (the specification automaton) with transition costs, and the optimal system behavior is captured by a cost function that is integrated over time. We construct a dynamic programming problem over the product of the underlying continuous-time, continuous-state system and the discrete specification automaton. To solve this dynamic program, we propose controller synthesis algorithms based on Approximate Dynamic Programming (ADP) for both linear and nonlinear systems under temporal logic constraints. We argue that ADP allows treating the synthesis problem directly, without forming expensive discrete abstractions. We show that, for linear systems under co-safe temporal logic constraints, the ADP solution reduces to a single semidefinite program.

Keywords:Automata, Supervisory control, Discrete event systems Abstract: A three-level relaxed coordination control framework of modular discrete-event systems is investigated. Unlike our previous papers, we focus on the maximal permissiveness issue, i.e., we propose sufficient conditions for the three-level coordination control synthesis to equal to the global control synthesis. It is shown how the three-level framework helps to weaken the well-known mutual controllability condition.

Keywords:Lyapunov methods, Delay systems, Stability of nonlinear systems Abstract: In this paper we present Lyapunov characterizations of the global asymptotic stability, the input-to-state stability and the incremental input-to-state stability for discrete-time nonlinear systems with unknown and time-varying time-delays. We provide necessary and sufficient conditions for the global asymptotic stability and for the input-to-state stability and sufficient conditions for the incremental input-to-state stability, in terms of discrete-time Lyapunov-Krasovskii functionals. In particular, the Lyapunov characterization of the notion of incremental input-to-state stability is motivated by problems concerning the construction of discrete abstractions approximating discrete-time nonlinear systems. Unknown and time-varying time-delays occur very frequently, for instance, in networked control systems. A numerical example is included which illustrates the proposed methodologies.

Keywords:Stability of nonlinear systems, Lyapunov methods Abstract: Output-to-State Stability (OSS) is a notion of detectability for nonlinear systems that is formulated in the ISS framework. We generalize the notion of OSS for systems evolving on manifolds and having multiple invariant sets. Building upon a recent extension of the ISS theory for this very class of systems, the paper provides equivalent characterizations of the OSS property in terms of asymptotic estimates of the state trajectories and, in particular, in terms of existence of Lyapunov-like functions.

Keywords:Stability of nonlinear systems, Lyapunov methods Abstract: In recent papers, the notions of Input-to-State Stability (ISS) and Integral ISS (iISS) have been generalized for systems evolving on manifolds and having multiple invariant sets, i.e. multistable systems. The well-known property of conservation of ISS under cascade interconnection has also been proven true for multistable systems in different scenarios. Unfortunately, multistability hampers a straightforward extension of analogous conservation properties for integral ISS systems. By means of counterexamples, this work highlights the necessity of the additional assumptions which yield the conservation of the iISS and Strong iISS properties in cascades of multistable systems. In particular, a characterization of the invariant set of the cascade is provided in terms of its finest possible decomposition.

Keywords:Lyapunov methods, Stability of hybrid systems Abstract: This paper studies stability of interconnections of hybrid dynamical systems, in the general scenario that the continuous or discrete dynamics of subsystems may have destabilizing effects. We analyze two existing methods of constructing Lyapunov functions for the interconnection based on candidate ISS Lyapunov functions for subsystems, small-gain conditions, and auxiliary timers modeling restrictions on jump frequency in terms of average dwell-time and reverse average dwell-time. We compare their feasibility and limitations for different types of subsystem dynamics, and examine a case that the combination of them is needed to establish global asymptotic stability.

Keywords:Lyapunov methods, Stability of nonlinear systems, Large-scale systems Abstract: This paper proposes a new method to construct Lyapunov functions for networks of integral input-to-state stable systems. The idea of the construction is to sum up Lyapunov functions of component systems. This sum-type construction can directly cover systems which are not input-to-state stable, although another popular construction of max-type cannot. According to the sum-type construction available in the literature, the growth order of the Lyapunov function with respect to state variables is a function of stability margin. As the margin approaches zero, i.e., as the largest amplification factor of components maintaining stability reduces to unity, the growth of the constructed Lyapunov function increases unboundedly. This paper proposes a technique of Lyapunov construction avoiding such rapid growth. This paper also highlights another unique advantage of reducing the number of tests a typical small-gain criterion requires.

Keywords:Stability of nonlinear systems, Lyapunov methods Abstract: Incremental stability describes the asymptotic behavior between any two trajectories of dynamical systems. Such properties are of interest, for example, in the study of observers or synchronization of chaos. In this paper, we develop the notions of incremental stability and incremental input-to-state stability (ISS) for discrete-time systems. We derive Lyapunov function characterizations for these properties as well as a useful summation-to-summation formulation of the incremental stability property.

Keywords:Quantized systems, Control over communications, Networked control systems Abstract: In this paper, we are interested in the stabilization of a linear plant based on output measurements that are subject to dynamic quantization. Moreover, to save communication resources, these measurements are transmitted to the controller using an output-based event-triggering condition. The proposed event-triggering mechanism and the dynamic quantization strategy ensure an input-to-state stability (ISS) property of a set around the origin with respect to the external disturbances. The existence of a strictly positive lower bound is ensured on both the inter-transmission times and the inter-zoom times in order to prevent the occurrence of Zeno behaviour. The chattering between zoom-in and zoom-out actions is avoided, and the zoom variable of the dynamic quantizer is guaranteed to be bounded. We characterize the inherent tradeoff between transmissions and quantization in terms of design parameters that can be tuned by the user. The effectiveness of the approach is illustrated on a numerical example.

Keywords:Sensor networks, Hybrid systems, Agents-based systems Abstract: In this paper, we investigate self-triggered synchronization of linear oscillators in the presence of communication failures caused by Denial-of-Service (DoS). A general framework is considered in which network links can fail independent of each other. A characterization of DoS frequency and duration to preserve network synchronization is provided, as well as an explicit estimate of the synchronization velocity. An example is given to substantiate the analysis.

Keywords:Discrete event systems, Delay systems, Predictive control for nonlinear systems Abstract: This paper studies the problem of event-triggered control design for general continuous-time nonlinear systems with time-varying input delay. Our methodology is based on the concept of predictor feedback and is capable of compensating arbitrarily large known time delays. Under mild conditions, we prove that as long as the delay-free system is globally input-to-state stabilizable, it can also be globally asymptotically stabilized via piecewise-constant event-triggered control. We prove that the proposed event-triggering design does not suffer from Zeno behavior as the inter-event times are uniformly lower bounded. We further show that our design achieves exponential stability for a controllable linear system and study the trade-off between convergence speed and communication cost. Various simulations illustrate our results.

Keywords:Delay systems, Sampled-data control, Observers for Linear systems Abstract: We develop a predictor approach to networked control with sampled-data and unknown time-varying transmission delays. First, we consider a state-feedback predictor. We show that an arbitrary small controller-to-actuators delay uncertainty may lead to a non-small residual error in networked control systems and reveal how to analyze such systems. Then we consider output-feedback control and design a sampled-data observer, which gives the state estimate used in a predictor. We emphasize the purely sampled-data nature of the measurements delays in the observer dynamics. This allows for an efficient analysis via the Wirtinger inequality, which is extended here to cope with exponential stability. To reduce the amount of sent measurements, we incorporate an event-triggering mechanism. Numerical examples illustrate that predictor-based control allows to increase essentially network-induced delays, whereas the event-triggering mechanism significantly reduces the network workload.

Keywords:Networked control systems Abstract: This paper treats the topic of periodic event-triggered control (PETC) for Networked Control Systems in a setup where the network provides a maximum sampling rate and a maximum number of successive packet losses. The packet loss is tackled with a non-monotonic approach, meaning that the trigger rules are designed such that a Lyapunov function is guaranteed to decrease only between two successful triggering instants. The stability properties of the resulting continuous-time sampled-data system are analyzed in two ways. The first one uses different restricted dynamical systems and the second one applies theory on non-monotonic Lyapunov functions. Based on this theory an example for another trigger rule is given that can be derived using this approach. The theoretical results are demonstrated through a known numerical example.

Keywords:Networked control systems, Communication networks, Stochastic systems Abstract: In practice often multiple control applications share a communication channel, requiring a smart and scalable scheduling mechanism to coordinate the access to the capacitylimited communication medium. In this paper, we propose a decentralized event-triggered medium access control (MAC) for multiple feedback control loops which are coupled through a capacity-limited communication medium. The individual control loops are assumed to be linear time-invariant (LTI) with stochastic heterogeneous plants. Noisy state measurements from local sensors are transmitted through a shared communication medium to their respective control units. Due to capacity limitations in the shared communication channel, not all sensors are allowed to transmit simultaneously. To allocate the scarce resources, a decentralized MAC which prioritizes the channel access according to a real-time error-dependent measure, is introduced. The prioritization is orchestrated via a combined deterministic and probabilistic mechanism aiming at the efﬁcient allocation of the limited capacity. We study stability of the described multi-loop NCS under the proposed MAC design in terms of Lyapunov stability in probability (LSP). It is demonstrated that the collision rate remains low by properly tuning the MAC parameters. Numerical results show that the proposed MAC design signiﬁcantly outperforms conventional time-triggered and random access schemes, while its performance closely follows the centralized TOD approach.

Keywords:Distributed parameter systems, Flexible structures, Smart structures Abstract: Transient shape control is considered for a tip interconnected flexible beam structure with embedded piezoelectric actuators. Based on the distributed-parameter mathematical model of the beam structure flatness-based motion planning is developed taken into account a Galerkin approximation of the equations of motion. The approach is complicated by the tip interconnection, which results in an algebraic constraint by means of a Lagrange multiplier. To address model uncertainties and disturbances the feedforward control is combined with an output error feedback controller realizing a two-degree-of-freedom control (2DOF) concept. Experimental results confirm the applicability of the approach and its tracking performance to achieve rest-to-rest motion.

Keywords:Distributed parameter systems, Output regulation, Chemical process control Abstract: In this paper, a backstepping observer and an output feedback control law are designed for the stabilization of the one-phase Stefan problem. The present result is an improvement of the recent full state feedback backstepping controller proposed in our previous contribution. The one-phase Stefan problem describes the time-evolution of a temperature profile in a liquid-solid material and its liquid-solid moving interface. This phase transition problem is mathematically formulated as a 1-D diffusion Partial Differential Equation (PDE) of the melting zone defined on a time-varying spatial domain described by an Ordinary Differential Equation (ODE). We propose a backstepping observer allowing to estimate the temperature profile along the melting zone based on the available measurement, namely, the solid phase length. The designed observer and the output feedback controller ensure the exponential stability of the estimation errors, the moving interface, and the H1-norm of the distributed temperature while keeping physical constraints, which is shown with the restriction on the gain parameter of the observer and the setpoint.

Keywords:Distributed parameter systems, Flexible structures, Optimization Abstract: In control of vibrations, the location, size, distribution and number of actuating and sensing devices are part of the controller design problem. For instance, in control of flexible structures and acoustic noise reduction, both the type of actuators and sensors, as well as their locations, can be chosen. Furthermore, due to advances in materials, the shape of the hardware is sometimes also a design variable. Previous work on optimal actuator location is generalized to include the situation where the actuator affects the internal dynamics of the system, and also for the design of optimal passive damping. Two examples are provided to illustrate the applicability of the result.

Keywords:Distributed parameter systems Abstract: This paper develops an extension of infinite-dimensional backstepping method for parabolic and hyperbolic systems in one spatial dimension with two actuators. Typically, PDE backstepping is applied in 1-D domains with an actuator at one end. Here, we consider the use of two actuators, one at each end of the domain, which we refer to as bilateral control (as opposed to unilateral control). Bilateral control laws are derived for linear reaction-diffusion, wave and 2 X 2 hyperbolic 1-D systems (with same speed of transport in both directions). The extension is nontrivial but straightforward if the backstepping transformation is adequately posed. The resulting bilateral controllers are compared with their unilateral counterparts in the reaction-diffusion case for constant coefficients, by making use of explicit solutions, showing a reduction in control effort as a tradeoff for the presence of two actuators when the system coefficients are large. These results open the door for more sophisticated designs such as bilateral sensor/actuator output feedback and fault-tolerant designs.

Keywords:Distributed parameter systems, Lyapunov methods Abstract: In this paper, for a class of distributed port-Hamiltonian systems defined on a one-dimensional spatial domain, an equivalent Brayton-Moser formulation is provided. The dynamic is expressed as a gradient equation with respect to a new storage function, the "mixed-potential," with the dimensions of power. The system is then passive with respect to a supply rate that is related to the reactive power, and that depends on the boundary port variables and on their time derivatives. This equivalent representation is the starting point for the development of boundary control laws able to shape the mixed-potential function. Differently from energy-balancing control schemes, this technique allows to deal with pervasive dissipation in the system in an effective way. The general theory is illustrated with the help of an example, the boundary stabilisation of a transmission line with internal dissipation.

Keywords:Distributed parameter systems, Output regulation Abstract: This paper presents a backstepping control design for a one-dimensional wave PDE with in-domain viscous damping, subject to a dynamical anti-damped boundary condition. Its main contribution is the design of an observer-based control law which stabilizes the wave PDE velocity, using only boundary mesurements. Numerical simulations on an oil-inspired example show the relevance of our result and illustrate the merits of this control design.

Keywords:Delay systems, Algebraic/geometric methods Abstract: Time-delay systems are infinite dimensional, thus standard differential geometric tools can not be applied in a straightforward way. Though, thanks to a suitable extended Lie Bracket - or Polynomial Lie Bracket - which has been introduced recently, it is still possible to build up a geometric framework to tackle the analysis and synthesis problems for nonlinear time delay systems. The major contribution herein is to show that those geometric generalizations are not just formal, but are interpreted in terms of successive forward and backward flows similarly to the Lie Bracket of delay free vector fields.

Groupe De Recherche Clinique Sur Les Myé Loproliferations A

Keywords:Delay systems, Biological systems, Lyapunov methods Abstract: A new mathematical model that represents the coexistence between normal and leukemic populations of cells is proposed and analyzed. It is composed by a nonlinear time-delay system describing the dynamics of ordinary stem cells, coupled to a differential-difference system governing the dynamics of mutated cells. A Lyapunov-like technique is developed in order to investigate the stability properties of a steady state where healthy cells survive while leukemic ones are eradicated. Exponential stability of solutions is established, estimate of their decay rate is given and a subset of the basin of attraction of the desired steady state is provided.

Keywords:Delay systems, Predictive control for linear systems Abstract: This paper focuses on the robustness problem for a specific class of dynamical systems, namely the piecewise affine (PWA) systems, defined over a bounded region of the state-space X. We will be interested in PWA systems emerging from linear dynamical systems controlled via feedback channels in the presence of varying transmission delays by a PWA controller defined over a polyhedral partition of the state-space. We exploit the fact that the variable delays are inducing some particular model uncertainty. Our objective is to characterize the delay invariance margins: the collection of all possible values of the time-varying delays for which the positive invariance of X is guaranteed with respect to the closed-loop dynamics. These developments can be useful for the analysis of different design methodologies and in particular for predictive control approaches. The proposed delay margins describes the admissible transmission delays for an MPC implementation. From a different perspective, it further provides the fragility margins of an MPC implementation via the on-line optimization and subject to variable computational time.

Keywords:Optimal control, Delay systems, Neural networks Abstract: Trajectory optimization considers the problem of deciding how to control a dynamical system to move along a trajectory which minimizes some cost function. Differential Dynamic Programming (DDP) is an optimal control method which utilizes a second-order approximation of the problem to find the control. It is fast enough to allow real-time control and has been shown to work well for trajectory optimization in robotic systems. Here we extend classic DDP to systems with multiple time-delays in the state. Being able to find optimal trajectories for time-delayed systems with DDP opens up the possibility to use richer models for system identification and control, including recurrent neural networks with multiple timesteps in the state. We demonstrate the algorithm on a two tank continuous stirred tank reactor. We also demonstrate the algorithm on a recurrent neural network trained to model an inverted pendulum with position information only.

Keywords:Differential-algebraic systems, Estimation, Delay systems Abstract: The backward observability (BO) of a part of the vector of trajectories of the system state is tackled for a general class of linear time-delay descriptor systems with unknown inputs. By following a recursive algorithm, we present easy testable sufficient conditions ensuring the BO of descriptor time-delay systems.

Keywords:Delay systems, H-infinity control, LMIs Abstract: In this paper, we will address the state-feedback control synthesis problem for linear systems with time-varying input delay under the integral quadratic constraint (IQC) framework. A new exact-memory control scheme is first proposed, which consists of a standard linear state-feedback control law and an internal delay loop. The delay loop is embedded in the controller structure so as to reproduce the input delay behavior of the plant. With this controller structure, the resulting delay control synthesis problem is fully characterized by a set of linear matrix inequalities (LMIs), which are convex on all design variables including the scaling factors associated with the IQC multipliers. The corresponding results on memoryless state-feedback control are also derived for cases when input-delay information is not available for feedback control. Numerical examples have been used to illustrate the effectiveness and advantages of the proposed approach.

Keywords:Differential-algebraic systems, Optimization Abstract: A nonsmooth open-loop optimal control problem is investigated. Using lexicographic differentiation, elements of the generalized gradient of the objective function, which may also be nonsmooth, are found after a general parametric discretization of the controls. These computationally relevant objects describe the sensitivity of the objective function to changes in the control parameterization and parameters associated with the embedded differential-algebraic equations governing the system dynamics. Using recent advancements in nonsmooth analysis, the unique solution of an auxiliary nonsmooth differential-algebraic equation system can be used to obtain said generalized gradient elements.

Keywords:Hybrid systems, Stability of hybrid systems, Stability of nonlinear systems Abstract: The extension of a solution to a hybrid system beyond its Zeno time is a simple exercise in modeling. However, assuring that the extended system is well-posed in a certain sense, in particular, that the extension of a solution depends reasonably on initial, pre-Zeno, conditions, has not been addressed. In this paper it is shown that these results hold for hybrid systems that exhibit Zeno behavior when the set of Zeno equilibria forms a continuum that has certain stability properties. Several scenarios of going past Zeno are presented. Dependence of limits of Zeno solutions, of Zeno times, and of reachable sets on initial conditions is also discussed.

Keywords:Hybrid systems, Optimal control, Linear systems Abstract: This paper deals with the problem of computing a state feedback optimizing a quadratic cost function for a class of linear hybrid systems. A solution to the finite-horizon and infinite-horizon Linear Quadratic optimal control problem is found through an hybrid extension of classical Differential and Difference Riccati Equations. Necessary and sufficient conditions, guaranteeing that the infinite-horizon optimal control stabilizes the closed loop system, are stated. A physically motivated example is reported.

Keywords:Differential-algebraic systems, Hybrid systems, Variational methods Abstract: The term differential-algebraic inclusions (DAIs) not only describes the dynamical relations using set-valued mappings, but also includes the static algebraic inclusions, and this paper considers the problem of existence of solutions for a class of such dynamical systems. The existence of solutions is proved using the tools from the theory of maximal monotone operators. The class of solutions that we study in the paper have the property that, instead of the whole state, only a certain component is absolutely continuous and unique. This framework, in particular, is useful for studying passive differential-algebraic equations (DAEs) coupled with maximal monotone relations. Certain class of irregular DAEs are also covered within the proposed general framework. Applications from electrical circuits are included to provide a practical motivation.

Keywords:Predictive control for nonlinear systems, Optimal control, Stability of nonlinear systems Abstract: We introduce a generalized framework for model predictive control (MPC) based on the repetitive utilization of finite horizon open loop optimal control (OLOC) with a current-state-dependent terminal constraint set and cost function (and control law). We employ continuously indexed terminal constraint sets, cost functions and control laws, and we allow for their (joint with the predicted state and control sequences) online optimization. The proposed parametrization of these terminal ingredients renders the related online optimization computationally feasible, and it facilitates a relaxation of the standard stabilizing MPC conditions. The developed framework outperforms conventional MPC in terms of structural properties, and it also enhances applicability and computability of our previously proposed discretely generalized MPC.

Keywords:Hybrid systems, Lyapunov methods, Stability of hybrid systems Abstract: We present results for forward invariance-based control of hybrid dynamical systems via static feedback. Using recent results on forward invariance for hybrid systems without inputs, we present conditions on the state-feedback laws to induce forward invariance of a set for hybrid systems with inputs. In addition, we propose a notion of control Lyapunov function (CLF) that is suitable for the study of forward invariance of sublevel sets. Conditions that guarantee the existence of CLF-based feedback laws inducing forward invariance of sublevel sets are established. Examples are given to illustrate the results.

Keywords:H-infinity control, Constrained control, Spacecraft control Abstract: In this paper, the problem of robust H_{infty} tracking control for 6 DOF spacecraft formation flying in the presence of parameter uncertainties, external disturbances and input saturation is addressed. Firstly, a robust H_{infty} controller constructed by the solution of the Hamilton-Jacobi-Inequality(HJI) is proposed. It is proved that the coupled 6 DOF tracking error system is stable and robust in respect to parameter uncertainties, and the H_{infty} norm between external disturbance and regulated output is ensured to be no more than a prescribed attenuation level. Subsequently, to find the solution of the HJI, the state dependent Riccati inequality (SDRI) method is applied, which is an effective approximation approaches by solving an algebraic Riccati inequality for each state online through the LMI tool instead of solving partial differential inequality directly. The robust H_{infty} controller based on the SDRI method not only has a simple structure, but also can be designed flexibly with state dependent coefficient (SDC) parameterizations selected. Further, the SDRI method can be utilized flexibly to deal with the nonlinear constrained on the control input by augmenting the original system. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed controller.

Keywords:H-infinity control, Electrical machine control, Robust control Abstract: The sensorless high speed-tracking control problem for a surface-mount permanent magnet synchronous motor via stator currents and voltages measurements is tackled, by interconnecting an H1–controller and a reduced order sliding-mode observer. The observer-control scheme is robust against external load disturbances. The rotor position and speed variables are estimated in finite time by means of a reduced order observer. Thus, an output-feedback H1–controller is designed such that the undisturbed system is uniformly stable around the desired speed reference, whereas the effects of the disturbances are attenuated. The feasibility of the proposed robust sensorless controller is supported by numerical simulations.

Keywords:Filtering, H-infinity control, Markov processes Abstract: The goal of this paper is to present new results for H-infinity filtering for continuous-time Markov jump linear systems with partial information on the jumping parameter. The central hypothesis considered here is the existence of a suitable detector which provides measurements of the Markov chain. This detector-based approach allows us to treat the case with complete observations, no information and cluster observations of the jumping process. The main result comprises a method for designing a mean square stable linear H-infinity filter by using the information given by the detector. The proposed filter design is given in terms of linear matrix inequalities. Furthermore, the result is applied to the state estimation of an unmanned aerial vehicle model.

Keywords:H-infinity control, LMIs, Optimization Abstract: In SDP-based H-infinity control, we often encounter numerical difficulties when solving SDPs by various pieces of software. It is empirically known that such numerical difficulty occurs if an SDP at hand or its dual has no interior point feasible solutions, and this is indeed the case of some SDPs in H-infinity control. To conceive a way for getting around such numerical difficulties in a concrete problem setting, in this paper, we focus on the dual SDP for the H-infinity control problem of the transfer function (1+PK)^{-1}P and simplify it. More precisely, by actively using the information of unstable zeros (non-minimum phase zeros) of the plant P, we reduce the original dual SDP into a set of simplified SDPs each of which and its dual have interior point feasible solutions. In this way, we show by numerical experiments that reliable numerical computation can be done by SDP software. On the other hand, once we have obtained simplified SDPs, it becomes possible to further reduce them into the computation of maximum singular values of matrices determined by unstable zeros. In this way, if the number of unstable zeros is moderate, we can obtain analytical expressions of the best achievable H-infinity performance or its lower bounds in terms of the unstable zeros.

Keywords:H-infinity control, Optimal control, Game theory Abstract: The problem of mixed H2/H-infinity control can be formulated as a two-player nonzero-sum differential game as done by Limebeer et al. in the 1990s. For linear systems the problem is characterised by two coupled algebraic Riccati equations. Solutions for such algebraic Riccati equations are not straight-forward to obtain, particularly for infinite-horizon problems. In this paper two algorithms for obtaining solutions for the coupled algebraic Riccati equations associated with the mixed H2/H-infinity control problem for scalar, linear systems is provided along with illustrative numerical examples.

Keywords:Optimization algorithms, H-infinity control, PID control Abstract: This paper presents a global optimization approach to the structured H infinity sensitivity problem. The problem is formulated as a min/max optimization problem, and is solved with a branch and bound algorithm based on interval arithmetic. The method is compared with other existing H infinity synthesis methods on an example and results are discussed.

Keywords:Power systems, Decentralized control, Networked control systems Abstract: We design decentralized frequency control of multi-area power systems that will re-balance power and drive frequencies to their nominal values after a disturbance. Both generators and controllable loads are utilized to achieve frequency stability while minimizing regulation cost. In contrast to recent results, the design is completely decentralized and does not require communication between areas. Our control enforces operational constraints not only in equilibrium but also during transient. Moreover, our control is capable of adapting to unknown load disturbance. We show that the closed-loop system is asymptotically stable and converges to an equilibrium that minimizes the regulation cost. We present simulation results to demonstrate the effectiveness of our design.

Keywords:Power systems, Optimization, Optimization algorithms Abstract: This paper is concerned with the power system state estimation (PSSE) problem, which aims to find the unknown operating point of a power network based on a given set of measurements. The measurements of the PSSE problem are allowed to take any arbitrary combination of nodal active powers, nodal reactive powers, nodal voltage magnitudes and line flows. This problem is non-convex and NP-hard in the worst case. We develop a set of convex programs with the property that they all solve the non-convex PSSE problem in the case of noiseless measurements as long as the voltage angles are relatively small. This result is then extended to a general PSSE problem with noisy measurements, and an upper bound on the estimation error is derived. The objective function of each convex program developed in this paper has two terms: one accounting for the non-convexity of the power flow equations and another one for estimating the noise levels. The proposed technique is demonstrated on the 1354-bus European network.

Keywords:Power systems, Optimization, Smart grid Abstract: We present a price-based approach to deal with the challenges of the electrical power distribution systems with renewable generations. In specific, we address the power loss minimization and voltage regulation taking into account the actual grid capacity. Analogously, the cost function is reformulated to represent a social welfare maximization problem. Distributed optimization formulations, which bridge the physical power grid to the market-based approach, are presented and analyzed.

Keywords:Power systems, Energy systems, Networked control systems Abstract: This paper studies the problem of optimally placing energy storage devices in power networks. We explicitly model capital and installation costs of storage devices because these fixed costs account for the largest cost component in most grid-scale storage projects. Finding an optimal placement strategy is a challenging task due to (i) the discrete nature of such placement problems, and (ii) the spatial and temporal transfer of energy via transmission lines and distributed energy storage resources. To develop an efficient placement framework with performance guarantees, we investigate the structural properties of the optimal value function for the multi-period economic dispatch problem with storage dynamics, and an analytical characterization of optimal storage controls and locational marginal prices. In particular, we provide a tight condition under which the optimal placement value function is submodular and an efficient computational method to certify the condition. When this condition is valid, a modified greedy algorithm for maximizing a submodular function subject to a knapsack constraint provides a (1 − 1/e)-optimal solution.

Keywords:Power systems, Energy systems, Optimization Abstract: The unit commitment (UC) problem aims to find an optimal schedule of generating units subject to the demand and operating constraints for an electricity grid. The majority of existing algorithms for the UC problem rely on solving a series of convex relaxations by means of branch-and-bound or cutting-planning methods. In this paper, we develop a strengthened semidefinite program (SDP) for the UC problem by first deriving certain valid quadratic constraints and then relaxing them to linear matrix inequalities. These valid inequalities are obtained by the multiplication of the linear constraints of the UC problem such as the flow constraints of two different lines. The performance of the proposed convex relaxation is evaluated on several instances of the UC problem. For most of the instances, globally optimal integer solutions are obtained by solving a single convex problem. Since the proposed technique leads to a large number of valid quadratic inequalities, an iterative procedure is devised to impose a small number of such valid inequalities. For the cases where the strengthened SDP does give a global integer solution, we incorporate other valid inequalities, including a set of Boolean quadric polytope constraints. The proposed relaxations are extensively tested on various IEEE power systems in simulations.

Keywords:Power systems, Energy systems Abstract: Power system electromechanical oscillation dynamics can be described using second-order consensus dynamics. The synchronizing torques that hold the machines together are determined by the Laplacian matrix of the consensus dynamics. This paper develops a framework to investigate the effect of connecting nontraditional generation (NTG), in the form of active and reactive current injection, on the consensus dynamics of a 2-machine power system. The damping of interarea oscillations power systems control problem is investigated for the linear model of a two-area test power system using reactive as well as active current injection. The control design is based on solving a LQR control problem. Results show that it is possible to control the power system dynamics through the use of nontraditional current injection. The relative effectiveness of the active and reactive components of the current injection is investigated, and the impact of the location of the injection is studied.

Keywords:Automotive control, Predictive control for linear systems, Constrained control Abstract: For control architectures of autonomous and semi-autonomous driving features, we design a vehicle steering controller with limited preview ensuring that the vehicle constraints are satisfied, and that any piecewise clothoidal trajectory, that is possibly generated by a path planner or supervisory algorithm and satisfies constraints on the desired yaw rate and the change of desired yaw rate, is tracked within a preassigned lateral error bound. The design is based on computing a non-maximal, yet polyhedral, robust control invariant (RCI) set for a system subject to bounded disturbances with state-dependent bounds, which also allows to determine the constraints describing the reference trajectories that can be followed. The RCI set is then enforced by model predictive control, where the cost function enforces additional objectives of the vehicle motion.

Keywords:Traffic control, Predictive control for nonlinear systems, Simulation Abstract: Advances in wireless communication allow enabling information exchange among connected vehicles, so that decision and control strategies can be improved with the aid of additional information within the vehicular system. In this paper, we present a fuel efficient control strategy for a group of connected vehicles passing several traffic lights in multiple-lane urban roads. Signal Phase and Timing (SPAT) information, lane changing decision and model predictive control are exploited to reduce stopping at red lights and improve the fuel economy. The major contribution of this work is to enable connected vehicles lane changing in multiple-lane roads. The simulation results indicate the group performance improvement for our proposed method.

Keywords:Automotive control, Predictive control for linear systems, Estimation Abstract: In this paper, a semi-active suspension Model Predictive Control (MPC) is designed for a full vehicle system equipped with 4 semi-active dampers. The main challenge in the semi-active suspension control problem is to tackle with the dissipativity constraints of the semi-active dampers. The constraints are here recasted as input and state constraints. The controller is designed in the MPC framework where the effects of the unknown road disturbances are taken into account. An observer approach allows to estimate the road disturbance information to be used by the controller during the prediction step. Then, the MPC suspension control law with road estimation (but without road preview) is computed by minimizing a quadratic cost function, giving a trade-off between the comfort and the handling, while guaranteeing phyiscal constraints of the semi-active dampers. Simulation results performed on a nonlinear full car model are presented in order to show the effectiveness of the proposed approach.

Keywords:Game theory, Autonomous systems, Machine learning Abstract: A hierarchical game theoretic decision making framework is exploited to model driver decisions and interactions in trafﬁc. In this paper, we apply this framework to develop a simulator to evaluate various existing autonomous driving algorithms. Speciﬁcally, two algorithms, based on Stackelberg policies and decision trees, are quantitatively compared in a trafﬁc scenario where all the human-driven vehicles are modeled using the presented game theoretic approach.

Keywords:Automotive control, Automotive systems, Control applications Abstract: Electrified turbocharger is a critical technology for engine downsizing and is a cost-effective solution for exhaust gas energy recovery. In conventional turbocharged diesel engines, the air path holds strong nonlinearity since the actuators are all driven by the exhaust gas. In an electrified turbocharged diesel engine (ETDE), the coupling is more complex, due to the electric machine mounted on the turbine shaft impacts the exhaust manifold dynamics as well. In distributed single-input single-output control methods, the gains tuning is time consuming and the couplings are ignored. To control the performance variables independently, developing a promising multi-input multi-output control method for the ETDE is essential. In this paper, a model-based multi variable robust controller is designed to control the performance variables in a systematic way. Both simulation and experimental results verified the effectiveness of the proposed controller.

Keywords:Automotive control, Automotive systems, Observers for nonlinear systems Abstract: In this work, an observer-based sliding mode (SM) control scheme for a vehicle considering roll dynamics, is presented. The proposal considers a nonlinear higher order sliding mode reduced observer for the lateral velocity, roll angle and roll velocity. Based on this observer, the controller is designed for the reference tracking of the lateral and yaw velocities of the vehicle, using adaptive super-twisting algorithm. In order to demonstrate the stability of the closed-loop system, Lyapunov functions for each of the algorithms are used. The proposed control scheme has finite-time convergence and the robustness in presence of plant parameters variations. This is demonstrated through the performed simulation.

Keywords:Biomolecular systems, Switched systems Abstract: Under suitable assumptions, the moments of a controlled stochastic biochemical reaction network can be computed as the solution of a switched affine system. Motivated by this application, we propose a new method to approximate projections of the reachable set of a switched affine system onto a plane of interest. Our method does not require the computation of the full reachable set, thus allowing us to efficiently analyze the moments of a species of interest in arbitrarily large biochemical networks. To illustrate the benefits of the proposed method we consider a controlled gene expression model involving two species: the mRNA and the corresponding protein. The proposed approach can be used to estimate the reachable set of the protein mean and variance, under less stringent assumptions than those adopted in the literature. Specifically, we address the cases of multiple controlled reactions and heterogeneous population.

Keywords:Biomolecular systems, Genetic regulatory systems, Uncertain systems Abstract: Controlling stochastic reactions networks is a challenging problem with important implications in various fields such as systems and synthetic biology. Various regulation motifs have been discovered or posited over the recent years, the most recent one being the so-called Antithetic Integral Control (AIC) motif [Briat, Gupta & Khammash, Cell Systems, 2016]. Several favorable properties for the AIC motif have been demonstrated for classes of reaction networks that satisfy certain irreducibility, ergodicity and output controllability conditions. Here we address the problem of verifying these conditions for large sets of reaction networks with fixed topology using two different approaches. The first one is quantitative and relies on the notion of interval matrices while the second one is qualitative and is based on sign properties of matrices. The obtained results lie in the same spirit as those obtained in [Briat, Gupta & Khammash, Cell Systems, 2016] where properties of reaction networks are independently characterized in terms of control theoretic concepts, linear programming conditions and graph theoretic conditions.

Keywords:Genetic regulatory systems, Biomolecular systems, Distributed control Abstract: A current challenge in the robust engineering of synthetic gene networks is context dependence, the unintended interactions among genes and host factors. Ribosome competition is a specific form of context dependence, where all genes in the network compete for a limited pool of translational resources available for gene expression. Recently, theoretical and experimental studies have shown that ribosome competition creates a hidden layer of interactions among genes, which largely hinders our ability to predict design outcomes. In this work, we establish a control theoretic framework, where these hidden interactions become disturbance signals. We then propose a distributed feedback mechanism to achieve disturbance decoupling in the network. The feedback loop at each node consists of the protein product transcriptionally activating a small RNA (sRNA), which forms a translationally inactive complex with mRNA rapidly. We illustrate that with this feedback mechanism, protein production at each node is only dependent on its own transcription factor inputs, and almost independent of hidden interactions arising from ribosome competition.

Keywords:Biomolecular systems, Cellular dynamics, Identification for control Abstract: Problems of identification and control of biological systems have recently attracted an increasing amount of attention. Most work in this field has classically focused either on gene or protein networks. In this manuscript, we focus on the control of a behavioral trait emerging from a signaling network: aerotaxis, the directed motion of bacteria towards (or away from) oxygen. To do so, we consider a bacterium, Bacillus subtilis, which is strongly attracted by oxygen, and we quantitatively probe the dynamics of accumulation of populations of this microorganism when exposed to tightly controlled gradients of oxygen generated in a microfluidic device. Combining in-vivo experiments with system identification methods, we determine a simple model of aerotaxis in B. subtilis, and we subsequently employ this model in order to compute the sequence of oxygen gradients needed to achieve regulation of the center of mass of the bacterial population. We then successfully validate both the model and the control scheme, by showing that in-vivo positioning control can be achieved via the application of the precomputed inputs in an open-loop configuration.

Keywords:Biomolecular systems, Estimation, Computational methods Abstract: Inferring quantities of interest from fluorescence microscopy time-lapse measurements of cells is a key step in parameterizing models of biomolecular reaction networks, and also in comparing different models. In this article, we propose a method which performs inference in continuous-time Markov chain models and thus takes into account the discrete nature of molecule counts. It targets the important situation of inference from many measured cells. Our method, a complement to a recently proposed approach, is based on particle Markov chain Monte Carlo and can be argued to have improved scaling behavior as the number of measured cells increases. We numerically demonstrate the performance of our algorithm on simulated data.

Keywords:Nonlinear systems identification, Kalman filtering, Machine learning Abstract: Control algorithms combined with microfluidic devices and microscopy have enabled in vivo real-time control of protein expression in synthetic gene networks. Most control algorithms rely on the a priori availability of mathematical models of the gene networks to be controlled. These models are typically black/grey box models, which can be obtained through the use of data-driven techniques developed in the context of systems identification. Data-driven inference of both model structure and parameters is the main focus of this paper. There are two main challenges associated with the inference of dynamical models for real-time control of gene regulatory networks in living cells. Since biological systems are typically evolving over time, the first challenge stems from the fact that model selection needs to be done online, which prevents the application of computationally expensive identification algorithms iterating through large amounts of streaming data. The second challenge consists in performing nonlinear model selection, which is typically too burdensome for Kalman filtering related techniques due the heterogeneity and nonlinearity of the candidate models. In this paper, we combine sparse Bayesian techniques with classic Kalman filtering techniques to tackle these challenges.

Keywords:Smart grid, Cooperative control, Agents-based systems Abstract: In smart grid, the consensus-based economic dispatch algorithm is to allocate multiple generation units to meet expected demand, while minimizing the total generation cost in a distributed manner. Since the network-induced time delays ubiquitously exist in smart grid, the investigation of the effect of time delays on the dispatch performance is of both theoretical merit and practical value. In this paper, under a well-developed consensus-based economic dispatch protocol, we exploit that no matter how large the uniform finite delay could be, there always exists a small enough learning gain parameter such that the convergence of the dispatch algorithm can be ensured. Further, we establish an upper bound for the learning gain parameter which explicitly depends on the time delay and the generation cost parameters. Finally, we present the update method for initial iterations when no neighboring information is received due to time delays, and show the achieved optimality. Simulation studies validate the theoretical results.

Keywords:Transportation networks, Optimization Abstract: We consider a large-scale road network in Eastern Massachusetts. Using real traffic data in the form of spatial average speeds and the flow capacity for each road segment of the network, we convert the speed data to flow data and estimate the origin-destination flow demand matrices for the network. Assuming that the observed traffic data correspond to user (Wardrop) equilibria for different times-of-the-day and days-of-the-week, we formulate appropriate inverse problems to recover the per-road cost (congestion) functions determining user route selection for each month and time-of-day period. Then, we formulate a system-optimum problem in order to find socially optimal flows for the network. We investigate the network performance, in terms of the total latency, under a user-optimal policy versus a system-optimal policy. The ratio of these two quantities is defined as the Price of Anarchy (POA) and quantifies the efficiency loss of selfish actions compared to socially optimal ones. Our findings contribute to efforts for a smarter and more efficient city.

Keywords:Stochastic systems, Formal verification/synthesis, Autonomous systems Abstract: We propose an assume-guarantee reasoning (AGR) framework for verification problem of a system with two components modeled by Markov Decision Process (MDP) and Partially Observable MDP (POMDP), respectively. MDP-POMDP model describes system's sensing, actuation and environment uncertainties, which can be used in the modeling of systems containing different subsystems, e.g., human-robot collaboration process. While the verification problem of MDP-POMDP asks whether or not a specification can be satisfied by the regulated behavior under certain control policies, our main contribution in this paper is to present and prove a sound and complete AGR rule based on POMDP strong simulation relation to reduce the verification complexity.

Keywords:Smart grid, Power systems, Energy systems Abstract: This paper presents a novel optimal power demand management method for power consumers by an aggregator considering state and control constraints. The aggregator is an organization who manages some consumers to achieve demand response efficiently. This paper proposes a power demand adjustment method for the aggregator to allocate power reduction among consumers in a distributed manner. Specifically, this method simultaneously derives the optimal power reduction of each consumer using a gradient method and determines the control inputs by solving a quadratic programming problem with state and input constraint conditions. This paper also shows the convergence of the proposed algorithm, and finally, numerical simulation results illustrate the effectiveness of our proposed method.

Keywords:Constrained control, Energy systems, Uncertain systems Abstract: In this paper a control strategy for the optimal energy management of a district heating power plant is proposed. The main goal of the control strategy is to reduce the running costs by optimally managing the boilers, the thermal energy storage and the flexible loads while satisfying a time-varying request and operation constraints. The optimization model includes a detailed modeling of boilers operating constraints, energy thermal energy exchange and the operating modes of the power plant layout. Furthermore, the uncertainty in power demand and renewable power output, as well as in weather conditions, is handled by formulating a two-stage stochastic problem and incorporating it into a model predictive control framework. A simulation evaluation based on the real data and the layout of a Finnish power plant is conducted to assess the performance of our proposed framework.

Keywords:Smart grid, Game theory, Optimization Abstract: The emerging sharing economy has disrupted the housing and transportation sectors. The underlining business model exploits underutilized infrastructure through sharing. In this paper, we explore sharing economy opportunities in electricity sector. There are considerable obstacles to sharing electricity. First, the flow of electricity is governed by Kirchoff's Laws and we cannot prescribe a point to point path for its flow. Second, regulatory and policy obstacles may impede sharing opportunities. As a result, early adopters will be in the context of behind-the-meter sharing opportunities. In this paper, we study one of these opportunities. Specifically, we consider a collection of firms that invest in storage to arbitrage against the time of use pricing they face. We show that the investment decision of the firms form a Nash equilibrium which supports the social welfare. We offer explicit expressions for optimal storage investments and equilibrium prices for shared storage in a spot market. Finally, we use field data to assess the performance of our proposed sharing scheme.

Keywords:Large-scale systems, Mechanical systems/robotics, Linear systems Abstract: This paper considers an n-link underactuated revolute planar robot with all the links moving in the same vertical plane. This paper studies two open problems of the linear controllability and observability of the robot with only an active intermediate joint or only active intermediate joints around the upright equilibrium point (UEP), where all the links are in the upright position. First, when the robot only has a single active intermediate joint or only has multiple active intermediate nonadjacent joints with the corresponding joint angle(s) being measured, this paper shows via an illustrative example that there always exists a set of mechanical parameters that renders the robot linearly uncontrollable and unobservable around the UEP. This, together with an existing result, shows that an n-link planar robot with an actuator and an encoder is linearly controllable and observable around the UEP, regardless of its mechanical parameters, if and only if the first or last link, or the last joint, with the corresponding angle is measured. Second, when the robot only has two intermediate adjacent joints with the corresponding joint angles being measured, this paper proves that the robot is linearly controllable and observable around the UEP regardless of its mechanical parameters. When neither the first nor last joint of the robot is active, this paper shows that the robot is linearly controllable and observable around the UEP if and only if there are at least two active adjacent joints of n-2 intermediate joints and the corresponding joint angles are measured.

Keywords:Mechanical systems/robotics, Lyapunov methods, Constrained control Abstract: 3D dynamical walking subject to precise footstep placements is crucial for navigating real world terrain with discrete footholds. We present a novel methodology that combines control Lyapunov functions—to achieve periodic walking—and control Barrier functions—to enforce strict constraints on step length and step width—unified in a single optimization-based controller. We numerically validate our proposed method by demonstrating dynamic 3D walking at 0.6 m/s on DURUS, a 23 degree-of-freedom underactuated humanoid robot.

Keywords:Mechanical systems/robotics, Robotics Abstract: Human-machine systems, such as those used for rehabilitation, must be safe for human use when performing a given operational task. Passivity-based controllers such as the passive velocity field control method helps in realizing safe operation of human-machine systems. However, active behavior toward the external environment, including human bodies, is required to realize a given task. Such active behavior is difficult for passivity-based controllers. This study focuses on ensuring that a manipulator behaves passively toward an external force when the kinetic energy is greater than or equal to a given threshold and actively otherwise. We present a newly developed velocity field control method with an energy compensation mechanism. Theoretical analysis shows the properties of the proposed method: when the passivity toward external forces increases the kinetic energy of the augmented system beyond the required limit, the energy converges to a given range for safety rehabilitation without external forces, and the closed-loop system tracks a given desired velocity field without external forces. As a further theoretical discussion, we show the energy flow between the manipulator and human. Numerical simulations demonstrate that (1) the closed-loop system tracks a given desired velocity field, which describes a rehabilitation task, without external forces, (2) the proposed method inhibits the decrease in the kinetic energy of a closed-loop system, and (3) the closed-loop system behaves passively toward external forces such as an unexpected reaction of a human.

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Keywords:Mechanical systems/robotics, Mechatronics, Robotics Abstract: In this paper, a practical control approach is suggested for series elastic actuators(SEAs) to generate the desired torque. Firstly, based on the analysis of a nonlinear SEA, the generic dynamics for a class of SEAs is summarized. Then the dynamic equations are transformed into a novel state-space form which is convenient for controller design. Finally, based on the recently developed finite-time control technique, a finite time disturbance observer and a continuous terminal sliding-mode control scheme are introduced to synthesize the control law. The finite-time stability of the proposed controller is theoretically ensured by Lyapunov analysis. Compared with most existing methods, the contribution of the paper is two-fold: (i) The proposed controller is suitable for not only linear, but also a class of nonlinear SEAs, which means that it is a more generic method for SEA torque control; (ii) It achieves faster convergence rate and works well even in the presence of unknown payload parameters and external disturbances. A series of experiments are carried out on the self-built SEA testbed to demonstrate the superior performance of the proposed controller by comparing it with the cascade-PID controller.

Keywords:Mechatronics, Mechanical systems/robotics Abstract: The passive dynamic control (PDC) is a mechanical system control method which places the most importance on safety. It positively uses brakes having variable characteristics. In this paper, the PDC is applied to an antagonistic two-link pneumatic artificial muscle manipulator set on a vertical plane. Since the original PDC has limitations of capacity, the authors propose an improved PDC which introduces the PID control into the basic PDC, and verify the effectiveness of the improved PDC through positioning control experiments.

Keywords:Mechatronics, MEMs and Nano systems, Sampled-data control Abstract: The resolution of precision mechatronic systems is fundamentally limited by the the noise and distortion performance of digital-to-analog converters. The sources of noise and distortion include quantization error, non-linearity, thermal noise, and semiconductor noise. In precision control applications, the primary limitation is harmonic distortion due to quantization and element mismatch. In this article, quantization noise and harmonic distortion are reduced by combinations of small noise dithers and large high-frequency periodic dithers. Theoretical predictions are confirmed experimentally on a closed-loop nanopositioning system. The results show reasonable correspondence to simulation and a significant reduction in noise due to quantization and element mismatch.

Keywords:Networked control systems, Network analysis and control, Distributed control Abstract: We show that the continuous-time saddle-point distributed convex optimization algorithm can be formulated as the trajectories of a distributed control systems, where the control input to the dynamics of each agent relies on an observer that estimates the average state. Using this observation and by incorporating a continuous-time version of the so-called push-sum algorithm, this paper relaxes the graph theoretic conditions under which the first component of the trajectories of this modified class of saddle-point dynamical systems for distributed optimization are asymptotically convergent to the set of optimizers. In particular, we prove that strongly connectivity is sufficient under this modified dynamics, relaxing the known weight-balanced assumption. As a by product, we also show that the saddle-point distributed optimization dynamics can be extended to time-varying weight-balanced graphs which satisfy a persistency condition on the min-cut of the sequence of Laplacian matrices.

Keywords:Network analysis and control, Control of networks, Optimization algorithms Abstract: The topology of a network directly influences the behaviour and controllability of dynamical processes on that network. Therefore, the design of network topologies is an important area of research when examining the control of distributed systems. We discuss a method for growing networks known as whiskering, as well as generalizations of this process, and prove that they preserve controllability. We then use techniques from submodular optimization to analyze optimization algorithms for adding new nodes to a network to optimize certain objectives, such as graph connectivity.

Keywords:Network analysis and control, Power systems Abstract: Optimal frequency controllers for power networks based on distributed averaging have previously been shown to be an effective means of distributing control authority among agents while maintaining a globally optimal operating point. Distributed control architectures however require an implicit trust between participating agents, in that each must faithfully communicate the appropriate control variables to neighboring agents. Here we study the case where some agents attempt to "cheat the system" by adding a bias to the averaging controller in order to lower their generation cost. We quantify the effect of this dishonesty on the resource allocation problem and introduce a "cost graph" whose weights measure the effect of the bias on the optimal equilibrium. Moreover, we propose an "honesty-enforcing" controller which counteracts the dishonest agents, and restores the optimal setpoint of the network.

Keywords:Network analysis and control, Control of networks, Agents-based systems Abstract: Near-optimal convergence speeds are found for perturbed networked systems, with N interacting agents that conform to k-nearest neighbour (k-NNR) connection rules, by allocating a finite leadership resource amongst selected nodes. These nodes continue averaging their state with that of their neighbours while being provided with the resources to drive the network to a new state. Such systems are represented by a directed graph Laplacian with two newly presented semi-analytical approaches used to maximise the consensus speed. The two methods developed typically produce near-optimal results and are highly efficient when compared with conventional numerical optimisation, where the asymptotic computational complexity is O(n^{3}) and O(n^{4}) respectively. The upper limit for the convergence speed of a perturbed k-NNR network is identified as the largest element of the first left eigenvector (FLE) of a graph's adjacency matrix. The first semi-analytical method exploits this knowledge by distributing leadership resources amongst the most prominent nodes highlighted by this FLE. The second method relies on the FLEs of manipulated versions of the adjacency matrix to expose different communities of influential nodes. These are shown to correspond with the communities found by the Leicht-Newman detection algorithm, with this method enabling optimal leadership selection even in low outdegree (<12 connections) graphs, where the first semi-analytical method is less effective.

Keywords:Network analysis and control, Sensor networks, Estimation Abstract: In this paper, we study the problem of jointly retrieving the state of a dynamical system, as well as the state of the sensors deployed to estimate it. We assume that the sensors possess a simple computational unit that is capable of performing simple operations, such as retaining the current state and model of the system in its memory. We assume the system to be observable (given all the measurements of the sensors), and we ask whether each sub-collection of sensors can retrieve the state of the underlying physical system, as well as the state of the remaining sensors. To this end, we consider communication between neighboring sensors, whose adjacency is captured by a communication graph. We then propose a linear update strategy that encodes the sensor measurements as states in an augmented state space, with which we provide the solution to the problem of retrieving the system and sensor states. The present paper contains three main contributions. First, we provide necessary and sufficient conditions to ensure observability of the system and sensor states from any sensor. Second, we address the problem of adding communication between sensors when the necessary and sufficient conditions are not satisfied, and devise a strategy to this end. Third, we extend the former case to include different costs of communication between sensors. Finally, the concepts defined and the method proposed are used to assess the state of an example of approximate structural brain dynamics through linearized measurements.

Keywords:Network analysis and control, Control of networks, Networked control systems Abstract: In this paper, we examine the properties of the Laplacian matrix defined on signed networks, referred to as the signed Laplacian matrix, from the graph-theoretic perspective. The connection between the stability of the signed Laplacian with the cut set of the network is then established, and the number of negative eigenvalues of the signed Laplacian is estimated in terms of the number of negatively weighted edges in the network. In order to stabilize the signed Laplacian dynamics, a distributed diagonal compensation approach is proposed; we show that the compensation is closely related to the structural balance of the network. Furthermore, the influence of the external input on the signed Laplacian dynamics is investigated.

Keywords:Agents-based systems, Distributed control, Estimation Abstract: In this paper we propose a novel local interaction protocol which solves the discrete time dynamic average consensus problem, i.e., the consensus problem on the average value of a set of time-varying input signals in an undirected graph. The proposed interaction protocol is based on a multi-stage cascade of consensus filters which tracks the average value of the inputs with small error. We characterize how the number of stages influences the steady state error. The main novelty of the proposed algorithm is that, with respect to other dynamic average consensus protocols, we do not exploit the k-th order derivatives of the inputs nor we require that the average of the network state is preserved to achieve convergence to the desired quantity, thus increasing the robustness of the method in several practical scenarios. In addition, the proposed design allows to trade-off convergence time with steady-state error by choosing a proper number of stages in the cascade. Finally, we provide a preliminary asynchronous and randomized version of the proposed protocol along with numerical examples to corroborate the theoretical findings.

Keywords:Agents-based systems, Decentralized control, Distributed control Abstract: In this paper, we propose a distance-based formation control strategy that can enable four mobile agents, which are modelled by a group of single-integrators, to achieve the desired formation shape speciﬁed by using six consistent interagent distances in a 2-dimensional space. The control law is closely related to a gradient-based control law formed from a potential function reﬂecting the error between the actual interagent distances and the desired inter-agent distances. There are already control strategies achieving the same objective in a distance-based control manner in the literature, but the results do not yet include a global as opposed to local stability analysis. We propose a control strategy modiﬁed from the existing gradient-based control law so that we can achieve almost global convergence to the desired formation shape, and the control law uses known properties for an associated formation shape control problem involving a four-agent tetrahedron formation in 3-dimensional space. Simulation results verifying our analysis are also presented.

Keywords:Agents-based systems, Delay systems, Time-varying systems Abstract: This paper studies synchronization among identical agents that are coupled through a time-varying network with nonuniform time-varying communication delay. Given an arbitrary upper bound for the delays, a controller design methodology without exact knowledge of the network topology is proposed so that multi-agent consensus in a set of time-varying networks can be achieved.

Keywords:Agents-based systems, Distributed control, Autonomous systems Abstract: We study the circle formation problem for a group of anonymous mobile agents in a plane, in which we require that all the agents converge onto a desired circle surrounding a preset target point asymptotically as well as they maintain any desired relative distance from their neighbors. Each agent is modeled as a kinematic point and can merely sense the relative position information of the target and its neighbors. A distributed control law is designed to solve the problem. One feature of the proposed control law is that it guarantees that no collision between agents ever takes place throughout the system's evolution. Both theoretical analysis and numerical simulations are given to show the effectiveness and performance of the proposed formation control law.

Keywords:Agents-based systems, Distributed control, Cooperative control Abstract: This paper presents novel results on the symmetric rigidity matrix. First, we provide a physical meaning of eigenvectors of the symmetric rigidity matrix. Then, new concepts in rigidity theory are proposed, including the worst-case, and imbalance rigidity indices of planar frameworks. These new indices are scale free and could be useful in synthesis problems of rigid networks.

Keywords:Agents-based systems, Distributed control, Cooperative control Abstract: In this study, we consider formation control of multi-agent systems with free rotation and translation, without free reflection. The desired formation can be described as a set with the freedom of the special Euclidean group SE(d) = SO(d) x R^d. Actually, the sets SO(d) and R^d correspond to the free rotation and translation of the formation, respectively. For a given communication topology, we design a best distributed controller in the sense that the most similar coordination is achievable to the set with the freedom of SE(d). The effectiveness of the proposed controllers is illustrated by simulation results.

Keywords:Cooperative control, Distributed control, Adaptive control Abstract: In this paper, we consider the formation control problem for uncertain homogeneous Lagrangian nonlinear multi-agent systems in a leader-follower scheme, under an undirected communication protocol. A distributed adaptive control protocol of minimal complexity is proposed that achieves prescribed, arbitrarily fast and accurate formation establishment between the following agents and the leader as well as the synchronization of the parameter estimates of all following agents. The estimation and control laws are distributed in the sense that the control signal and update laws of each agent are calculated based solely on local relative state information from its neighborhood set. Moreover, provided that the communication graph is connected and contrary to the related works on multi-agent systems, the controller-imposed transient and steady state performance bounds are fully decoupled from: i) the underlying graph topology, ii) the control gains selection and iii) the agents' model uncertainties, and are solely prescribed by certain designer-specified performance functions. Finally, a simulation study with hovercraft platforms clarifies and verifies the approach.

Keywords:Cooperative control, Distributed control, Estimation Abstract: This paper investigates the weighted centroid formation tracking control for multi-agent systems. First, a class of novel distributed observers is developed for each agent to infer the formation’s weighted centroid in finite time. Then, the distance-based control law is proposed based on the estimations, such that the weighted centroid of the formation is driven to track the assigned time-varying reference, meanwhile maintaining the prescribed formation shape. Moreover, the formation stabilization error is shown to converge to zero using the proposed observer-controller scheme utilizing the finite-time Lyapunov stability of the observers. Finally, all the theoretical results are further validated through numerical simulations.

Keywords:Robotics, Cooperative control, Autonomous robots Abstract: Bimanual manipulation tasks require strong coordination between the two hands performing the task. Trajectories of both arms must be temporally synchronized while satisfying certain spatial constraints while performing the task. In this paper, control laws for the desired trajectory tracking and synchronization of multiple agents modeled using dynamic movement primitives (DMPs) are developed. The control laws are developed using contraction analysis of nonlinear systems. Specific control laws and tracking and synchronization constraints for bimanual tasks are developed. Experimental results suggest that the proposed control laws are robust to spatial perturbations and on-the-fly goal location changes.

Keywords:Cooperative control, Distributed control, Output regulation Abstract: In this paper, we generalize the cooperative output regulation problem of multi-agent systems, and we consider the case where agents in the system only receive incomplete measurements from the exosystem. In other words, we consider the case where no agent receives sufficient information through its measurements to estimate the exosystem states. Under certain intuitive assumptions on the connectivity between the agents and their combined detectability property, we propose a distributed control law that solves the cooperative output regulation problem under the considered problem constraints. A numerical example is offered to illustrate the effectiveness of the proposed control solution.

Keywords:Cooperative control, Distributed control Abstract: This paper investigates the relation between graph signal processing and consensus of multi-agent systems. The graph signal processing is a technique to process graph signals, that is, signals whose values are on the vertices of graphs and whose structures are specified by the edges. By considering the combination of the states of agents and the graph describing the network structure between them as a graph signal, we show that the multi-agent consensus corresponds to low-pass filtering of the graph signal. This reveals a connection between the two distinct areas, i.e., the graph signal processing and the control of multi-agent systems. In addition, we provide a design method of consensus controllers based on the graph signal processing. In the proposed method, the controllers of agents are designed so that the spatial frequency of the states of the agents becomes a desired one. This enables us to construct controllers of multi-agent systems in the spatial frequency domain.

Keywords:Cooperative control, Control over communications, Optimal control Abstract: In this paper, we propose a distributed control algorithm for consensus of dynamical multi-agent systems based on maximum hands-off control with sampled-data state observation. Maximum hands-off control is a control that maximizes the time duration on which the control is exactly zero among the feasible controls, which can reduce fuel or electricity consumption while the control signals take the value of zero. We give theorems for feasibility, characterization and stability for the proposed control that reaches consensus. A simulation result is shown to illustrate the effectiveness of the proposed control.

Keywords:Biological systems, Network analysis and control, Markov processes Abstract: This paper introduces a theoretical framework for the analysis and control of the stochastic susceptible-infected-removed (SIR) spreading process over a network of heterogeneous agents. In our analysis, we analyze the exact networked Markov process describing the SIR model, without resorting to mean-field approximations, and introduce a convex optimization framework to find an efficient allocation of resources to contain the expected number of accumulated infections over time. Numerical simulations are presented to illustrate the effectiveness of the obtained results.

Keywords:Control of networks, Decentralized control Abstract: We study an SIS epidemic model over an arbitrary fixed network topology where the n agents, or nodes of the network, have partial information about the epidemic state. The agents react by distancing themselves from their neighbors when they believe the epidemic is currently prevalent. An agent's awareness is weighted from three sources of information: the fraction of infected neighbors in their contact network, their social network, and a global broadcast of the fraction of infected nodes in the entire network. The dynamics of the benchmark (no awareness) and awareness models are described by discrete-time 2^n-state Markov chains. Through a coupling technique, we establish monotonicity properties between the benchmark and awareness models. Particularly, we show that the expectation of any increasing random variable on the space of sample paths, e.g. eradication time or total infections, is lower for the awareness model. In addition, we give a characterization for this difference of expectations in terms of the coupling distribution. In simulations, we evaluate how different sources of information affect the spread of an epidemic.

Keywords:Network analysis and control, Large-scale systems, Agents-based systems Abstract: We consider a class of opinion dynamics on networks where at each time-step, each node in the network disregards the opinions of a certain number of its most extreme neighbors and updates its own opinion as a weighted average of the remaining opinions. When all nodes disregard the same number of extreme neighbors, previous work has shown that consensus will be reached if and only if the network satisfies certain topological properties. In this paper, we consider the implications of allowing each node to have a personal threshold for the number of extreme neighbors to ignore. We provide graph conditions under which consensus is guaranteed for such dynamics. We then study random networks where each node's threshold is drawn from a certain distribution, and provide conditions on that distribution, together with conditions on the edge formation probability, that guarantee that consensus will be reached asymptotically almost surely.

Keywords:Network analysis and control, Agents-based systems Abstract: A symmetric signed Laplacian matrix uniquely defines a resistive electrical circuit, where the negative weights correspond to negative resistances. The positive semidefiniteness of signed Laplacian matrices is studied in this paper using the concept of effective resistance. We show that a signed Laplacian matrix is positive semidefinite with a simple zero eigenvalue if, and only if, the underlying graph is connected, and a suitably defined effective resistance matrix is positive definite.

Keywords:Networked control systems, Sampled-data control, Lyapunov methods Abstract: This paper considers discrete-time networked control systems in which distributed sensors, controllers, and actuators communicate through a shared communication medium that introduces large and bounded time-varying transmission delays. Access to the communication medium is orchestrated by a weighted try-once-discard protocol that determines which sensor node can access the network and transmit its corresponding data. The closed-loop system is modelled as a novel discrete-time hybrid system with time-varying delays in the dynamics and in the reset conditions. By Lyapunov method a new condition is derived for the exponential stability of the delayed hybrid systems with respect to the full state and not only to the partial state. An example of a discrete-time cart-pendulum illustrates the efficiency of the time-delay approach.

Keywords:Network analysis and control, Optimization, Algebraic/geometric methods Abstract: We consider Boolean networks defined on directed graphs in which the state of every node belongs to the set {0,1}. We think of a node in state 1 as having `failed'. The state of every node at the next time instant is a function of the states of those nodes that link to it. Nodes fail according to a set of rules, and once a node fails it stays so forever. We develop a mathematical framework that allows us to find the smallest set of nodes whose failure at time zero causes the eventual failure of all nodes in a desired target set. Our methods are based on modeling network dynamics using Boolean polynomials and exploiting their properties. Rather than propagating the state forward using a nonlinear map, we characterize all possible steady-state configurations as the fixed points of the network's dynamics, and provide a simple algorithm for finding all such `stable' configurations. We demonstrate the utility of our framework with the help of illustrative examples.

Keywords:Decentralized control, Large-scale systems, Machine learning Abstract: In this paper, we propose a distributed secondorder method for reinforcement learning. Our approach is the fastest in literature so-far as it outperforms state-of-the-art methods, including ADMM, by significant margins. We achieve this by exploiting the sparsity pattern of the dual Hessian and transforming the problem of computing the Newton direction to one of solving a sequence of symmetric diagonally dominant system of equations. We validate the above claim both theoretically and empirically. On the theoretical side, we prove that similar to exact Newton, our algorithm exhibits super-linear convergence within a neighborhood of the optimal solution.Empirically, we demonstrate the superiority of this new method on a set of benchmark reinforcement learning tasks.

Keywords:Optimization, Optimization algorithms Abstract: In this paper we introduce disciplined convex-concave programming (DCCP), which combines the ideas of disciplined convex programming (DCP) with convex-concave programming (CCP). Convex-concave programming is an organized heuristic for solving nonconvex problems that involve objective and constraint functions that are a sum of a convex and a concave term. DCP is a structured way to define convex optimization problems, based on a family of basic convex and concave functions and a few rules for combining them. Problems expressed using DCP can be automatically converted to standard form and solved by a generic solver. Widely used implementations include YALMIP, CVX, CVXPY, and Convex.jl. In this paper we propose a framework that combines the two ideas, and includes two improvements over previously published work on convex-concave programming, specifically the handling of domains of the functions, and the issue of subdifferentiability on the boundary of the domains. We describe a Python implementation called DCCP, which extends CVXPY, and give examples.

Keywords:Optimization, Optimization algorithms Abstract: Many popular first order algorithms for convex optimization, such as forward-backward splitting, Douglas-Rachford splitting, and the alternating direction method of multipliers (ADMM), can be formulated as averaged iteration of a nonexpansive mapping. In this paper we propose a line search for averaged iteration that preserves the theoretical convergence guarantee, while often accelerating practical convergence. We discuss several general cases in which the additional computational cost of the line search is modest compared to the savings obtained.

Keywords:Optimization, Decentralized control, Numerical algorithms Abstract: This paper considers the problem of distributed optimization over time-varying undirected graphs. We discuss a distributed algorithm, which we call DIGing, for solving this problem based on a combination of an inexact gradient method and a gradient tracking technique. This algorithm deploys fixed step size but converges exactly to the global and consensual minimizer. Under strong convexity assumption, we prove that the algorithm converges at an R-linear (geometric) convergence rate as long as the step size is less than a specific bound; we give an explicit estimate of this rate over uniformly connected graph sequences and show it scales polynomially with the number of nodes. Numerical experiments demonstrate the efficacy of the introduced algorithm and validate our theoretical findings.

Keywords:Optimization, Optimization algorithms, Networked control systems Abstract: We consider distributed convex optimization problems that involve a separable objective function and nontrivial convex local constraints, such as Linear Matrix Inequalities (LMIs). We propose a decentralized, computationally inexpensive algorithm to solve such problems over time-varying directed networks of agents, that is based on the concept of approximate projections. Our algorithm is one of the consensus based methods in that, at every iteration, every agent performs a consensus update of its decision variables followed by an optimization step of its local objective function and local constraint. Unlike other methods, the last step of our method is not a projection to the feasible set, but instead a subgradient step in the direction that minimizes the local constraint violation. We show that the algorithm converges almost surely, i.e., every agent agrees on the same optimal solution, when the objective functions and constraint functions are nondifferentiable and their subgradients are bounded. We provide simulation results on a decentralized SDP (optimal gossip averaging), which involves large numbers of LMI constraints.

Keywords:Optimization, Large-scale systems, Agents-based systems Abstract: This paper considers networks of agents that seek to cooperatively solve a general class of nonsmooth convex optimization problems with an inherent distributed structure. We characterize the asymptotic convergence properties of distributed continuous-time coordination algorithms whose design relies on the saddle-point dynamics associated with an augmented Lagrangian. The main technical novelty is the identification of a nonsmooth Lyapunov function which, under mild convexity and regularity assumptions on the optimization problem data, allows us to further characterize the exponential convergence rates of the proposed algorithms for optimization subject to either equality or inequality constraints.

Keywords:Systems biology, Biomedical, Optimal control Abstract: Impulsive systems model continuous-time frame- works with control actions occurring at discrete time instants. Among the others, such models assume relevance in medical situations, where the physical system under control evolves con- tinuously in time, whilst the control therapy is instantaneously administered, e.g. by means of intra-venous injections. This note proposes a discretization algorithm for an impulsive system, whose methods relies on the Carleman embedding techinique. The discretization times are given by the impulsive control action and do not require to have a fixed discretization period. On the ground of the resulting discrete-time system (which can be computed with arbitrary level of accuracy) we propose an optimal control algorithm on a finite horizon. Simulations are carried out on a model exploited for anti-angiogenic tumor therapies and show the effectiveness of the theoretical results.

Keywords:Optimal control, Communication networks, Networked control systems Abstract: In this paper LQG control over unreliable communication links is examined. That is to say, the communication channels between the controller and the actuators and between the sensors and the controller are unreliable. This is of growing importance as networked control systems and use of wireless communication in control are becoming increasingly common. A proposed approach is to use tree codes to turn lossy channels into ones with a random delay. The problem of how to optimize LQG control in this case is examined, and it is found that to optimize LQG control previous control signals must also be used. Only the situation where communication between the components is done with acknowledgments is examined. An optimal solution is derived for finite horizon discrete hold-input LQG control for this case. The solution is compared with standard LQG control in simulations, which demonstrate that a significant improvement in the cost can be achieved when the probability of delay is high.

Keywords:Variational methods, Algebraic/geometric methods, Nonholonomic systems Abstract: In this paper, we present a geometric variational algorithm for optimizing the gaits of kinematic locomoting systems. The dynamics of this algorithm are analogous to the physics of a soap bubble, with the system's Lie bracket supplying an ``inflation pressure'' that is balanced by a ``surface tension'' term derived from a Riemannian metric on the system's shape space. We demonstrate this optimizer on a variety of system geometries (including Purcell's swimmer) and for optimization criteria that include maximizing displacement and efficiency of motion for both translation and turning motions.

Keywords:Optimal control, Constrained control, Robust control Abstract: We consider discrete-time deterministic optimal control problems in which termination at some finite, but not predetermined nor a-priori bounded time is mandatory. We characterize the value function as the maximal fixed point of a suitable dynamic programming operator and establish the convergence of both exact and approximate value iteration under very general assumptions, which cover the classical deterministic shortest path problem and its extension to hypergraphs as well as reachability and minimum-time problems for sampled versions of continuous control systems under constraints. In particular, the state and input alphabets are infinite sets or metric spaces, and the plant dynamics may be nonlinear and subject to disturbances and constraints. The optimization is in the minimax (or maximin) sense, the additive, extended real-valued running and terminal costs are undiscounted and may be unbounded and of arbitrary signs, the value function is typically discontinuous, and our results do apply to the maximization of non-negative rewards under hard constraints.

Peoples' Friendship Univ. of Russsia, Faculty of Science, D

Keywords:Optimal control, Constrained control Abstract: In this paper we consider a nonlinear optimal control problem with equality endpoint constraints. We introduce a new natural definition of singular control for which we obtain second-order necessary optimality conditions.

Keywords:Optimal control, Constrained control Abstract: A supremum-of-quadratics representation for a class of convex barrier-type constraints is developed and applied in a class of continuous time state constrained linear regulator problems. Using this representation, it is shown that any linear regulator problem constrained by such a convex barrier-type constraint can be equivalently formulated as an unconstrained two-player linear quadratic game.

Keywords:Air traffic management, Optimization algorithms Abstract: Air traffic flow management is an important component in an air traffic control system and has significant effects on the safety and efficiency of air transportation. In this paper, we propose a distributed air traffic flow management strategy to minimize the airport departure and arrival schedule deviations. The scheduling problem is formulated based on an en-route air traffic system model consisting of air routes, waypoints and airports. A cell transmission flow dynamic model is adopted to describe the system dynamics under safety related constraints such as the capacities of air routes and airports, and the aircraft speed limits. Our air traffic flow management problem is formulated as an integer quadratic programming problem. To overcome the computational complexity, we first solve a relaxed quadratic programming problem by a distributed approach based on Lagrangian relaxation. Then a heuristic algorithm based on forward-backward propagation is proposed to obtain the final integer solution. Experimental results demonstrate the effectiveness of the proposed scheduling strategy.

Keywords:Optimization algorithms, Optimal control, Estimation Abstract: Distributed algorithms for sparse, large-scale optimization problems are preferable over centralized solvers when the computational units are physically far apart from each other or the problem size is too large for the available memory. However, most distributed methods sacrifice convergence speed for simpler computations. In this paper, we propose a novel algorithm for a certain class of nonconvex, separable optimization problems that combines both distributed computations and locally quadratic convergence. It is based on the principle of primal decomposition with exact Hessian information but uses soft coupling between the agents to avoid global calculations and adapt faster to online data changes. An important application field of the presented method is nonlinear parameter estimation, where increasing the number of experiments may lead to problem dimensions that are prohibitive for conventional solvers. We assess the performance of our method on the identification of an Airborne Wind Energy (AWE) system using real-world experimental data.

Keywords:Optimization algorithms, Distributed control, Sensor fusion Abstract: We consider regularized distributed optimization problems over networks. The problem arises from many existing domains, such as coordinated control, sensor fusion and distributed learning. We propose a new framework based on Bregman method and operator splitting, which allows us to come up with a general distributed algorithm, termed Distributed Forward-Backward Bregman Splitting (D-FBBS). The proposed algorithm, though derived from a different perspective, is shown to have close connections with some existing algorithms. In addition, we show that the proposed algorithm is able to seek a saddle point which solves the above primal problem as well as its dual simultaneously. We also establish a non-ergodic convergence rate of o(1/k) in terms of fixed point residual. A simple example of sensor fusion problem is provided to illustrate the effectiveness of the algorithm.

Keywords:Optimization algorithms, Optimal control, Predictive control for nonlinear systems Abstract: Direct optimal control methods first discretize a continuous-time Optimal Control Problem (OCP) and then solve the resulting Nonlinear Program (NLP). Sequential Quadratic Programming (SQP) is a popular family of algorithms to solve this finite dimensional optimization problem. In the specific case of a least squares cost, the Generalized Gauss-Newton (GGN) method is a popular approach which works very well under some assumptions. This paper proposes a Sequential Convex Quadratic Programming (SCQP) scheme which exploits additional convexities in the NLP in order to generalize the GGN algorithm, possibly extend its applicability and improve its local convergence. These properties are studied in detail for the proposed SCQP algorithm, which will be compared to the classical GGN method using a numerical case study of the optimal control of an inverted pendulum.

Keywords:Optimization algorithms, Optimal control, Smart grid Abstract: The uncoordinated charging of large electric vehicle (EV) fleets could have an adverse influence on power network operation. To guarantee the secure and economic operation of power grids, vehicle charging needs to be coordinated to minimize the power supply cost, while catering vehicle charging requests. Provisioning large-scale fleets scheduled at fine timescales, the task of EV scheduling is tackled here by properly adopting the Frank-Wolfe method. Upon devising an optimal step size rule, the novel scheme is shown to enjoy fast convergence rate, especially during the first iterations. The derived charging protocol features affordable computational requirements from vehicle controllers and minimal information exchange between vehicles and their aggregator. To cope with random cyber delays in the communication links between vehicles and the aggregator, an asynchronous version of the charging scheme is also studied. Interpreted as a block stochastic Frank Wolfe algorithm, the latter ensures feasibility across iterations, converges in the mean, and enjoys the same order of convergence rate attained by its synchronous counterpart. Numerical tests demonstrate the advantage of our deterministic scheme over a state-of-the-art projected gradient descent alternative, as well as the robustness of its stochastic counterpart to asynchronous updates.

Keywords:Optimization, Optimization algorithms, Adaptive control Abstract: Many real world applications require multiple conflicting objectives to be optimized. However, explicit functions mapping the system variables to outputs are often unknown, making traditional optimization approaches impossible. Extremum Seeking Control (ESC) is one method to tackle the latter problem by estimating the local gradient of the objective functions. Extensive literature on ESC focuses on single objective optimization, which use sinusoids as the dither signal. An inherent disadvantage with the sinusoidal nature of the dither is that after convergence the output continues to move around in a neighborhood of the optimal set-point, with the size of the neighborhood proportional to the amplitude of the dither signal. This paper focuses on using square waves as dithers and proves that the square wave can produce a constant output, in contrast to the typical sinusoid where the undesirable dithering effect still exists at the output. The basic ESC scheme is extended to execute Multiple Gradient Descent Algorithm (MGDA) to solve a Multi Objective Optimization Problem (MOOP). A two-stage ESC estimates the local gradient of each objective function, then estimates the optimal weighting of gradients to move to the Pareto front. This eliminates the need for a decision maker as required in a priori scalarization solutions a MOOP. Simulation results show that ESC using MGDA is able to find the Pareto optimal solutions, starting from different initial conditions.

Keywords:Stochastic optimal control, Constrained control Abstract: This paper considers stochastic optimal control of a class of nonlinear discrete-time systems with disturbances modeled by a Markov chain. The objective is to maximize the expected time or the expected total yield until prescribed constraints are violated. Conditions for the existence of an optimal solution are derived, and a new algorithm is developed that converges to the optimal solution faster than conventional value iteration / dynamic programming. Two numerical examples of stochastic adaptive cruise control and glider flight management are treated.

Keywords:Stochastic optimal control, Fault detection Abstract: This paper studies attackers with control objectives and explicit detection constraints against cyber-physical systems. The cyber-physical system is equipped with a Kalman filter and an attack detector that uses the innovations process of the Kalman filter. The attacker performs an integrity attack on the actuators and sensors of the system with the aim of moving the system to a target state under the constraint that the probability of him or her being detected is equal to the false alarm probability of the attack detector. We formulate and solve a constrained optimization problem that gives the optimal sequence of attacks and demonstrate our attack strategy in a numerical example.

Keywords:Stochastic optimal control, Formal verification/synthesis, Computational methods Abstract: Correct-by-design automated construction of con- trol systems has attracted a tremendous amount of attention. However, most existing algorithms for automated construction suffer from the "curse of dimensionality", i.e., their run time scales exponentially with increasing dimensionality of the state space. As a result, typically, systems with only a few degrees of freedom are considered. In this paper, we propose a novel algorithm based on the tensor-train decomposition that solves stochastic optimal control problems with syntactically co-safe linear temporal logic specifications. We show that, under certain conditions, the run time of the proposed algorithm scales polynomially with the dimensionality of the state space and the rank of the optimal cost-to-go function. We demonstrate the algorithm in a six-dimensional problem instance involving a simple airplane model. In this example, the proposed algorithm provides up to four orders of computational savings when compared to the standard value iteration algorithm.

Keywords:Stochastic optimal control, Hybrid systems, Optimal control Abstract: A class of stochastic hybrid systems with both autonomous and controlled switchings and jumps is considered where autonomous and controlled state jumps at the switching instants are accompanied by changes in the dimension of the state space. Optimal control problems associated with this class of stochastic hybrid systems are studied where in addition to running and terminal costs, switching between discrete states incurs costs. Necessary optimality conditions are established in the form of the Stochastic Hybrid Minimum Principle. A feature of special importance is the effect of hard constraints imposed by switching manifolds on diffusion-driven state trajectories which influence the boundary conditions for the stochastic Hamiltonian and adjoint processes.

Keywords:Stochastic optimal control, Markov processes, Optimal control Abstract: We present the infinite dimensional approach to control of a general class of doubly stochastic or otherwise known Q-mark Markov Jump Diffusion (Q-MJD) processes. The governing dynamics for the the probability density function (PDF) of this class of Q-MJD processes is a Partial Integro Differential Equation (PIDE). The infinite dimensional Minimum Principle (MP) is applied to control these PIDE dynamics. We qualitatively compare the infinite dimensional MP and the stochastic Dynamic Programming Principle (DPP) frameworks as applied to control of Q-MJD processes. The developed sampling based algorithms illustrate how the presented framework is a multi trajectory optimization method to solve nonlinear stochastic optimal control problems for Q-MJD processes.

Keywords:Stochastic optimal control, Optimal control, Linear systems Abstract: This work deals with an optimal covariance control problem for stochastic discrete-time linear systems subject to mean sum constraints involving quadratic functions of the state and the control input sequences under the assumption of full state information. We show that the stochastic optimal control problem is equivalent to a deterministic nonlinear program, which, under a judicious choice of the decision variable, can be brought to a form in which its performance index is a convex, quadratic function subject to both equality and inequality quadratic constraints. The key challenge here stems from the fact that the equality constraints that result from the terminal constraints on the state covariance may not be necessarily convex. We show, however, that by employing a simple relaxation technique, the nonlinear program is associated with a convex program, which can be addressed by means of robust and efficient algorithms. Despite the fact that the solution to the relaxed convex program will not necessarily give closed-loop trajectories whose endpoints follow exactly the goal Gaussian distribution, a representative sample of such trajectories are expected to have endpoints that will be more concentrated near the origin than if there were drawn from the goal Gaussian distribution. Finally, numerical simulations that illustrate some key ideas of the paper are presented.

Keywords:Estimation, Adaptive systems, Kalman filtering Abstract: The accuracy of state estimation can be enhanced by simultaneously estimating unknown inputs. This paper presents an extension of retrospective cost input estimation (RCIE) that directly updates the estimates of all states. We show that RCIE can be used for systems in which the transmission zeros from the estimated input to the measurement are nonminimum phase. We demonstrate this ability on numerical examples, and we compare the estimates from RCIE to estimates from prior methods for input estimation. Finally, we use this technique to estimate the acceleration of a flight vehicle using camera data, and we assess the accuracy of the acceleration estimates by transforming the onboard body-frame acceleration measurements to the camera frame.

Keywords:Aerospace, Estimation, Observers for nonlinear systems Abstract: We revisit the gradient based nonlinear attitude complementary filters (observers) on the Special Orthogonal group SO(3) and provide time-explicit solutions of the norm of the attitude estimation error dynamics. One constant-gain and two state-dependent-gain attitude observers are considered. The stability and performance properties of these attitude observers can be easily deduced from the obtained closed-form solutions. We show that the traditional (constant-gain) complementary attitude filter, previously proposed in the literature, is not Input-to-State-Stable (ISS) with respect to bounded measurement disturbances, while the state-dependent-gain versions are. We also show that the state-dependent-gain versions of the attitude complementary filter exhibit better convergence rates. Simulation results are provided to illustrate our results.

Keywords:Estimation, Filtering, Stochastic optimal control Abstract: An efficient technique for the state estimator for multi-dimensional linear dynamic systems with additive Cauchy distributed process noises and measurement noises is discussed. The characteristic function (CF) of the unnormalized conditional probability has been shown to be an analytic and recursive sum of terms composed of a coefficient function of the measurements times on exponential, whose argument has directions operating on the spectral vector. We uncover several fundamental properties of the CF, including the direction co-alignment, term combination and reconstruction of the coefficient terms. Based on these properties, a pre-computational technique is developed to enhance the computational efficiency. Numerical simulations of a three-state system demonstrates the performance of the Cauchy estimator under both Cauchy noise environment and Gaussian noise environment, compared to the standard Kalman Filter.

Keywords:Estimation, Identification, Linear parameter-varying systems Abstract: A recursive algorithm for estimating the statistics of the Normal distribution is designed, making it adaptive in the sense that the forgetting factor is driven by data. A mechanism to suppress obsolete information is proposed, following the principles of Bayesian decision-making. Specifically, the best combination of two time-evolution model hypotheses in terms of the geometric mean is performed. The first hypothesis assumes no change in the parameter evolution, while the second one assumes that all parameter changes are equally admitted. In order to provide data-driven forgetting, complementary probabilities assigned to each hypothesis are determined as the maximizers of the decision problem. Simulations, including a performance comparison with a recently proposed self-tuning estimator, are presented.

Keywords:Estimation, Identification Abstract: In this work, we develop min-min type of biased estimators for the deterministic parameter vector in a linear regression model under the condition that an ellipsoidal prior knowledge is either available or is inferred from the measurements, leading to the non-blind and blind designs, respectively. As the design specifications for the former, from which the latter is developed, domination over the least-squares (LS) estimator with respect to all weighted mean-squared error (MSE) measures and the corresponding admissibility condition are ensured. The blind counterpart of this solution is then built based on an ellipsoidal set that is estimated from the LS approach. This nonlinear estimator admits a closed-form solution and is proved to outperform the LS estimator under a wide range of conditions. Numerical comparisons of the developed non-blind solution, referred to as the constrained min-min (CMM) estimator, to alternatives demonstrate the superior weighted MSE performance of our solution when the true parameters are not nearby the boundary of the ellipsoid. On the other hand, as the case with all blind approaches, the blind CMM (BCMM) estimator is also more likely to have a major improvement over the LS estimator in problems of relatively high dimension. When compared to existing blind approaches, the BCMM estimator is more preferable when various weighted MSE measures are taken into account in the performance evaluation.

Keywords:Estimation, Kalman filtering, Filtering Abstract: The paper deals with resilient state estimation of cyber-physical systems subject to switching signal attacks and fake measurement injection. In particular, the random set paradigm is adopted in order to model the switching nature of the signal attack and the fake measurement injection via Bernoulli and/or Poisson random sets. The problem of jointly detecting a signal attack and estimating the system state in presence of fake measurements is then formulated and solved in the Bayesian framework leading to the analytical derivation of a hybrid Bernoulli filter that updates in real-time the joint posterior density of the detection attack Bernoulli set and of the state vector. Exploiting a Gaussian-mixture implementation of the filter, a simulation example is developed in order to demonstrate the effectiveness of the proposed method.

Keywords:Identification, Estimation Abstract: In this paper, we estimate the continuous-time nonlinear rotational dynamics of a DJI F450 quadcopter which is controlled and stabilized by an onboard unrooted Android phone with a PID controller. Since the Android phone contains the only IMU in the system, we only have measurements provided by the Android Java API for estimation, which are subject to significant latencies because Android is not realtime system. Although prediction error methods are typically preferred for estimating general continuous-time nonlinear models, we show that the standard prediction error estimates are highly sensitive to the initial guess, and hence we introduce a total least-squares approach for estimating the initial model. Finally, we compare the estimated models to the model obtained from a traditional inertia measurement device, namely, a Bifilar test stand.

Keywords:Identification, Estimation Abstract: This paper presents a new algorithm to estimate the parameters and the time delay of continuous-time (CT) systems. The proposed algorithm uses the Simplified Refined Instrumental Variable (SRIVC) method to estimate the plant parameters while using a Gauss-Newton method to find the time delay of the system. The time delay cost function is filtered through multiple low-pass filters with different cut-off frequencies to generate a set of cost functions that share the same global minimum while having different local minima. This cost function set is then used to overcome the local minima and achieve convergence to the global minimum of the time delay optimization problem. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.

Keywords:Human-in-the-loop control, Closed-loop identification Abstract: We present results from an experiment in which 44 human subjects each interact with a dynamic system 40 times over a one-week period. For each interaction, a subject is asked to perform a command-following task. For each subject and each interaction, the dynamic system is the same; however, the task (i.e., reference command to be followed) is not necessarily the same. We use the experimental results to examine the effect of changing task on the learning process. Experimental results show that the subjects are able to generalize a control strategy learned on one task to a different task. Results also suggest that subjects are able to learn without relying on prediction, but their ability without prediction is more limited.

Keywords:Identification, Estimation, Machine learning Abstract: This paper proposes a parameter estimation method for ARMAX models based on the variational Bayesian method. In order to obtain the posterior distribution in an exact form, we convert the original estimation problem into another one in which the equation to be solved is linear in the unknown parameter by employing an artificial unknown parameter. Then the resulting estimation algorithm is derived based on the constrained optimization technique.

Keywords:Identification, Linear parameter-varying systems, Estimation Abstract: In this paper, we present an approach to identify linear parameter-varying (LPV) systems with a state-space (SS) model structure in an innovation form where the coefficient functions have static and affine dependency on the scheduling signal. With this scheme, the curse of dimensionality problem is reduced, compared to existing predictor based LPV subspace identification schemes. The investigated LPV-SS model is reformulated into an equivalent impulse response form, which turns out to be a moving average with exogenous inputs (MAX) system. The Markov coefficient functions of the LPV-MAX representation are multi-linear in the scheduling signal and its time-shifts, contrary to the predictor based schemes where the corresponding LPV auto-regressive with exogenous inputs system is multi-quadratic in the scheduling signal and its time-shifts. In this paper, we will prove that under certain conditions on the input and scheduling signals, the ell_2 loss function of the one-step-ahead prediction error for the LPV-MAX model has only one unique minimum, corresponding to the original underlying system. Hence, identifying the LPV-MAX model in the prediction error minimization framework will be consistent and unbiased. The LPV-SS model is realized by applying an efficient basis reduced Ho-Kalman realization on the identified LPV-MAX model. The performance of the proposed scheme is assessed on a Monte Carlo simulation study.

Keywords:Identification, Linear systems, Filtering Abstract: A dynamic system with both input and output measurement errors is termed as an errors-in-variables (EIV) system. %Deployment Employment of traditional identification methods for EIV systems will result in biased estimates, and methods like Bias Eliminated Least Squares (BELS), Subspace EIV methods may not always provide good parameter estimates. To address these open issues, this paper presents a maximum-likelihood (ML) approach for the identification of EIV systems.To avoid the difficulties associated with maximizing the likelihood function directly, we use the Expectation Maximization (EM) algorithm to iteratively solve the ML problem. The efficacy of the proposed method is demonstrated with an experimental tank system case study.

Keywords:Adaptive control, Hybrid systems, Lyapunov methods Abstract: In this paper, we develop an adaptive control approach for hidden mode tracking of uncertain hybrid systems in Brunovsky form that are subject to actuator input amplitude and rate constraints, as well as bounded disturbances. Our approach adapts to the parameters of the hidden mode, and relies on a systematic modification of the reference model to deal with input constraints and disturbances in a stable manner. Global tracking capability is shown for input-to-state stable systems, while for input-to-state unstable systems, the local regions of attraction are characterized. The effectiveness of our input-constrained hidden mode tracking approach is illustrated with a robot walking example.

Keywords:Direct adaptive control, Adaptive control, Data storage systems Abstract: This paper proposes a novel direct adaptive control method for rejecting unknown deterministic disturbances and tracking unknown trajectories in systems with uncertain dynamics when the disturbances or trajectories are the summation of multiple sinusoids with known frequencies, such as periodic profiles or disturbances. The proposed algorithm does not require a model of the plant dynamics and does not use batches of measurements in the adaptation process. Moreover, it is applicable to both minimum and non--minimum phase plants. The algorithm is a "direct" adaptive method, in the sense that the identification of system parameters and the control design are performed simultaneously. In order to verify the effectiveness of the proposed method, an add--on controller is designed and implemented in the servo system of a hard disk drive to track unknown nano--scale periodic trajectories.

Keywords:Adaptive systems, Delay systems, Stability of nonlinear systems Abstract: We present a Newton-based extremum seeking algorithm for maximizing higher derivatives of unknown maps in the presence of time delays. Different from previous works about extremum seeking for higher derivatives, arbitrarily long input-output delays are allowed. We incorporate a predictor feedback with a perturbation-based estimate for the Hessian’s inverse using a differential Riccati equation. As a bonus, the convergence rate of the real-time optimizer can be made user-assignable, rather than being dependent on the unknown Hessian of the higher-derivative map. Furthermore, exponential stability and convergence to a small neighborhood of the unknown extremum point can be obtained for locally quadratic derivatives by using backstepping transformation and averaging theory in infinite dimensions. We also give a numerical example in order to highlight the effectiveness of the proposed predictor- based extremum seeking for time-delay compensation.

Keywords:Adaptive control, Fault tolerant systems, Constrained control Abstract: In this paper, we present a novel adaptive fault tolerant control (FTC) scheme for a class of nonlinear systems with actuator faults and constraint requirement on the system output tracking error. The gain functions of the nonlinear systems under discussion can be unknown and state dependent, without assuming any known information for the lower and upper bounds of the gain functions as well as the actuator faults. We show that under the proposed adaptive FTC scheme, exponential convergence of the output tracking error into a small set around zero is guaranteed, while the constraint requirement on the system output tracking error will not be violated during operation.An illustrative example is presented to further demonstrate the effectiveness of the proposed control scheme.

Keywords:Adaptive control, Mechatronics, Closed-loop identification Abstract: This work proposes a novel PI-like composite adaptive control architecture for the uncertain Euler-Lagrange (EL) systems. The composite adaptive law is strategically designed to be proportional to the parameter estimation error in addition to the tracking error, leading to parameter convergence. Unlike conventional adaptive control laws which require the regressor function to be persistently exciting (PE) for parameter convergence, the proposed method guarantees parameter convergence from a milder initially exciting (IE) condition on the regressor. The IE condition is significantly less restrictive than PE, since it does not rely on the future values of the signal and that it can be verified online. Further, the design methodology does not assume the knowledge of acceleration in the adaptive update law development. As far as the authors are aware, this is the first work on EL dynamics that achieves exponential convergence of the tracking and the parameter estimation errors to zero once the sufficient IE condition is met.

Keywords:Adaptive control, Observers for Linear systems, Variable-structure/sliding-mode control Abstract: Adaptive observers have been applied successfully in many control areas, including adaptive control and fault detection problems. Recently it has been shown that finite-time parameter estimation can improve the overall performance of adaptive controls. If the controller is based on an adaptive observer, then it is natural to assume that the same improvement can be achieved if the observer converges in finite-time. This problem is addressed in this work for SISO LTI systems. The proposed adaptive observer not only converges in finite-time to the states and parameters, but it also provides a bound of the convergence time which is independent of the initial error. In this sense, it is said that the observer converge in fixed-time.

Keywords:Fault detection, Distributed parameter systems, Power systems Abstract: We develop a set of algorithms for identifying covert data manipulators in distributed optimization loops for estimating oscillation modes in power systems. The fundamental set-up for the optimization is based on Alternating Direction Multiplier Method (ADMM), implemented via message passing between a set of local estimators and a central coordinator. Some of these local estimators are assumed to be compromised by malicious attackers that send incorrect values of their local estimates to the coordinator. Even a small amount of such bias can easily destabilize the ADMM loop. In our first algorithm, we catch the identity of these attackers by employing the standard ADMM but adjusting the value of the penalty factor used in the update of the primal variable. We show that this adjustment can amplify the attack signature, and help in identification, especially when the attack magnitude is small. In our second algorithm, we employ a Round-Robbin variant of ADMM, and catch the manipulators by simply observing the evolution of the dual variable. We illustrate the results using simulations of the IEEE 68-bus power system model.

Keywords:Fault detection, Fault diagnosis Abstract: Many induction motor models are available in the literature for modeling, simulation, control as well as fault diagnosis. In this paper, novel induction motor models are formulated based on stationary, rotor and synchronously rotating reference frames. All these proposed models are compared and analyzed in terms of their diagnostic relevance to stator inter-turn faults. Ability to generate distinct residual signatures is a key for model-based diagnostics. Performance of these models in term of their ability to diagnose a fault is compared and best suited models are suggested based on a discriminatory ability index proposed in this paper. As continuous-time extended Kalman filter (CTEKF) is the most commonly used estimator for state estimation, the same has been considered. Computer simulations are carried out for a 4- hp squirrel-cage induction motor using MATLAB. The results prove that all induction motor models do not perform equally well when it comes to fault diagnosis.

Keywords:Fault detection, Large-scale systems Abstract: In this paper, we propose a novel distributed fault detection method to monitor the state of a linear system, partitioned into interconnected subsystems. The approach hinges on the definition of a partition-based distributed Luenberger estimator, based on the local model of the subsystems and that takes into account the dynamic coupling terms between the subsystems. The proposed methodology computes – in a distributed way – a bound on the variance of a properly defined residual signal, considering the uncertainty related to the state estimates performed by the neighboring subsystems. This bound allows the computation of suitable local thresholds with guaranteed maximum false-alarms rate. The implementation of the proposed estimation and fault detection method is scalable, allowing Plug & Play operations and the possibility to disconnect the faulty subsystem after fault detection. Theoretical conditions guaranteeing the convergence of the estimates and of the bounds are provided. Simulation results show the effectiveness of the proposed method.

Keywords:Fault detection, Linear systems Abstract: This paper focuses on comparing fault detection (FD) performance of two robust FD approaches, namely the set-theoretic unknown input observer-based approach and the interval observer-based approach. The former is implemented using the set theory and the unknown input observer (UIO), where the set theory and the UIO are used to decouple the effect of unknown inputs in passive and active ways, respectively. The latter is based on the set theory and the Luenberger observer, which completely relies on the set-based passive decoupling to obtain FD robustness. The former is a new method recently proposed by the authors, while the latter is a well-known robust FD method. The objective of this paper is to analyze these two FD approaches in a systematic way and to compare their FD sensitivity based on mathematical analysis. Eventually, an explicit criterion used to choose which method is better for FD of a system is given by using invariant sets. At the end of this paper, an example is used to illustrate the obtained results.

Keywords:Networked control systems, Fault detection, Observers for nonlinear systems Abstract: This paper presents an attack-resilient estimation scheme for uniformly observable nonlinear systems having redundant sensors when a subset of sensors is corrupted by adversaries. We first design an individual high-gain observer from each measurement output so that partial information of system state is obtained. Then, a nonlinear error correcting problem is formulated by collecting all the information from each partial observers and it can be solved by exploiting redundancy. For most of the time, a computationally efficient monitoring system is running and it detects every influential attacks. A simple switching logic explores another combination of output measurement to find a correct candidate only when a residual signal exceeds its threshold.

Keywords:Fault detection, Process Control, Stochastic systems Abstract: In the context of sensor attacks on linear time-invariant cyber-physical systems, we propose a model-based cumulative sum (CUSUM) procedure for identifying falsified sensor measurements. To fulfill a desired detection performance–given the system dynamics, control and estimation schemes, and noise statistics–we derive tools for designing and tuning the CUSUM procedure. We characterize the state degradation that a stealthy attacker can induce to the system while remaining undetected by the detection procedure. Moreover, we quantify the advantage of using a dynamic detector (CUSUM), which leverages the history of the state, over a static detector (Bad-Data) which uses a single measurement at a time. Simulation experiments are presented to illustrate the performance of the detection scheme.

Keywords:Stability of nonlinear systems, Adaptive control, Lyapunov methods Abstract: This paper proposes a constructive control method for a class of non-affine nonlinear systems under certain assumptions. The key step in the method, which is motivated from the Immersion and Invariance adaptive control strategy, is to develop an extended system being dynamically immersed to a designed target system. A Lyapunov based analysis demonstrates the locally/globally asymptotic stability of the closed-loop system. Numerical example is provided to illustrate the control design.

Keywords:Spacecraft control, Aerospace, Lyapunov methods Abstract: The growing level of autonomy of unmanned space missions has attracted a significant amount of research in the aerospace field towards feedback orbit control. Existing Lyapunov-based controllers can be used to to transfer a spacecraft between two elliptic orbits of given size and orientation, but do not consider the stabilization of the spacecraft phase angle along the orbit, which is a key requirement for application to formation flying missions. This paper presents a control law based on the orbital element parametrization, which is able to track a given true longitude (i.e. a reference phase angle), in addition to the parameters describing the reference orbit shape and orientation. A numerical simulation of an orbital rendez-vous demonstrates the effectiveness of the proposed approach.

Keywords:Lyapunov methods, Algebraic/geometric methods, Stability of nonlinear systems Abstract: The paper addresses the problem of preserving the stabilizing performances of a continuous-time feedback under sampling. The discussion is developed with reference to a two-block feedforward system whose equilibrium is assumed globally stable. The design is passivity-based and exploits the construction of a Lyapunov function for the uncontrolled cascade.

Keywords:Human-in-the-loop control, Lyapunov methods, Switched systems Abstract: Abstract--- Functional electrical stimulation (FES) is commonly used in rehabilitation therapy for people with injuries or various neurological disorders. Noninvasive treatments use surface electrodes to provide a potential field across the muscle and induce contractions/output force. The placement of the electrodes has a significant impact on the induced force output. As the muscle geometry changes (i.e., muscle lengthening or shortening), the force induced by the static electrode placement may also change. In this paper, an array of electrodes is placed across the biceps brachii and the electric field is switched across the electrodes (i.e., channels) to maximize the induced muscle force throughout the arm's range of motion, despite changes in the muscle geometry. To yield this outcome, a switched systems approach is used to develop a position-based switching law for the uncertain nonlinear system. Specifically, a switched robust sliding mode controller is developed to track a desired angular trajectory about the elbow. Lyapunov-based methods for switched systems are used to prove global exponential tracking and experimental results demonstrate the performance of the switched control system.

Keywords:Stability of nonlinear systems, LMIs, Lyapunov methods Abstract: In this paper we are interested in the incremental stability of piecewise-affine (PWA) systems. We present conditions to compute an upper bound to the incremental L2-gain based on dissipativity analysis. These conditions are expressed as linear matrix inequalities (LMI) allowing the construction of a continuous piecewise quadratic storage function. It is also shown that these conditions imply incremental asymptotic stability of the system. The result is illustrated with numerical examples.

Keywords:Lyapunov methods, Robust control, Predictive control for nonlinear systems Abstract: This paper investigates conditions for input-to-state stability (ISS) and input-to-state practical stability (ISpS) of nonlinear discrete-time systems in terms of Lyapunov functions. A well known condition for input-to-state stability is the existence of an ISS-Lyapunov function for which, in every time step, the rate of decrease is bounded in the norm of the state, and the rate of increase due to an input is bounded in the norm of the input. We show that input-to-state stability can be established by means of ISS-Lyapunov functions which satisfy a weaker decrease condition defined over a bounded time interval. Furthermore, we characterize ISS (ISpS) with respect to a set of states (e.g. a consensus subspace) instead of only considering the origin. We illustrated the applicability of the proposed relaxed conditions by studying conditions under which suboptimal model predictive control (MPC) is input-to-state stable.

Keywords:Robust control, Control over communications Abstract: In this paper, aperiodic control of linear discrete-time systems subject to bounded additive disturbances is considered. We present a framework for event- and self-triggered controllers that achieve the same worst-case bounds on the system state (up to a predeﬁned factor, which is a design parameter) as a given linear controller that is updated at every point in time. We demonstrate in an example that the proposed event- and self-triggered controllers achieve a considerable reduction in the communication rate even without increasing the guaranteed worst-case error bounds.

Keywords:Hybrid systems, Networked control systems, Linear systems Abstract: We present a framework for the analysis and design of dynamic and static event-triggered controllers with time regularization for linear systems. This framework leads to guarantees on global exponential stability, L2-stability, and a positive minimum inter-event time, in addition to a reduction in the number of events compared to regular time-triggered controllers and other event-triggered controllers in literature. By using new analysis tools tailored to linear systems, we achieve a significant reduction in conservatism, in the sense that the novel framework yields new event-generator designs with much larger inter-event times and much tighter bounds on the L2-gain and convergence rate of the event-triggered control system compared to previous results for more general nonlinear systems. We demonstrate the benefits of our new results via a numerical example, and show that the conservatism in the estimates of the L2-gain is indeed small.

Keywords:Networked control systems, Stochastic optimal control, Optimal control Abstract: In this paper, we define two desired consistency properties for event-triggered control: (i) it should result in a better trade-off between average transmission rate and closed-loop performance than traditional periodic control; (ii) it should require no sensor updates (i.e., operate in open loop) in the absence of disturbances. We propose an event-triggered controller for linear systems with full state feedback that guarantees these two properties when performance is measured by an average quadratic cost. Simulation results highlight the efficiency of the proposed solution.

Keywords:Networked control systems, Formal verification/synthesis, LMIs Abstract: In networked control systems, the advent of event-triggering strategies in the sampling process has resulted in the usage reduction of network capacities, such as communication bandwidth. However, the aperiodic nature of sampling periods generated by event-triggering strategies has hindered the schedulability of such networks. In this study, we propose a framework to construct a timed safety automaton that captures the sampling behavior of perturbed LTI systems with an mathcal{L}_2-based triggering mechanism proposed in the literature. In this framework, the state-space is partitioned into a finite number of convex polyhedral cones, each cone representing a discrete mode in the abstracted automaton. Adopting techniques from stability analysis of retarded systems accompanied with a polytopic embedding of time, LMI conditions to characterize the sampling interval associated with each region are derived. Then, using reachability analysis, the transitions in the abstracted automaton are derived.

Keywords:Decentralized control, Sampled-data control, Networked control systems Abstract: Asynchronous event-triggered control (AETC) is a control strategy that is particularly suited for wireless networked implementations whose sensor nodes have limited energy supplies. Local thresholds allow the sensors to sample and to transmit local measurements independently of each other. AETC uses only one bit for each measurement transmission while still guarantees stability and predesigned performance of the closed-loop. In this paper, we extend the previous work on AETC, and study the stability and L_2-performance of periodic asynchronous event-triggered control (PAETC) for implementations with disturbances. In PAETC, the local event-triggered conditions are verified periodically at every sampling time. A dynamic controller is introduced to the PAETC framework, and the decision to transmit the controller outputs is also included in the asynchronous event-triggered mechanism to save network bandwidth. The developed theory is illustrated in a numerical example.

Keywords:Intelligent systems, Learning, Autonomous systems Abstract: In this paper we formulate the infinite-horizon game-theoretic problem in an adaptive learning framework, so that the optimal performance is guaranteed when the continuous sampling of the state is relaxed by using an event-triggering condition. Then, a Q-learning framework combined with an actor/critic approach approximates the optimal cost, the optimal control, and the worst case disturbance without any knowledge of the system model. The overall closed-loop system is model as an impulsive system and the asymptotic stability of its equilibrium is proved. A simulation with a numerical example is used to illustrate the results.

Keywords:Distributed parameter systems, Adaptive systems, Robust adaptive control Abstract: In this paper, we present a sub-optimal controller for semilinear partial differential equations, with partially known nonlinearities, in the dyadic perturbation observer (DPO) framework. The dyadic perturbation observer uses a two-stage perturbation observer to isolate the control input from the nonlinearities, and to predict the unknown parameters of the nonlinearities. This allows us to apply well established tools from linear optimal control theory to the controlled stage of the DPO. The small gain theorem is used to derive a condition for the robustness of the closed loop system.

Keywords:Decentralized control, Distributed control, Large-scale systems Abstract: We consider a class of spatially distributed linear systems with finite bandwidth. By means of spatial localization techniques, it is shown that exponential stability of this class of systems can be verified in a decentralized and spatially localized fashion, which is practically relevant to many real-world applications. Our proposed necessary and sufficient stability certificates are independent of the dimension of the entire system. Moreover, they only require localized knowledge about the state matrix of the system, which makes these verifiable conditions desirable for design of robust spatially distributed linear systems against subsystem failure and replacement.

Keywords:Distributed parameter systems, Fault diagnosis, Estimation Abstract: In this brief paper we are concerned with the fault detection (FD) problem of single-input multi-output infinite dimensional (Inf-D) systems. We develop a geometric methodology to detect a fault in presence of a disturbance signal. In other words, the detection decision making process is decoupled from the disturbance signal. Specifically, we first consider the invariant subspaces of Inf-D systems and derive sufficient conditions for convergence of the computing algorithm corresponding to conditioned invariant subspaces. Then, by using the developed methodology necessary and sufficient conditions for solvability of the FD problem are provided.

Keywords:Distributed parameter systems, Delay systems, Linear systems Abstract: Coprimeness of a fractional representation plays various crucial roles in many different contexts, for example, stabilization of a given plant, minimality of a state space representation, etc. It should be noted however that coprimeness depends crucially on the choice of a ring (or algebra) where such a representation is taken, which reflects the choice of a plant, and particular problems that one studies. Such relationships are particularly delicate and interesting when dealing with infinite-dimensional systems. This paper discusses various coprimeness issues for different rings, typically for Hinf and pseudorational transfer functions. The former is related to H^infty-stabilizability, and the latter to controllability of behaviors. We also give some intricate example where a seemingly non-coprime factorization indeed admits a coprime factorization over Hinf. Some future directions are also indicated.

Keywords:Distributed parameter systems, Adaptive control, Estimation Abstract: In this paper, we propose a new method to design an unknown input type state observer for an unstable 1-d heat equation with external disturbance. A disturbance estimator can be reduced from the observer. A stabilizing state feedback control is designed for observer by a new backstepping method, which is an observer based output feedback control for original system. The well-posedness and stability of the closed-loop system are concluded. The numerical simulations show that the proposed scheme is quite effectively.

Keywords:Distributed parameter systems, Algebraic/geometric methods Abstract: The goal of this article is to propose an efficient way of empirically improving suboptimal solutions designed from the recent method of finite-horizon parameterizing manifolds (PMs) introduced in Chekroun and Liu ["Finite-horizon parameterizing manifolds, and applications to suboptimal control of nonlinear parabolic PDEs," Acta Applicandae Mathematicae, vol. 135, no. 1, pp. 81–144, 2015] (referred to as [CL15] hereafter) and concerned with the (sub)optimal control of nonlinear parabolic partial differential equations (PDEs). Given a finite horizon [0,T] and a reduced low-mode phase space, a finite-horizon PM provides an approximate parameterization of the high modes by the low ones so that the unresolved high-mode energy is reduced --- in an L^{2} sense --- when this parameterization is applied.

In [CL15], various PMs were constructed analytically from the uncontrolled version of the underlying PDE that allow for the design of reduced systems from which low-dimensional suboptimal controllers can be efficiently synthesized. In this article, the analytic approach from [CL15] is briefly recalled and an empirical post-processing procedure is introduced to improve the PM-based suboptimal controllers. It consists of seeking for a high-mode parametrization aiming to reduce the energy contained in the high modes of the PDE solution, when the latter is driven by a PM-based suboptimal controller. This is achieved by solving simple regression problems. The skills of the resulting empirically post-processed suboptimal controllers are numerically assessed for an optimal control problem associated with the Burgers-Sivashinsky equation.

Keywords:Delay systems, Linear systems Abstract: It is well known that the secondary dynamic modes of thermoacoustic systems come to prominence during the modal stabilization attempts. To this date; however, there has been no exhaustive analytical explanation given for this interesting phenomenon. In this work we examine a Rijke tube with a passive Helmholtz resonator and perform an active feedback control to suppress instabilities. The core dynamics is represented by a linear time-invariant multiple time delay system of neutral type. Non-conservative stability of this infinite-dimensional dynamics is investigated using a recent analytical tool: cluster treatment of characteristic roots (CTCR) paradigm. First, we examine the parametric stability outlook with the Helmholtz resonator using a holistic approach in contrast to conventional modal studies. We then select an unstable operating point and impose a time-delayed integral feedback control over this structure and inquire the stabilizing controller parameters using the CTCR methodology. This procedure also declares the potential unexpected instabilities caused by the secondary modes. Analytical work is presented with validations using an experimental Rijke tube set-up.

Keywords:Delay systems, Networked control systems, H-infinity control Abstract: The problem of attitude and angular velocity tracking in the presence of exogenous disturbances and where feedback measurements are subjected to unknown time-varying delays is addressed. Sufficient conditions which guarantee stability and disturbance attenuation performance in the H∞ sense are provided. Results are presented in the form of LMIs, which allow the conditions to be simply and efficiently computed. Using a simple quaternion-based linear state feedback controller and a feedforward term to compensate the nonlinearities of the system dynamics, simulation results illustrate that the control law is able to effectively track desired trajectories and reject disturbances even in the presence of large time-varying delays.

Keywords:Networked control systems, Mechanical systems/robotics, Delay systems Abstract: Time domain passivity control, a well known control scheme widely used for teleoperation systems, normally works under the constraint of zero division. Small force or velocity signals can cause the occurrence of zero division which ultimately leads the system to be unstable. This paper presents a novel switching time domain passivity control scheme for multilateral teleoperation systems which not only ensures the stability of the system but also avoids zero division. In contrast to bilateral teleoperation systems, the multilateral teleoperation system is much more complex as it involves increased number of master and slave hardware, multiple operators and transmission of multiple signals over the communication network. A new framework for the communication channel has been proposed which incorporates the use of weighting coefficients to give masters and slaves authority depending upon the requirements of the operation. As the switching time domain passivity control keeps the system passive all the time, the stability is guaranteed. The proposed control scheme is valid for n masters and n slaves. Simulations with two masters and two slaves are carried out to verify the effectiveness of the proposed scheme.

Keywords:Delay systems, Observers for Linear systems, Estimation Abstract: This paper investigates an unknown input observer design for a large class of linear systems with unknown inputs and commensurate delays. An impulsive finite-time observer is proposed by involving only the past and actual values of the system output. Sufficient conditions are given to guarantee the existence of such an impulsive finite-time observer.

Keywords:Delay systems, Uncertain systems, Optimization Abstract: We extend an established method for the robust optimization of parametrically uncertain systems to the case of delay differential equations with parameter and state dependent delays. More precisely, the case of robustness with a loss of stability due to Hopf bifurcations and a certain generalization thereof is treated. We derive constraints for robust stability for the general system class and apply them to the optimization of a three stage supply chain model. While an optimization fails if stability properties are not accounted for, the proposed method identifies a robust and optimal point of operation for the supply chain.

Keywords:Delay systems, Observers for nonlinear systems Abstract: The problem of observer design is addressed for a class of triangular nonlinear systems in presence of output measurement sampling and time-delay. A major difficulty with the considered nonlinear systems is that the state matrix is dependent on the "undelayed output signal" which is not accessible to measurement, making existing observers inapplicable. A new observer is designed where the effects of time-delay and sampling are compensated for using an output predictor. Defined by a couple of first-order ordinary differential equations (ODEs), the present predictor turns out to be much simpler compared to previous predictors involving output and state predictors. Using the small gain technique, sufficient conditions for the observer to be exponentially convergent are established in terms of the maximum time-delay and sampling interval.

Keywords:Predictive control for linear systems, Formal verification/synthesis, Algebraic/geometric methods Abstract: A method based on a quantifier elimination algorithm is suggested for obtaining explicit model predictive control (MPC) laws for linear time invariant systems with quadratic objective and polytopic constraints. The structure of the control problem considered allows Weispfenning's 'quantifier elimination by virtual substitution' algorithm to be used. This is applicable to first order formulas in which quantified variables appear at most quadratically. It has much better practical computational complexity than general quantifier elimination algorithms, such as cylindrical algebraic decomposition. We show how this explicit MPC solution, together with Weispfenning's algorithm, can be used to check recursive feasibility of the system, for both nominal and disturbed systems. Extension to cases beyond linear MPC using Weispfenning's algorithm is part of future work.

Keywords:Predictive control for linear systems, Linear parameter-varying systems, Optimal control Abstract: Currently available model predictive control methods for linear parameter-varying systems assume that the future behavior of the scheduling trajectory is unknown over the prediction horizon. In this paper, an anticipative tube MPC algorithm for polytopic linear parameter-varying systems under full state feedback is developed. In contrast to existing approaches, the method explicitly takes into account expected future variations in the scheduling variable: its current value is measured exactly, while the future values over the prediction horizon are assumed to belong to a sequence of sets describing expected deviations from a nominal trajectory. Through this mechanism, the controller "anticipates" upon future changes in the system dynamics. The algorithm constructs a tube homothetic to a terminal set and employs gain scheduled vertex control laws. A worst-case cost is minimized: the corresponding optimization problem is a single linear program with complexity linear in the prediction horizon. Numerical examples show the validity of the approach.

Keywords:Predictive control for linear systems, Optimal control, Variational methods Abstract: This article presents two different approximations to linear infinite-horizon optimal control problems arising in model predictive control. The dynamics are approximated using a Galerkin approach with parametrized state and input trajectories. It is shown that the first approximation represents an upper bound on the optimal cost of the underlying infinite dimensional optimal control problem, whereas the second approximation results in a lower bound. We analyze the convergence of the costs and the corresponding optimizers as the number of basis functions tends to infinity. The results can be used to quantify the approximation quality with respect to the underlying infinite dimensional optimal control problem.

Keywords:Predictive control for linear systems, Switched systems, Power electronics Abstract: Common approaches for direct model predictive control (MPC) for current reference tracking in power electronics suffer from the high computational complexity encountered when solving integer optimal control problems over long prediction horizons. Recently, an alternative method based on approximate dynamic programming showed that it is possible to reduce the computational burden enabling sampling times under 25 mus by shortening the MPC horizon to a very small number of stages while improving the overall controller performance. In this paper we implemented this new approach on a small size FPGA and validated it on a variable speed drive system with a three-level voltage source converter. Time measurements showed that only 5.76 mus are required to run our algorithm for horizon N = 1 and 17.27 mus for N = 2 while outperforming state of the art approaches with much longer horizons in terms of currents distortion and switching frequency. To the authors' knowledge, this is the first time direct MPC for current control has been implemented on an FPGA solving the integer optimization problem in real-time and achieving comparable performance to formulations with long prediction horizons.

Keywords:Predictive control for linear systems, Uncertain systems Abstract: We present a novel approach for output feedback model predictive control (MPC) of constrained discrete-time linear systems subject to unknown state and output disturbances. The approach is based on combining a recently proposed class of stabilizing relaxed barrier function based MPC schemes with suitable state estimation procedures in a certainty equivalence output feedback fashion. Robust stability of the overall closed-loop system is shown under standard assumptions on the underlying state estimation, including the important cases of Luenberger observers and Kalman filtering.

Keywords:Predictive control for linear systems, Optimization algorithms Abstract: We analyze the robust stability properties of iteration schemes for the algorithmic implementation of model predictive control for linear discrete-time systems. The underlying optimization employs a relaxed barrier function based problem formulation and performs only a limited, possibly arbitrarily small, number of optimization algorithm iterations per sampling instant. Based on the input-to-state stability concept, the resulting overall closed-loop system consisting of system state and optimizer dynamics is shown to be robustly stable with respect to both external and internal disturbances. Implications for the case of certainty equivalence output feedback as well as possible extensions are also discussed.

Keywords:Robust control, Computational methods, Energy systems Abstract: Robust optimization has emerged as a tractable methodology for coping with parameter uncertainty in an optimization problem. In order to avoid conservative solutions, i.e. overly protective and expensive solutions, Ben-Tal and Nemirovski introduced the notion of affine adaptability. However, their approach significantly increases the program size and threatens its tractability, especially in the context of mixed-integer programming. In this paper, we focus on robust mixed-integer linear programs. We propose a tractable numerical strategy for solving them and demonstrate the computational efficiency of our method when applied to a real energy management problem. In addition, we propose a practical data-driven methodology for designing the uncertainty set of robust programs.

Keywords:Robust control, Constrained control, Linear systems Abstract: This paper presents novel results on robust positively invariant (RPI) sets for linear discrete-time systems with additive disturbances. In particular, we determine how RPI sets change with scaling of the disturbance set. In this context, we analyze families of RPI sets for a given interval of scaling factors. Such parametric RPI sets are useful to study the sensitivity of the system to changes in the disturbance strength.

Keywords:Robust control, Constrained control, Lyapunov methods Abstract: The Explicit Reference Governor is a simple and systematic approach that provides constraint handling capabilities to pre-stabilized nonlinear systems. The approach consists in translating state and input constraints into a constraint on the value of the Lyapunov function which is then enforced by suitably manipulating the derivative of the applied reference. This paper extends the Explicit Reference Governor approach by addressing its robustness in the presence of external disturbances and parametric uncertainties. Using ISS arguments, it will be shown that the robustness with respect to external disturbances can be ensured by simply restricting the domain of the applied reference. Parametric uncertainties can instead be accounted for using suitable bounds on the Lyapunov function. Numerical simulations show the effectiveness of the proposed method.

Keywords:Robust control, Control education, Biological systems Abstract: Robust control theory studies the effect of noise, disturbances, and other uncertainty on system performance. Despite growing recognition across science and engineering that robustness and efficiency tradeoffs dominate the evolution and design of complex systems, the use of robust control theory remains limited, partly because the mathematics involved is relatively inaccessible to nonexperts, and the important concepts have been inexplicable without a fairly rich mathematics back- ground. This paper aims to begin changing that by presenting the most essential concepts in robust control using human stick balancing, a simple case study popular in both the sensorimotor control literature and extremely familiar to engineers. With minimal and familiar models and mathematics, we can explore the impact of unstable poles and zeros, delays, and noise, which can then be easily verified with simple experiments using a standard extensible pointer. Despite its simplicity, this case study has extremes of robustness and fragility that are initially counter-intuitive but for which simple mathematics and experiments are clear and compelling. The theory used here has been well-known for many decades, and the cart-pendulum example is a standard in undergrad controls courses, yet a careful reconsidering of both leads to striking new insights that we argue are of great pedagogical value.

Keywords:Robust control, Uncertain systems, Optimization Abstract: This paper develops a Linear Quadratic Regulator (LQR), which is robust to disturbance variability, by using the total variation distance as a metric. The robust LQR problem is formulated as a minimax optimization problem, resulting in a robust optimal controller which in addition to minimizing the quadratic cost it also minimizes the level of disturbance variability. A procedure for solving the LQR problem is also proposed and an example is presented which clearly illustrates the effectiveness of our developed methodology.

Keywords:Robotics Abstract: This paper introduces a novel control approach for motion tracking and damping assignment in compliantly actuated robotic systems. The approach follows the idea of shaping the link side dynamics such that the closed loop dynamics follows a given reference trajectory while injecting additional damping for improving vibration suppression. The modification of the apparent link side dynamics is amended by a desired dynamics on the motor side. In contrast to classical feedback linearization the design aims at only a minimal modification of the dynamics, both for the link side and the motor side. The time-varying closed loop dynamics is shown to be globally, uniformly stable. The effectiveness of the resulting feedback control law was evaluated by simulations as well as experiments on a highly nonlinear and highly compliant robot arm.

Keywords:Power systems, Estimation, Network analysis and control Abstract: This paper analyzes the joint impact of uncertainties in the input data on the power system state estimator. The approach is based on the sensitivity analysis of the estimated telemetry data with respect to the measurement data and the branch parameters with the main goal of locating relevant input components. In order to find relevant inputs, we analyze the normalized sensitivity matrix by sparse principal component analysis (PCA). The non-zero entries of the loading vectors related to the dominant principal components are considered to be the relevant inputs to the state estimator as they mainly contribute to the amplification of the estimated values. It turns out that PCA shows an elementary structure of the sensitivity matrix: All non-zero entries of a loading vector corresponding to a positive singular value belong either to the telemetry data or to the branch data. We show that this property is also valid for PCA with different sparsity-promoting constraints on the loading vector. The proposed analysis method is demonstrated by a numerical study.

Keywords:Power systems, Fault detection, Statistical learning Abstract: We address the problem of predicting the transient stability status of a power system as quickly as possible in real time subject to probabilistic risk constraints. The goal is to minimise the average time taken after a fault to make the prediction, and the method is based on ideas from statistical sequential analysis. The proposed approach combines probabilistic neural networks with dynamic programming. Simulation results show an approximately three-fold increase in prediction speed when compared to the use of pre-committed (fixed) prediction times.

Keywords:Power systems, Game theory, Network analysis and control Abstract: We consider the setting in which generators compete in scalar-parameterized supply functions to serve an inelastic demand spread throughout a transmission constrained power network. The market clears according to a locational marginal pricing mechanism, in which the independent system operator (ISO) determines the generators' production quantities so as to minimize the revealed cost of meeting demand, subject to transmission and generator capacity constraints. Under the assumption that both the ISO and generators choose their strategies simultaneously, we establish the existence of Nash equilibria for the underlying game, and derive a tight bound on its price of anarchy. Under the more restrictive setting of a two-node power network, we present a detailed comparison of market outcomes predicted by the simultaneous-move formulation of the game against those predicted by the more plausible sequential-move formulation, where the ISO observes the generators' strategy profile prior to determining their production quantities.

Keywords:Power systems, Game theory, Predictive control for nonlinear systems Abstract: We present a mechanism for socially efficient implementation of model predictive control (MPC) algorithms for load frequency control (LFC) in the presence of self-interested power generators. Specifically, we consider a situation in which the system operator seeks to implement an MPC-based LFC for aggregated social cost minimization, but necessary information such as individual generators' cost functions is privately owned. Without appropriate monetary compensation mechanisms that incentivize truth-telling, self-interested market participants may be inclined to misreport their private parameters in an effort to maximize their own profits, which may result in a loss of social welfare. The main challenge in our framework arises from the fact that every participant's strategy at any time affects the future state of other participants; the consequences of such dynamic coupling has not been fully addressed in the literature on online mechanism design. We propose a class of real-time monetary compensation schemes that incentivize market participants to report their private parameters truthfully at every time step, which enables the system operator to implement MPC-based LFC in a socially optimal manner.

Keywords:Power systems, Game theory, Uncertain systems Abstract: In the restructured electricity industry, Generation Expansion Planning (GEP) is an oligopoly of strategic Generation Companies (GenCos) with private information investing in a highly uncertain environment. Strategic planning and uncertainties can result in market manipulation and underinvestment (short-term planning).

We present a forward moving approach to the problem of investment expansion planning in the restructured electricity industry. This approach accounts for technological, political and environmental uncertainties in the problem's environment and leads to long-term planning. At each step of the approach we present a block investment market mechanism that has the following features. (F1) It is individually rational. (F2) It is budget balanced. (F3) The expansion and production allocations corresponding to the unique Nash Equilibrium (NE) of the game induced by the mechanism are the same as those that maximize the sum of utilities of the producers and the demand. (F4) It is price efficient that is, the price for electricity at equilibrium is equal to the marginal utility of the demand and to the marginal cost of production by producers with free capacity.

Keywords:Power systems, Network analysis and control, Control system architecture Abstract: The problem of primary control of high-voltage direct-current transmission systems is addressed in this paper, which contains three main contributions. First, to propose a new nonlinear, more realistic, model for the system suitable for primary control design, which takes into account nonlinearities introduced by conventional inner controllers. Second, to determine necessary conditions—dependent on some free controller tuning parameters—for the existence of equilibria. Third, to formulate additional (necessary) conditions for these equilibria to satisfy the power sharing constraints. The usefulness of the theoretical results is illustrated via numerical calculations on a four-terminal example.

Keywords:Automotive control, Linear parameter-varying systems, Automotive systems Abstract: The paper presents a new variable-geometry suspension system which is applied in-wheel electric vehicles. It is able to realize the steering of the vehicle by independent wheel camber angles and wheel steering and create differential yaw moment by harmonizing the longitudinal forces. In order to perform the trajectory tracking of the vehicle the control signals are the virtual signals, such as differential yaw moment and steering by wheel camber angles. In the suspension system two physical active torques are realized on either side of the front axle and longitudinal forces are realized by in-wheel motors. The control design of the variable-geometry suspension system is based on a hierarchical structure. The purpose of the high-level controller is to calculate the virtual control inputs based on the performance specifications for the road trajectory. The purpose of the low-level controller is to realize the physical active torque of the wheels and track the required differential yaw moment.

Keywords:Automotive control, Linear parameter-varying systems, Automotive systems Abstract: Since there is a coupling between lateral and vertical dynamics, the interactions between control components must be taken into consideration. The paper presents the effects of vertical load variations on the controlled invariant set of the steering system. In the model the nonlinear characteristics of the tire force are approximated by the polynomial form. The analysis is based on Sum-of-Squares programming method and parameter-dependent polynomial control Lyapunov functions. The Maximum Controlled Invariant Sets of the steering as a function of vertical loads are illustrated through a simulation example. The results of the analysis are built into the control design of the suspension system. A semi-active suspension system using preview control is applied. The operation of the controller is illustrated through simulation examples.

Keywords:Automotive control, Multivehicle systems, Traffic control Abstract: Within the context of autonomous driving, this paper presents a method for the coordination of multiple automated vehicles using priority schemes for decoupled motion planning for multi-lane one- and bi-directional traffic flow control. The focus is on tube-like roads and non-zero velocities (no complete standstill maneuvers). We assume inter-vehicular communication (car-2-car) and a centralized or decentralized coordination service. We distinguish between different driving modes including adaptive cruise control (ACC) and obstacle avoidance (OA) for the handling of dynamic driving situations. We further assume that any controllable vehicle is equipped with proprioceptive and exteroceptive sensors for environment perception within a particular range field. In case of failure of the inter-vehicle communication system, the controllable vehicles can act as autonomous vehicles. The motivation is the control of a) one-directional multi-lane roads available for automated as well as unautomated objects with potentially, but not necessarily, varying reference speeds, and b) bi-directional traffic flow control making use of all available lanes, allowing, in general, object- and direction-wise variable reference speeds. For the one-directional case, we discuss a suitable deterministic priority scheme for throughput maximization and quickly reaching of a platooning state. For the bi-directional scenario, we derive a binary integer linear program (BILP) for the assignment of lanes to one of the two road traversal directions that can be solved optimally via linear programming (LP). The approach is evaluated on three numerical simulation scenarios.

U.S. Army Tank Automotive Res. Development, and Engineering

Keywords:Automotive control, Optimal control, Optimization Abstract: The resistance of Lithium-ion cells increases at sub-zero temperatures reducing the cells’ power availability. One way to improve the cells’ performance in these adverse operation conditions is to proactively heat them. In this paper, we consider the scenario in which a cell is heated from both inside and outside; a current is drawn from the cell to power a convective heater; Joule heating warms the cell from inside. A problem formulation to derive the time-limited energy-optimal current policy is presented, analyzed and numerically solved. It is observed that the optimal current policy resembles a sequence of constant voltage, constant current and phases, mirroring conventional wisdom. Finally, the notion of productive warm-up—a warm-up procedure that ensures that the cell can perform work once warmed-up—is introduced; and an approximation of the optimal solution is used to identify the lowest state of charge at various operating conditions (portion of the state-space) from which productive warm-up is feasible.

Keywords:Automotive control, Predictive control for linear systems, Optimal control Abstract: In this paper, a vehicle speed controller aiming at minimizing fuel consumption in car-following scenarios is developed. The optimal longitudinal control of torque and brake is calculated and applied under Model Predictive Control (MPC). For a given car-following distance modulation range, the controller searches for the optimal gear selection at each step in the prediction horizon to generate the minimum fuel control, and triggers gear shifts optimally by vehicle state. The search process with optimality in torque, brake, and gear all ensured is originally highly time consuming. However, in this study, a cooperative method is developed to achieve the optimal solution in real time. The numerically complicated problem is partitioned into a series of simplified subproblems by a deduction method. Fast quasi-optimal solutions are given to the subproblems using an optimal driving pattern derived by Pontryagin Minimum Principle (PMP). To solve for different speed scenarios, a Finite State Machine (FSM) is designed for problem partitioning and fast solving. As the result, the search space is efficiently narrowed down for each MPC step, and the computation speed is fast enough for real-time application. A simulation study shows that the developed controller can generate a fuel saving benefit of 14% for the tested scenarios.

Keywords:Automotive control, Predictive control for nonlinear systems, Reduced order modeling Abstract: This paper presents a study on tackling full load request in air path control of a turbocharged diesel engine. The adopted approach is based on nonlinear model predictive control that employs a specially tailored model that can be embedded and simulated at engine control unit. The derived air path model of a turbocharged engine comprises of one differential equation and a set of algebraic equations with fixed polynomial structure that allow cheap evaluation of Jacobians and integration with fixed Euler step. The main advantage of this approach is that the simulation and problem construction boils down to evaluation of explicit polynomial functions which has favorable properties for real-time implementation. On top of this model, a nonlinear model predictive control problem is formulated and solved using sequential quadratic programming. The approach is demonstrated in a simulation study that focuses on abrupt load request in the boost pressure setpoint.

Keywords:Optimal control, Quantum information and control, Algebraic/geometric methods Abstract: The optimal control of an ensemble of Bloch equations describing the evolution of an ensemble of spins is the mathematical model used in Nuclear Resonance Imaging and the associated costs lead to consider Mayer optimal control problems. The Maximum Principle allows to parameterize the optimal control and the dynamics is analyzed in the framework of geometric optimal control. This leads to numerical implementations or suboptimal controls using averaging principle.

Keywords:Biomolecular systems, Distributed parameter systems, Systems biology Abstract: Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such signal. Meanwhile, the diffusion of the signal is itself affected by the changes in shape and size of the organism. In other words, there is a complete coupling between the diffusion of the signal and the change of the shapes. In this paper, we introduce a mathematical model to investigate such coupling. The shape is given by a manifold, that varies in time as the result of a deformation given by a transport equation. The signal is represented by a density, diffusing on the manifold via a diffusion equation. We show the noncommutativity of the transport and diffusion evolution by introducing a new concept of Lie bracket between the diffusion and the transport operator. We also provide numerical simulations showing this phenomenon.

Keywords:Biomedical, Optimal control, Simulation Abstract: Quantitative photoacoustic tomography is a hybrid imaging technique for soft tissues. It consists in exciting the body to reconstruct with a laser pulse and measuring the induced acoustic waves due to the inhomogenous heating and then expansion of the tissues. We present a simplified mathematical model of this phenomenon, which writes as a system of two coupled equations, namely a wave equation and a diffusion approximation of a radiative transfer equation. The inverse problem of reconstructing the optical absorption coefficient is written as an optimal control problem where the control is the parameter we seek to reconstruct. Necessary conditions for optimality of a control and numerical results for this approach are given in the case of a small number of sensors.

Keywords:Pattern recognition and classification, Biomedical, Biological systems Abstract: One of the challenging problems in fMRI data analysis is the absence of natural time scale at which to consider the traces of the resting state}, the aggregate name for the processes in the brain happening in the absence of task of strong external stimuli. This necessitates development of the tools that are able to extract from the time series information invariant with respect to reparametrization of the time coordinate. A recently developed notion of cyclicity, based on the hierarchy of {em iterated path integrals} and corresponding algorithms were applied to several hundreds of the fMRI records, to reveal potential presence of an

Keywords:Biological systems, Modeling, Optimal control Abstract: This work is motivated by our desire to substantially improve our understanding of prion assembly formation and spreading, which could provide a better insight into underpinnings of many neurodegenerative diseases, including Alzheimer's, Parkinson's and Prion diseases. Moreover, our investigation may help lay the foundation for designing experiments to identify key steps in the kinetic pathway of prion assembly formation which could serve as potential therapeutic targets in rational drug design. Our approach is based on employing geometric optimal control to analyze fragmentation of prion assemblies with a focus on the role of singular extremals. It may help to significantly accelerate the current amplification protocols, such as the Protein Misfolding Cyclic Amplification, and hence substantially reduce the time needed to diagnose many neurodegenerative diseases.

Keywords:Identification, Reduced order modeling Abstract: In this paper we propose a model reduction and identification approach for multilinear dynamical system (MLDS) driven by noise. Compared to standard linear dynamical system based approaches which fit vector or matrix models to tensor time series, MLDS provides more natural, compact and accurate representation of tensorial data with fewer model parameters. The proposed algorithm for identifying MLDS parameters employs techniques from multilinear subspace learning: mulilinear Principal Component Analysis and multilinear regression. In addition compact array normal distribution is used to represent and estimate model error and output noise. We illustrate the benefits of the proposed approach on some real world datasets.

Keywords:Control applications, Emerging control applications, Embedded systems Abstract: Real-time scheduling algorithms proposed in the literature are often based on worst-case estimates of task parameters and the performance of an open-loop scheme can therefore be poor. To improve on such a situation, one can instead apply a closed-loop scheme, where feedback is exploited to dynamically adjust the system parameters at run-time. We propose an optimal control framework that takes advantage of feeding back information of finished tasks to solve a real-time multiprocessor scheduling problem with uncertainty in task execution times, with the objective of minimizing the total energy consumption. Specifically, we propose a linear programming-based algorithm to solve a workload partitioning problem and adopt McNaughton's wrap around algorithm to find the task execution order. Simulation results for a PowerPC 405LP and an XScale processor illustrate that our feedback scheduling algorithm can result in an energy saving of approximately 40% compared to an open-loop method.

Keywords:Data storage systems, Information theory and control, Queueing systems Abstract: Complete data center failures may occur due to disastrous events such as earthquakes or fires. To attain robustness against such failures and reduce the probability of data loss, data must be replicated in another data center sufficiently geographically separated from the original data center. Implementing geo-replication is expensive as every data update operation in the original data center must be replicated in the backup. Running the application and the replication service in parallel is cost effective but creates a trade-off between potential replication consistency and data loss and reduced application performance due to network resource contention. We model this trade-off and provide a control-theoretical solution based on Model Predictive Control to dynamically allocate network bandwidth to accommodate the objectives of both replication and application data streams. We evaluate our control solution through simulations emulating the individual services, their traffic flows, and the shared network resource. The MPC solution is able to maintain the most consistent performance over periods of persistent overload, and is quickly able to indiscriminately recover once the system return to a stable state. Additionally, the MPC balances the two objectives of consistency and performance according to the proportions specified in the objective function.

Keywords:Predictive control for nonlinear systems, Information technology systems, Hybrid systems Abstract: High rate cluster reconfigurations is a costly issue in Big Data Cloud services. Current control solutions manage to scale the cluster according to the workload, however they do not try to minimize the number of system reconfigurations. Event-based control is known to reduce the number of control updates typically by waiting for the system states to degrade below a given threshold before reacting. However, computer science systems often have exogenous inputs (such as clients connections) with delayed impacts that can enable to anticipate states degradation. In this paper, a novel event-triggered approach is presented. This triggering mechanism relies on a Model Predictive Controller and is defined upon the value of the optimal cost function instead of the state or output error. This controller reduces the number of control changes, in the normal operation mode, through constraints in the MPC formulation but also insures a very reactive behavior to changes of exogenous inputs. This novel control approach is evaluated using a model validated on a real Big Data system. The controller efficiently scales the cluster according to specifications, while reducing its reconfigurations.

Keywords:Emerging control applications, Information technology systems Abstract: The computational density of modern processors is so high, that operating all their units at full power would destroy the device by thermal runaway. Hence, temperature control solutions are required that guarantee a safe operation without unduly limiting speed, thus integrating with the power/performance tradeoff management. Moreover, the said solutions have to be simple and computationally light themselves, as millisecond-scale response may be required. Finally, as processors are installed in heterogeneous devices and face a variety of operating conditions, an easy and reliable post-silicon tuning is a must. We present such a solution by exploiting event-based control, and a hardware/software partition aimed at maximising efficiency and flexibility. We show our proposal in action on real hardware, evidencing its advantages over the state of the art.

Keywords:Large-scale systems, Linear parameter-varying systems, Nonlinear systems identification Abstract: This paper presents an LPV approach to dynamic modeling of a web-server hosted on a private cloud. The cloud hosting web-server is a variable capacity system with two control inputs, first is the number of virtual machines which is indicative of the capacity of the cloud and second is the admission control used for regulating the workload. As the workload and the hosting conditions change frequently, the linear parameter varying (LPV) framework is well suited to derive the model. For the hosted web-server, we obtain a MIMO LPV model with performance metrics such as the response time and the throughput. The identification and validation experiments are performed on the open source Eucalyptus Cloud platform.

Keywords:Human-in-the-loop control, Control of networks, Biologically-inspired methods Abstract: In this paper, we propose and explain a novel control system that mimics the intrinsic human thinking and decision-making processes. Specifically, we propose a neuromorphic-computing-based cognitive feedback control framework, which consists of a neuronic network model and a hybrid controller, for the supervisory control of a general dynamical system. The dynamical system is controlled by the hybrid controller embedded with consensus and optimization, while the neuronal network model mimics the brain dynamics and determines the safe/unsafe mode of the hybrid controller. Several theoretical results are given, and computer simulation with unknown disturbances added helps illustrate the ideas presented in this paper.

Keywords:Multivehicle systems, Agents-based systems, Distributed control Abstract: In the dynamical environment with forbidden areas, the achievement of multiple unmanned aerial vehicles (UAVs) executing cooperative missions strongly depends on the validity of mission planning results, which may be affected by the error of flight time estimation. In this paper, a hierarchical path generation scheme for improving the adaptability and performance of the distributed mission planning (DMP) system of the UAVs is proposed. The effectiveness of the market-based task allocation is enhanced by conducting a rough path planning beforehand, where only the neighboring forbidden areas of the vehicles are considered for a tradeoff between the planning accuracy and the computation. The subsequent refined path planning, which provides the guidance information to the control system, is also presented to assess the precision level of the rough path planning and the mission execution reward of the UAV fleet. The simulation results demonstrate the advantages and effectiveness of the proposed method for multiple UAVs executing missions in stochastic scenarios.

Keywords:Multivehicle systems, Optimal control, Hybrid systems Abstract: Vehicle platooning has great potential for the reduction of greenhouse gas emissions and fuel consumption of heavy-duty vehicles. However, previous works on fuel-efficient platoon control largely ignore the effect of gear changes, even though experimental studies have shown that gear shifts have a large impact on the behavior and fuel consumption of vehicle platoons. In particular, the interruption in traction force during a gear shift can cause large deviations in the tracking of the reference speed and inter-vehicle distance and can result in the braking of the vehicles. In this paper, we discuss a control architecture that includes the management of gear shifts and we propose a method to select the gears that takes fuel-efficiency into account, but also targets the good behavior of the platoon. In detail, the proposed method is based on a dynamic programming formulation that computes the optimal sequence of gear shifts necessary for the fuel-efficient and smooth tracking of a given reference speed profile. The performance of the proposed approach is finally analyzed by means of simulations by comparing it with the performance of alternative solutions.

Keywords:Multivehicle systems, Optimal control, Air traffic management Abstract: Multi-agent differential games are important and useful tools for analyzing many practical problems. With the recent surge of interest in using UAVs for civil purposes, the importance and urgency of developing tractable multi-agent analysis techniques that provide safety and performance guarantees is at an all-time high. Hamilton-Jacobi (HJ) reachability has successfully provided safety guarantees to small-scale systems and is flexible in terms of system dynamics. However, the exponential complexity scaling of HJ reachability prevents its direct application to large scale problems when the number of vehicles is greater than two. In this paper, we overcome the scalability limitations of HJ reachability by using a mixed integer program that exploits the properties of HJ solutions to provide higher-level control logic. Our proposed method provides safety guarantee for three-vehicle systems -- a previously intractable task for HJ reachability -- without incurring significant additional computation cost. Furthermore, our method is scalable beyond three vehicles and performs significantly better by several metrics than an extension of pairwise collision avoidance to multi-vehicle collision avoidance. We demonstrate our proposed method in simulations.

Keywords:Multivehicle systems, Optimization algorithms, Agents-based systems Abstract: We consider a class of scheduling problems that concern the routing of a set of mobile agents over the edges of an underlying guidepath network. These problems are motivated by (i) the operations of some unit-load, automated material handling systems that are employed in many contemporary production and distribution facilities, and also by (ii) the operations that take place in the physical layouts implementing the elementary logical operations that are employed in quantum computing. The presented results include (a) a systematic formulation of the considered scheduling problems as mixed integer programs (MIPs), (b) a Lagrangian relaxation of these MIP formulations, and (c) the development of a customized dual-ascent algorithm for the systematic and expedient solution of the corresponding dual problem. The latter provides lower bounds for the original MIP formulations and potentially useful information for the construction of near-optimal routing schedules for the original problems.

Keywords:Multivehicle systems, IVHS, Traffic control Abstract: This paper investigates scheduling and control co-deign of vehicle platoons subject to packet dropouts and communication capacity limitation. Each vehicle is modeled as a switching system with multiple modes according to the packet dropouts status and network access status. A scheduling control co-design algorithm is established based on switching system theory. The co-design algorithm is derived by introducing a binary function to resolve the communication conflicts and by using a switching controller to remove the effect of packet dropouts and guarantee the string stability of the platoon. Numerical simulations and experiments with laboratory-scale Arduino cars have demonstrated the effectiveness of the presented methodology.

Keywords:Multivehicle systems, IVHS Abstract: Autonomous vehicles joining a fully autonomous vehicle platoon or mingling in normal traffic may choose a leader and predecessor following spacing policy for safely keeping smaller distances. Avoiding inconsistency in spacing policies would require an agreement among the platoon participants via communication, which is not possible with human driven vehicles. An alternative approach is proposed, where the aggregated spacing policy of a part of the platoon is identified. The platoon between the leader and the predecessor vehicles is represented by a virtual predecessor vehicle whose virtual spacing policy is computed using a dynamic inversion based unknown input and state observer. It is shown that the spacing policy of the leader and predecessor following autonomous vehicle can be made consistent with the rest of the platoon by using the identified virtual spacing policy. The usefulness of the method is illustrated by simulation examples.

Keywords:Optimization, Network analysis and control, Decentralized control Abstract: In this paper, we give an equivalence condition for incremental passivity in terms of convex gradients and perform output regulator design for incrementally passive systems. To derive the equivalence condition, we focus on the class of incremental passive systems with quadratic storage functions, which can be transformed into a particular realization called a self-dual realization. On the basis of the self-dual realization, in which the input matrix necessarily coincides with the transpose of the output matrix, we show that the convexity of potential functions is necessary and sufficient for the incremental passivity of systems whose vector field is given as the gradient of potential functions. Furthermore, we show that the equilibrium of such convex gradient systems can be analyzed via the convex conjugate defined by the Legendre-Fenchel transformation. Combining these facts, we then develop a design method of output regulators that have a potential to improve a degree of stability while leaving the original equilibrium of integrator- based control systems invariant. The stability improvement is demonstrated though an example of power systems control, in which the resultant output regulator is shown to have a low-pass property with the nonlinearity of input saturation.

Keywords:Large-scale systems, Optimization algorithms, Networked control systems Abstract: Solving a system of linear algebraic equations is a fundamental problem, especially when there is a large number of design variables. To this purpose, we consider a collaborative framework with multiple interconnected agents that are distributed among different nodes of a network, and each agent maintains a state vector to compute the solution. Under local interactions, we propose an iterative algorithm for each agent to update the state vector via a convex combination of a consensus mechanism and a projector, which pushes the state vector toward a local constraint set. We show the {em exponential} convergence to the solution if the network is strongly connected for fixed graphs or uniformly jointly strongly connected for time-varying graphs. As an important application, we adopt this algorithm to distributedly solve the Google's PageRank problem. Moreover, we discuss the implications and relations to the relevant literature.

Keywords:Network analysis and control, Decentralized control, Networked control systems Abstract: Recently a distributed algorithm has been pro- posed for multi-agent networks to solve a system of linear algebraic equations, by assuming each agent only knows part of the system and is able to communicate with nearest neighbors to update their local solutions. This paper investigates how the network topology impacts exponential convergence of the proposed algorithm. It is found that networks with higher mean degree, smaller diameter, and homogeneous degree distribution tend to achieve faster convergence. Both analytical and numerical results are provided.

Keywords:Network analysis and control, Quantized systems, Cooperative control Abstract: This paper proposes and analyzes a novel multi-agent opinion dynamics model in which agents have access to actions which are quantized version of the opinions of their neighbors. The model produces different behaviors observed in social networks such as disensus, clustering, oscillations, opinion propagation, even when the communication network is connected. The main results of the paper provides the characterization of preservation and diffusion of actions under general communication topologies. A complete analysis allowing the opinion forecasting is given in the particular cases of complete and ring communication graphs. Numerical examples illustrate the main features of this model.

Keywords:Network analysis and control, Control of networks, Large-scale systems Abstract: Placement of sensors and actuators in a linear network model is pursued, with the aim of achieving desirable invariant-zero characteristics for input-output channels (primarily, minimum phase dynamics). Graph-theoretic analyses of the network model's invariant zeros and phase-response properties are undertaken, and used to develop simple insights into and algorithms for sensor and actuator placement.

Keywords:Network analysis and control, Smart grid Abstract: In this paper, we study the multi-leader selection problem in complex networks. While selecting a single leader can be done via various centrality measures, selecting multiple leaders is much more involved than a simple order of the nodes in terms of centrality measures. In many situations, it is often desirable to see that the multiple leaders selected are as representative as possible. Motivated by this, a clustering based two-step approach is proposed in this paper. Specifically, in order to select k leaders in a complex network, we first partition the network into k clusters and then find a leader within each cluster. For network partitioning, we propose a hierarchical algorithm by exploiting the properties of the Fiedler vector. For the single leader selection in each cluster, we resort to the eigenvector centrality, the closeness centrality and the effective resistance as useful tools. Examples on several real-world networks are worked out to illustrate the effectiveness of our method.

Keywords:Agents-based systems, Cooperative control Abstract: In this paper, the problem of semi-global bipartite consensus is examined for a group of homogeneous generic linear agents subject to input saturation under directed interaction topology. Distributed feedback controllers with a parameter adjusted by use of the low gain feedback technique are proposed to reach the semi-global bipartite consensus of multi-agent systems with input saturation, when each agent is asymptotically null controllable with bounded controls and the interaction network described by a signed diagraph is structurally balanced and has a spanning tree. Numerical simulations are given to illustrate the effectiveness of the proposed distributed control scheme.

Keywords:Agents-based systems, Distributed control, Hybrid systems Abstract: This paper deals with the problem of asymptotically stabilizing the splay state configuration of a network of identical pulse coupled oscillators through the design of their phase response function. The network of pulse coupled oscillators is modeled as a hybrid system. The design of the phase response function is performed to achieve asymptotic stability of a set wherein oscillators' phases are evenly distributed on the unit circle. To establish such a result, a novel Lyapunov function is proposed. Finally, the effectiveness of the proposed methodology is shown in two examples.

Keywords:Agents-based systems, Distributed control, Network analysis and control Abstract: We consider networks the nodes of which are interconnected via directed edges, each able to admit a flow within a certain interval, with nonnegative end points that correspond to lower and upper flow limits. The paper proposes and analyzes a distributed algorithm for obtaining admissable and balanced flows, i.e., flows that are within the given intervals at each edge and are balanced (the total in-flow equals the total out-flow) at each node. The algorithm can also be viewed as a distributed method for obtaining a set of weights that balance a digraph for the case when there are upper and lower limit constraints on the edge weights. The proposed iterative algorithm assumes that communication among pairs of nodes that are interconnected is bidirectional (i.e., the communication topology is captured by the undirected graph that corresponds to the network digraph), and allows the nodes to asymptotically (with geometric rate) reach a set of balanced feasible flows, as long as the circulation conditions on the given digraph, with the given flow/weight interval constraints on each edge, are satisfied.

Keywords:Agents-based systems, Distributed control, Quantized systems Abstract: We consider distributed integer weight balancing in networks of nodes that are interconnected via directed edges, each able to admit a positive integer weight within a certain interval, captured by a lower and an upper limit. A digraph with positive integer weights on its edges is weight-balanced if, for each node, the sum of the weights of the incoming edges equals the sum of the weights of the outgoing edges. This paper proposes and analyzes a distributed algorithm for obtaining admissable and balanced integer weights; this can also be viewed as a distributed method for obtaining a set of integer flows that balance a flow network, for the case when there are lower and upper limit constraints on the flows. The proposed iterative algorithm assumes that communication among pairs of nodes that are interconnected is bidirectional, and allows the nodes to reach a set of balanced feasible integer weights/flows after a finite number of iterations.

Keywords:Agents-based systems, Estimation, Observers for Linear systems Abstract: This paper addresses estimation of states and control parameters in cyclic pursuit systems. Classical observability tests are employed to derive conditions under which system states (i.e. agent positions) are observable in several types of cyclic pursuit schemes, including constant bearing and beacon-referenced pursuit systems. Under straightforward conditions on the system control parameters, it is demonstrated that the relative positions and control parameters of the other agents (as well as the beacon, when applicable) can be accurately estimated by an observer agent based only on direct sensing of one neighbor. Since the observer node can be viewed as an infiltrator agent, the results suggest applications in characterizing unknown members of a collective.

Keywords:Agents-based systems, Information technology systems, Optimization Abstract: In the realm of Internet of Things, sensitive information is distributed among several data owners, while multiple data users wish to access different aspects of this information. This paper presents an approach for a multiowner multi-user (MOMU) system where data owners require privacy guarantees before offering their private data. In such a setting each owner has different privacy needs against each user, whereas, users may seek to collaborate in order to violate owners’ privacy. Using approximate differential privacy, we focus on the case where n data owners possess a real-valued private data and m data users wish to learn a linear query of this data. We consider a Gaussian mechanism, derive the constraints on the covariance matrix for the mechanism to be multi-owner multiuser private, and propose a convex semi-definite relaxation to design the covariance. Finally, we illustrate our approach to a synthetic scenario where n agents act both as data owners and data users and we evaluate the privacy and the accuracy of the resulted mechanism.

Keywords:Cooperative control, Formal verification/synthesis, Communication networks Abstract: In this paper, we propose an intermittent communication framework for mobile robot networks. Specifically, we consider robots that move along the edges of a connected mobility graph and communicate only when they meet at the nodes of that graph giving rise to a dynamic communication network. Our proposed distributed controllers ensure intermittent communication of the network and path optimization, simultaneously. We show that the intermittent connectivity requirement can be encapsulated by a global Linear Temporal Logic (LTL) formula. Then we approximately decompose it into local LTL expressions which are then assigned to the robots. To avoid conflicting robot behaviors that can occur due to this approximate decomposition, we develop a distributed conflict resolution scheme that generates non-conflicting discrete motion plans for every robot, based on the assigned local LTL expressions, whose composition satisfies the global LTL formula. By appropriately introducing delays in the execution of the generated motion plans we also show that the proposed controllers can be executed asynchronously.

Keywords:Cooperative control, Autonomous robots, Agents-based systems Abstract: Connectivity maintenance is an essential task in multi-robot systems and it has received a considerable attention during the last years. However, a connected system can be broken into two or more subsets simply if a single robot fails. Then, a more robust communication can be achieved if the network connectivity is guaranteed in the case of one-robot failures. The resulting network is called biconnected. In [1] we presented a criterion for biconnectivity check, which basically determines a lower bound on the third-smallest eigenvalue of the Laplacian matrix. In this paper we introduce a decentralized gradient-based protocol to increase the value of the third-smallest eigenvalue of the Laplacian matrix, when the biconnectivity check fails. We also introduce a decentralized algorithm to estimate the eigenvectors of the Laplacian matrix, which are used for defining the gradient. Simulations show the effectiveness of the theoretical findings.

Keywords:Cooperative control, Lyapunov methods Abstract: We address the controller synthesis problem for distributed formation control. Our solution requires only rel- ative bearing measurements (as opposed to full translations), and is based on the exact gradient of a Lyapunov function with only global minimizers (independently from the formation topology). These properties allow a simple proof of global asymptotic convergence, and extensions for including distance measurements, leaders and collision avoidance. We validate our approach through simulations and comparison with other state- of-the-art algorithms.

Keywords:Cooperative control, Multivehicle systems, Hybrid systems Abstract: We consider the problem of controlling the movement of multiple cooperating agents so as to minimize an uncertainty metric associated with a finite number of targets. In a one-dimensional mission space, we adopt an optimal control framework and show that the solution is reduced to a simpler parametric optimization problem: determining a sequence of locations where each agent may dwell for a finite amount of time and then switch direction. This amounts to a hybrid system which we analyze using Infinitesimal Perturbation Analysis (IPA) to obtain a complete on-line solution through an event-driven gradient-based algorithm which is also robust with respect to the uncertainty model used. The resulting controller depends on observing the events required to excite the gradient-based algorithm, which cannot be guaranteed. We solve this problem by proposing a new metric for the objective function which creates a potential field guaranteeing that gradient values are non-zero. This approach is compared to an alternative graph-based task scheduling algorithm for determining an optimal sequence of target visits. Simulation examples are included to demonstrate the proposed methods.

Department of Information Engineering, Univ. of Padova

Keywords:Cooperative control, Networked control systems, Agents-based systems Abstract: In this paper we discuss a particular case of synchronization involving a finite population of nonlinearly coupled oscillators. We employ a discrete time approximation of the Kuramoto model in order to achieve the coordination of the heading directions of N identical vehicles moving at a constant speed in a 2D environment; this model acts as a base for a more complex distributed control, the aim of which is to direct the vehicles towards a target, adjusting their trajectories alongside their formation in the process, while avoiding collisions.

Keywords:Variable-structure/sliding-mode control, Autonomous robots, Decentralized control Abstract: We present a decentralized sliding mode control strategy for collective payload transport by a team of robots. The controllers only require robots' measurements of their own heading and velocity, and the only information provided to the robots is the target speed and direction of transport. The control strategy does not rely on inter-robot communication, prior information about the load dynamics and geometry, or knowledge of the transport team size and configuration. We initially develop the controllers for point-mass robots that are rigidly attached to a load and prove the stability of the system, showing that the speed and direction of the transported load will converge to the desired values in finite time. We also modify the controllers for implementation on differential-drive mobile robots. We demonstrate the effectiveness of the proposed controllers through simulations with point-mass robots, 3D physics simulations with realistic dynamics, and experiments with small mobile robots equipped with manipulators.

Keywords:Large-scale systems, Distributed control Abstract: Composite systems are large-scale plants composed of multiple individual units. We apply classical input-output techniques to controller design problems for such composite systems. Before being able to apply these techniques, the core issue is to establish a quadratic inequality on the composite input-output tuples, given only distinct quadratic inequalities on the individual input-output tuples of the entities constituting the composite system. Having established a technique to derive such quadratic inequalities, we apply the feedback theorem for conic relations, the small-gain theorem, and the feedback theorem for passive systems to our class of composite systems. Our results connect to the internal model principle, the S-procedure, and the simultaneous stabilization problem.

Keywords:Optimization algorithms, Distributed control, Smart grid Abstract: Primal-dual gradient methods have recently attracted interest as a set of systematic techniques for distributed and online optimization. One of the proposed applications has been optimal frequency regulation in power systems, where the primal-dual algorithm is implemented online as a dynamic controller. In this context however, the presence of external disturbances makes quantifying input/output performance important. Here we use the H2 system norm to quantify how effectively these distributed algorithms reject external disturbances. For the linear primal-dual algorithms arising from quadratic programs, we provide an explicit expression for the H2 norm, and examine the performance gain achieved by augmenting the Lagrangian. Our results suggest that the primal-dual method may perform poorly when applied to large-scale systems, and that Lagrangian augmentation can partially (or completely) alleviate these scaling issues. We illustrate our results with an application to power system frequency control by means of distributed primal-dual controllers.

Keywords:Power systems, Network analysis and control, Smart grid Abstract: Wide deployment of sensing and actuation capabilities in the electric power grid, along with changing dynamical characteristics, are necessitating analysis of power-system swing dynamics from an input-output perspective. In this article, the input-output properties of the swing dynamics, including the finite and infinite zeros, are characterized from a dynamical-networks perspective. Specifically, an explicit algebraic characterization is given for a matrix whose eigenvalues are the zeros, and in turn structural and graph-theoretic conditions for the absence and presence of nonminimum phase dynamics are developed. Based on these structural results and also an illustrative example, it is demonstrated that the zeros of the swing dynamics are important for analyzing transients and oscillations in the power transmission network, using reduced-order models, and designing controls.

Keywords:Networked control systems, Network analysis and control, Control of networks Abstract: This paper proposes a design methodology for pattern control in a network of identical oscillators. Patterns correspond to a stable equilibrium in an oscillator network over different coupling coefficients and available network topologies. We show that the discrete graph based version of the Ginzburg-Landau equation, referred to as the graph Ginzburg-Landau dynamics, exhibits n pattern equilibrium for an n-node cycle graph with the sign of the oscillator coupling coefficient dictating the stability of the pattern. The pattern control problem is cast as a discrete Markov Decision Process (MDP) whose state space is the set of patterns realizable on subgraphs of the network. Actions in the MDP correspond to the selection of coupling coefficients and edge switches in the network. Transition sampling is applied to generate the transition probabilities. Dynamic programming can then be used to calculate a stochastic policy that maximizes the expected total reward over an infinite horizon.

Keywords:Control of networks, Time-varying systems Abstract: This paper considers the problem of controlling a linear time-invariant network by means of (possibly) time-varying set of control nodes. As control metric, we adopt the worst-case input energy to drive the network state from the origin to any point on the unit hypersphere in the state space. We provide a geometric interpretation of the controllability Gramian of networks with time varying input matrices, and establish a connection between the controllability degree of a network and its eigenstructure. Based on the geometric structure of the controllability Gramian, we then propose a scheduling algorithm to select control nodes over time so as to improve the network controllability degree. Finally, we numerically show that, for a class of clustered networks, our algorithm improves upon the performance obtained by a constant set of control nodes, and outperforms an existing heuristic-based on column subset selection.

Keywords:Networked control systems, Control over communications, Information theory and control Abstract: Communication is of key importance for networked control in cyber physical systems (CPSs). Motivated by the second law of thermodynamics, Shannon entropy is used to characterize the disorderliness of the physical dynamics in CPSs; thus communication provides negative entropy, namely information, to compensate the generation of entropy. Under mild conditions, it is shown that the entropy reduction in the physical dynamics is upper bounded by the information provided by the communication system. Hence, similarly to the Carnot heat engine efficiency, the information efficiency in CPS is defined to characterize the information utilization. Both upper and lower bounds are obtained for the information efficiency under various scenarios. The discussion on generic CPSs is then applied in concrete examples of Szilard engine and scalar linear dynamics. Numerical results for the maximal information efficiency, obtained from numerical optimizations, are provided.

Keywords:Autonomous systems, Optimization algorithms, Networked control systems Abstract: We study a class of local filtering algorithms for consensus-based distributed optimization in the presence of faulty or adversarial nodes. These algorithms do not require the regular nodes to know anything about the global network (other than their own neighbors), and are thus highly scalable. For this class of algorithms, we provide graph-theoretic conditions that guarantee consensus among the regular nodes under various bounds on the number of adversarial nodes (either across the entire network, or in the local neighborhood of any regular node). We prove that a consequence of reaching consensus is that the states of the regular nodes converge to the convex hull of the minimizers of their individual functions, regardless of the actions taken by the adversarial nodes.

Keywords:Optimization algorithms, Large-scale systems, Optimization Abstract: In this paper we consider a distributed optimization scenario in which a set of processors aims at minimizing the maximum of a collection of "separable convex functions" subject to local constraints. This set-up is motivated by peak-demand minimization problems in smart grids. Here, the goal is to minimize the peak value over a finite horizon with: (i) the demand at each time instant being the sum of contributions from different devices, and (ii) the local states at different time instants being coupled through local dynamics. The min-max structure and the double coupling (through the devices and over the time horizon) makes this problem challenging in a distributed set-up (e.g., well-known distributed dual decomposition approaches cannot be applied). We propose a distributed algorithm based on the combination of duality methods and properties from min-max optimization. Specifically, we derive a series of equivalent problems by introducing ad-hoc slack variables and by going back and forth from primal and dual formulations. On the resulting problem we apply a dual subgradient method, which turns out to be a distributed algorithm. We prove the correctness of the proposed algorithm and show its effectiveness via numerical computations.

Keywords:Network analysis and control, Agents-based systems, Optimization algorithms Abstract: The Perron-Frobenius theorem has numerous applications, including to Markov chains, economics, and ranking of webpages. In this paper, we develop a class of continuous-time distributed algorithms and a gossip algorithm, which enable each node i in an undirected and connected graph to compute the ith entry of the Perron-Frobenius eigenvector of a symmetric, Metzler, and irreducible matrix associated with the graph, as well as the corresponding eigenvalue, when node i knows only row i of the matrix. We show that each continuous-time distributed algorithm in the class is a nonlinear networked dynamical system with a skew-symmetric structure, whose state is guaranteed to stay on a sphere, remain nonnegative, and converge asymptotically to the said eigenvector. We also show that under a mild assumption on the gossiping pattern, the gossip algorithm is able to do the same.

Keywords:Optimization algorithms, Large-scale systems Abstract: We consider a general class of convex optimization problems over time-varying, multi-agent networks, that naturally arise in many application domains like energy systems and wireless networks. In particular, we focus on programs with separable objective functions, local (possibly different) constraint sets and a coupling inequality constraint expressed as the non-negativity of the sum of convex functions, each corresponding to one agent. We propose a novel distributed algorithm to deal with such problems based on a combination of dual decomposition and proximal minimization. Our approach is based on an iterative scheme that enables agents to reach consensus with respect to the dual variables, while preserving information privacy. Specifically, agents are not required to disclose information about their local objective and constraint functions, nor to assume knowledge of the coupling constraint. Our analysis can be thought of as a generalization of dual gradient/subgradient algorithms to a distributed set-up. We show convergence of the proposed algorithm to some optimal dual solution of the centralized problem counterpart, while the primal iterates generated by the algorithm converge to the set of optimal primal solutions. A numerical example demonstrating the efficacy of the proposed algorithm is also provided.

Keywords:Optimization algorithms, Machine learning Abstract: The Vu-Condat algorithm is a standard method for finding a saddle point of a Lagrangian involving a differentiable function. Recent works have tried to adapt the idea of random coordinate descent to this algorithm, with the aim to efficiently solve some regularized or distributed optimization problems. A drawback of these approaches is that the admissible step sizes can be small, leading to slow convergence. In this paper, we introduce a coordinate descent primal-dual algorithm which is provably convergent for a wider range of step size values than previous methods. In particular, the condition on the step-sizes depends on the coordinate-wise Lipschitz constant of the differentiable function's gradient. We discuss the application of our method to distributed optimization and large scale support vector machine problems.

Keywords:Optimization, Optimization algorithms, Large-scale systems Abstract: This paper considers large scale constrained convex programs. These are often difficult to solve by interior point methods or other Newton-type methods due to the prohibitive computation and storage complexity for Hessians or matrix inversions. Instead, large scale constrained convex programs are often solved by gradient based methods or decomposition based methods. The conventional primal-dual subgradient method, also known as the Arrow-Hurwicz-Uzawa subgradient method, is a low complexity algorithm with the O(1/sqrt{t}) convergence rate, where t is the number of iterations. If the objective and constraint functions are separable, the Lagrangian dual type method can decompose a large scale convex program into multiple parallel small scale convex programs. The classical dual gradient algorithm is an example of Lagrangian dual type methods and has convergence rate O(1/sqrt{t}). Recently, the authors of the current paper proposed a new Lagrangian dual type algorithm with faster O(1/t) convergence. However, if the objective or constraint functions are not separable, each iteration requires to solve a large scale unconstrained convex program, which can have huge complexity. This paper proposes a new primal-dual type algorithm, which only involves simple gradient updates at each iteration and has O(1/t) convergence.

Keywords:Optimal control, Control applications Abstract: In this paper a class of infinite horizon optimal control problems with an isoperimetrical constraint, also interpreted as a budget constraint, is considered. Herein a linear both in the state and in the control dynamic is allowed. The problem setting includes a weighted Sobolev space as the state space. We investigate the question of existence of an optimal solution and formulate a corresponding theorem. Which influence the isoperimetrical constraint may have on the feasible set and on the existence of an optimal solution is illustrated in details at hand of a linear-quadratic regulator model.

Keywords:Queueing systems, Decentralized control, Optimal control Abstract: We are interested in the modeling of people's queueing behavior and influencing this behavior through the use of incentives. This setting is motivated by applications wherein a customer may choose to postpone his entry into a queue by accepting to take a so-called textit{diversion}, where this diversion is in some way more pleasant than waiting in the queue. The goal is thus to determine the minimal incentive to be provided by the queue organizing agent to entice users to take the diversion, to an extent sufficient to reduce the overall waiting time of the queue.

We propose a formulation for this problem using stochastic dynamic programming. The goal is to determine the optimal strategy in terms of the incentive and service level so as to reduce overall waiting time while limiting the cost borne by organizing agent. We further propose a decentralized version of the model where thetextit{ service agent} and the textit{organizing agent} do not wish to share all the state information. We show that it is possible to ensure that the solution of the decentralized problem is as efficient as that of the centralized system through the use of transfer contracts between the two agents.

Keywords:Electrical machine control, Optimal control, LMIs Abstract: We present a method for finding current waveforms for induction motors that minimize resistive loss while achieving a desired average torque output. Our method is not based on reference-frame theory for electric machines, and therefore directly handles induction motors with asymmetric winding patterns, nonsinusoidally distributed windings, and a general winding connection. We do not explicitly handle torque ripple or voltage constraints. Our method is based on converting the torque control problem to a nonconvex linear-quadratic control problem, which can be solved by using a (tight) semidefinite programming relaxation.

Keywords:Optimal control, Estimation Abstract: In this paper, we consider the problem of estimating the parameters of an optimal control objective function based on measurements of the closed loop system. In contrast to previous work on inverse optimal control, we consider measurements that are noise-corrupted and contain only partial-state information. We propose an inverse optimal control method based on a new soft-optimality constrained methodology of state estimation. We establish a sufficient condition for recovery of the unknown objective function parameters given complete-state information, and develop results characterising the performance of our method for linear systems. We illustrate our proposed soft-optimality approach through simulations of a nonlinear and fully-actuated mechanical system.

Keywords:Optimal control, H-infinity control, Stability of nonlinear systems Abstract: In this paper, we develop a unified framework to solve the two-players zero-sum differential game problem over the infinite time horizon. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that can clearly be seen to be the solution to the steady-state form of the Hamilton-Jacobi-Isaacs equation, and hence, guaranteeing both asymptotic stability and the existence of a saddle point for the system's performance measure. The overall framework provides the foundation for extending optimal linear-quadratic controller synthesis to differential games involving nonlinear dynamical systems with nonlinear-nonquadratic performance measures. Connections to optimal linear and nonlinear regulation for linear and nonlinear dynamical systems with quadratic and nonlinear-nonquadratic cost functionals in the presence of exogenous disturbances are also provided.

Keywords:Discrete event systems, Hybrid systems, Optimal control Abstract: There exists a class of discrete event systems involving the control of tasks with real-time constraints. It has been shown that in an on-line setting where event times are unknown, Receding Horizon (RH) approaches can be utilized to control such systems. In order to guarantee the real-time constraints, worst-case estimation needs to be used in the planning horizon of the RH controller. The direct effect of worst-case estimation is increased cost, which is highly undesirable, especially when the tasks' arrival rate is low. In this paper, we design a new RH control mechanism with relaxed worst-case estimation. We prove that using the new approach, feasibility can still be guaranteed. Simulation results show that the performance of the new RH controller can be over 50% better than that of the original RH controller.

Keywords:Optimization, Optimization algorithms, Control of networks Abstract: We provide a worst-case competitive analysis for two types of primal-dual greedy algorithms for a broad class of online conic optimization problems. This class contains problems such as online resource allocation, online routing in networks, online bipartite matching, Adwords, and Adwords with concave returns. One algorithm updates the primal and dual variables sequentially at each step, while the other algorithm updates them simultaneously. We derive a sufficient condition on the objective function that leads to a bound on the competitive ratio (using the ratio of the objective function to its Fenchel conjugate, which can be seen as a measure of ``curvature"). We show how Nesterov's smoothing technique can be utilized to improve the competitive ratio, and in case of online Linear Programs, provide the optimal competitive ratio. We apply our results to a graph formation problem as a new example on the positive semidefinite cone that satisfies our sufficient condition.

Keywords:Optimization algorithms, Optimization, Decentralized control Abstract: This paper considers consensus optimization problems where each node of a network has access to a different summand of an aggregate cost function. Nodes try to minimize the aggregate cost function, while they exchange information only with their neighbors. We modify the dual decomposition method to incorporate a curvature correction inspired in the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method. The resulting dual D-BFGS method is a fully decentralized algorithm in which nodes approximate curvature information of themselves and their neighbors through the satisfaction of a secant condition. Dual D-BFGS is of interest in consensus optimization problems that are not well conditioned, making first order decentralized methods ineffective, and in which second order information is not readily available, making decentralized second order methods infeasible. Asynchronous implementation is discussed and convergence of D-BFGS is established formally for both, synchronous and asynchronous implementations. Performance advantages relative to alternative decentralized algorithms are shown numerically.

Keywords:Optimization algorithms, Optimization, Distributed control Abstract: We consider a network of agents, each with its own private cost consisting of the sum of two possibly nonsmooth convex functions, one of which is composed with a linear operator. At every iteration each agent performs local calculations and can only communicate with its neighbors. The goal is to minimize the aggregate of the private cost functions and reach a consensus over a graph. We propose a primal-dual algorithm based on emph{Asymmetric Forward-Backward-Adjoint} (AFBA), a new operator splitting technique introduced recently by two of the authors. Our algorithm includes the method of Chambolle and Pock as a special case and has linear convergence rate when the cost functions are piecewise linear-quadratic. We show that our distributed algorithm is easy to implement without the need to perform matrix inversions or inner loops. We demonstrate through computational experiments how selecting the parameter of our algorithm can lead to larger step sizes and yield better performance.

Keywords:Optimization algorithms, Optimization, LMIs Abstract: The goal of this paper is to develop an algorithm for solving optimization problems subject to bilinear matrix inequalities (BMIs). We propose a sequential semidefinite programming (SDP) algorithm mainly motivated from the recently developed convex-concave programming approach, the pathfollowing approach, and the general non-convex programming approaches. New convex over approximations of the BMI constraints are used. Finally, numerical experiments are provided for comparative analysis.

Keywords:Optimization algorithms, Optimization, Machine learning Abstract: We analyze a fast incremental aggregated gradient method for optimizing nonconvex problems of the finite-sum form. Specifically, we analyze the SAGA algorithm within an Incremental First-order Oracle framework, and show that it converges to a stationary point provably faster than both gradient descent and stochastic gradient descent. We also discuss a Polyak’s special class of nonconvex problems for which SAGA converges at a linear rate to the global optimum. Finally, we analyze the practically valuable regularized and minibatch variants of SAGA. To our knowledge, this paper presents the first analysis of fast convergence for an incremental aggregated gradient method for nonconvex problems.

Keywords:Optimization algorithms, Optimization, Modeling Abstract: We consider a class of structured covariance completion problems which aim to complete partially known sample statistics in a way that is consistent with the underlying linear dynamics. The statistics of stochastic inputs are unknown and sought to explain the given correlations. Such inverse problems admit many solutions for the forcing correlations, but can be interpreted as an optimal low-rank approximation problem for identifying forcing models of low complexity. On the other hand, the quality of completion can be improved by utilizing information regarding the magnitude of unknown entries. We generalize theoretical results regarding the rast norm approximation and demonstrate the performance of this heuristic in completing partially available statistics using stochastically-driven linear models.

Keywords:Stochastic optimal control, Optimal control, Machine learning Abstract: Policy gradient methods for approximate optimal control and reinforcement learning fix parameterized form of the controller and then perform gradient descent on the cost-to-go function. In reinforcement learning for stochastic state-feedback problems, it has been shown that the natural gradient of the cost-to-go function can be approximated via samples of the state and step-cost, using no information about the plant model. There, the natural gradient is the gradient with respect to the Riemannian metric defined by the Fisher information matrix of the controller parameters. We give a general method for approximating the natural gradient for nonlinear output-feedback stochastic control problems with dynamic controllers. For linear systems, we give explicit formulas to compute the natural gradient when plant matrices are known, in both state and output feedback cases.

Keywords:Stochastic optimal control, Optimal control, Stochastic systems Abstract: This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be expressed as a, possibly infinite, system of deterministic linear ordinary differential equations. By casting the problem as a deterministic control problem in moment space, semidefinite programming is used to find a lower bound on the optimal solution. The constraints in the semidefinite program are imposed by the ordinary differential equations for moment dynamics and semidefiniteness of the outer product of moments. From the solution to the semidefinite program, an approximate optimal control strategy can be constructed using a least squares method. In the linear quadratic case, the method gives an exact solution to the optimal control problem. In more complex problems, an infinite number of moment differential equations would be required to compute the optimal control law. In this case, we give a procedure to increase the size of the semidefinite program, leading to increasingly accurate approximations to the true optimal control strategy.

Keywords:Stochastic optimal control, Queueing systems, Information technology systems Abstract: Consider a centralized system where requests for authentication arrive from different users. The system has multiple authentication methods available and a controller must decide how to assign a method to each request. We analyze the system dynamics using queueing models and propose a stochastic dynamic control methodology to assigning authentication methods to incoming tasks. We consider three different performance measures: usability, operating cost, and security. We model the trade-offs between these performance measures using a cost-based approach and a constraints-based approach, and derive structural and computational results on the optimal control strategies. We also provide a numerical example to illustrate the trade-offs between the three performance metrics, and show how to use our models to build an efficient frontier.

Keywords:Stochastic optimal control, Stochastic systems, Markov processes Abstract: We show that stochastic dynamical control systems are capable of information transfer from control processes to output processes, with operational meaning as defined by Shannon. Moreover, we show that optimal control strategies have a dual role, specifically, i) to transfer information from the control process to the output process, and ii) to stabilize the output process. We illustrate that information transfer is feasible by considering general Gaussian Linear Decision Models, and relate it to the well-known Linear-Quadratic-Gaussian (LQG) control theory.

Keywords:Stochastic optimal control, Markov processes, Uncertain systems Abstract: We analyze the infinite horizon minimax discounted cost Markov Control Model (MCM), for a class of controlled process conditional distributions, which belong to a ball, with respect to total variation distance metric, centered at a known nominal controlled conditional distribution with radius R taking values in [0,2], in which the minimization is over the control strategies and the maximization is over conditional distributions. Through our analysis (i) we derive a new discounted dynamic programming equation, (ii) we show the associated contraction property, and (iii) we develop a new policy iteration algorithm. Finally, the application of the new dynamic programming and the corresponding policy iteration algorithm are shown via an illustrative example.

Keywords:Stochastic optimal control, Uncertain systems, Stochastic systems Abstract: We propose a novel methodology for stochastic trajectory optimization which is based on merging the theory of spectral expansions with Differential Dynamic Programming. Specifically, we employ polynomial chaos expansions to handle parametric uncertainties and utilize the Karhunen-Loeve transformation to represent stochastic forces. This allows us to build a generic framework and avoid relying on restrictive assumptions regarding the form of stochasticity. In addition, Differential Dynamic Programming provides an iterative algorithm for finding optimal controls which attains scalability and, under mild assumptions, fast convergence. The obtained method is capable of controlling the distribution of the system’s trajectory and can be used in both planning and control. Last but not least, we formulate a variational integration scheme for uncertain systems that are represented by spectral expansions. Simulated examples validate the applicability and numerical efficiency of the proposed approach.

Keywords:Estimation, Kalman filtering, Nonlinear systems identification Abstract: The Gauss-Hermite quadrature filter (GHQF) can achieve arbitrary degree of accuracy and high stability, but it suffers from heavy computational burden. Alternative high accurate filters, such as high-degree cubature Kalman filter (CKF) and high-degree sparse-grid quadrature filter (SGQF), can greatly reduce the computational cost but may have stability concerns. To give consideration to both filtering stability and efficiency, a cross approximation-based quadrature filter is proposed in this paper. The filter can achieve the same accuracy and stability as GHQF with much less computational burden. Firstly, tensors in GHQF are unfolded into matrices to incorporate cross approximation method, and low-rank representations of the unfolding matrices are obtained by only sampling a small subset of the sigma points. Secondly, taking advantage of the low-rank representations, the computational cost is further reduced using low-rank matrix operations. Simulation results show that the proposed filter only samples about 3% of the sigma points of 3-point GHQF in a 10-dimension target tracking problem, but achieves the same performance as GHQF.

Keywords:Estimation, Kalman filtering, Stochastic optimal control Abstract: We consider the problem of mean-square estimation of the state of a discrete time dynamical system having additive non-Gaussian noise. We assume that the noise has the structure that at each time instant, it is a projection of a fixed high-dimensional noise vector with a log-concave density. We derive conditions which guarantee that, as the dimension of this noise vector grows large relative to the dimension of the state space, the observation space, and the time horizon, the optimal estimator of the problem with Gaussian noise becomes near-optimal for the problem with non-Gaussian noise. The results are derived by first showing an asymptotic Gaussian lower bound on the minimum error which holds even for nonlinear systems. This lower bound is shown to be asymptotically tight for linear systems. For nonlinear systems this bound is tight provided the noise has a strongly log-concave density with some additional structure. These results imply that estimates obtained by employing the Gaussian estimator on the non-Gaussian problem satisfy an approximate orthogonality principle. Moreover, the difference between the optimal estimate and the estimate derived from the Gaussian estimator vanishes strongly in L^2. For linear systems with high-dimensional log-concave noise of this structure, we get that the Kalman filter serves as a near-optimal estimator. A key ingredient in the proofs is a recent central limit theorem of Eldan and Klartag.

Keywords:Estimation, Kalman filtering, Stochastic systems Abstract: In this paper we consider the problem of state estimation for linear discrete-time Gaussian systems with intermittent observations resulting from packet dropouts. We assume that the receiver does not know the sequence of packet dropouts. This is a typical situation, e.g., in wireless sensor networks. Under this hypothesis, the problem of state estimation has been previously solved by the authors using a detection-estimation approach consisting of two stages: the first is a nonlinear optimal detector, which decides if a packet dropout has occurred, and the second is a time-varying Kalman filter, which is fed with both the observations and the decisions from the first stage. This work extends that solution, introducing a refinement stage whose purpose is to significantly improve the decision on packet dropouts and, in turn, on state estimation. The overall estimator has finite memory and the tradeoff between performance and computational complexity can be easily controlled. Numerical results highlight the effectiveness of the approach based on detection-estimation with refinement, which outperforms both the estimator without refinement and the optimal linear filter of Nahi.

Keywords:Estimation, Kalman filtering Abstract: For nonlinear state space systems with additive noises, sometimes the number of process noise signals could be less than the dimension of the state space. In order to improve the accuracy and stability of nonlinear state estimation, this paper provides for the first time the derivation of the full information estimator (FIE) for such nonlinear systems. We verify our derivation of the FIE by firstly proving the unbiasedness and minimum-variance of the FIE for linear time varying (LTV) systems, then showing the equivalence between the Kalman filter/smoother and the FIE for LTV systems. Finally, we prove that the FIE will provide more accurate state estimates than the extended Kalman filter (EKF) and smoother (EKS) for nonlinear systems.

Keywords:Estimation, Linear parameter-varying systems, Lyapunov methods Abstract: This paper addresses the problem of estimating the position of a body moving in n-dimensional Euclidean space using body velocity measurements and the measurements of direction(s) between the body and one (or several) source point(s) whose location(s) is (are) known. The proposed solutions exploit the Continuous Riccati Equation (CRE) to calculate observer gains yielding global uniform exponential stability of zero estimation errors, even when the measured body velocity is biased by an unknown constant perturbation. These results are obtained under persistent excitation (p.e.) conditions depending on the number of source points and body motion that ensure both uniform observability and good conditioning of the CRE solutions. With respect to previous contributions on the subject the proposed framework encompasses the static case, when the body is motionless and at least two source points are needed to recover its position, and the non-static case, when body motion and a single source are sufficient. Simple and explicit observability conditions under which uniform exponential stability is achieved are also worked out for each case. Simulation results illustrate the performance of the proposed observers.

Keywords:Estimation, Linear systems, Distributed parameter systems Abstract: We use a backstepping technique with time-varying kernels to derive an observer that estimates unknown boundary parameters and the states in 2 x 2 linear hyperbolic PDEs from sensing anti-collocated with the uncertain parameters. The theory is demonstrated in a simulation.

Keywords:Identification, Linear systems Abstract: In this contribution, we propose a kernel-based method for the identification of linear systems from noisy and incomplete input-output datasets. We model the impulse response of the system as a Gaussian process whose covariance matrix is given by the recently introduced stable spline kernel. We adopt an empirical Bayes approach to estimate the posterior distribution of the impulse response given the data. The noiseless and missing data samples, together with the kernel hyperparameters, are estimated maximizing the joint marginal likelihood of the input and output measurements. To compute the marginal-likelihood maximizer, we build a solution scheme based on the Expectation-Maximization method. Simulations on a benchmark dataset show the effectiveness of the method.

Keywords:Identification, Lyapunov methods, Variable-structure/sliding-mode control Abstract: In this work, a novel procedure for identifying the parameters of a polynomial systems is introduced. In order to get a regression form of the system, and to avoid the necessity of time-derivatives of input/output signals, the modulating function method is applied. In contrast to other available techniques for achieving estimates in finite-time, the real-time inversion of square matrices is not required. Instead, a nonlinear gradient algorithm is used to let the estimate converge in fixed-time. This procedure allows a continuous and recursive update of the parameter estimates and avoids the computational burdens of inversion-based estimation schemes.

Keywords:Closed-loop identification, Model Validation, Control applications Abstract: In this paper, attempt is made to explore real time plant modelling based on asymmetrical relay feedback test with step input as an excitation signal. The simulated and experimental investigations result in a set of modified analytical expressions for identification of stable first order plus dead time, non-minimum phase first order plus dead time and overdamped non-minimum phase second order plus dead time processes. These expressions are further utilized for identification of processes in presence of measurement noise using curve fitting tool. Well known examples from literature are included for validation of proposed modelling and identification scheme. Yokogawa distributed control system centum CS3000 with field instruments are utilized for conducting real time experiment on level control system.

Keywords:Identification, Modeling, Linear systems Abstract: In system identification, the more data is collected, the more accurate model is obtained. However, under limited communication bandwidth or computational resources, it is sometimes difficult to collect and store the all measured data, so it is desired to collect and store only useful data for improvement of modeling accuracy. This paper focuses on Lebesgue sampling, which uses thresholds on signal level for triggering sampler and proposes a system identification method with using information obtained in intervals between Lebesgue sampled data. The asymptotic variance of the estimated parameter is analyzed and effectiveness of the proposed method is examined through numerical examples.

Keywords:Identification, Nonlinear systems identification, Machine learning Abstract: We propose a novel approach to input design for identification of nonlinear state space models. The optimal input sequence is obtained by maximizing a scalar cost function of the Fisher information matrix. Since the Fisher information matrix is unavailable in closed form, it is estimated using particle methods. In addition, we make use of Gaussian process optimization to find the optimal input and to mitigate the problem of a large computational cost incurred by the particle method, as the method reduces the number of functional evaluations. Numerical examples are provided to illustrate the performance of the resulting algorithm.

Keywords:Identification, Process Control, Emerging control applications Abstract: An important practical consideration in system identification is the judicious use of information for input signal design. Typically, only limited process knowledge is available a priori; hence the input design parameters are not always optimally selected. The quality of the data substantially improves if input design parameters can be refined during experimental execution. The purpose of this paper is to present an enhanced identification test monitoring procedure for multivariable systems that incorporates these ideas to achieve experiments with the shortest possible duration and that are adequately informative for identification purposes. This is enabled by "on-the-go" manipulation of amplitude, duration, and/or frequency content of the input signals. The decision to continue, modify, or halt the experiment is achieved by a stopping criterion based on a robust control metric that is developed in the paper. These computations are performed using an orthogonal-in-frequency spectral input design, and relying on a computational method that estimates transfer functions (and associated uncertainties) taking into account the system noise and transient behavior. Results are evaluated through a simulation study using a chemical process system under diverse realistic noise structures.

Keywords:Adaptive control, Optimization Abstract: Most extremum seeking design approaches consider optimising the steady state output of a plant with stationary input-output behaviour. However, when the plant is subject to a time-varying exogenous disturbance, the plant extremum point may vary accordingly. This paper firstly considers the effect of slowly varying exogenous inputs on the performance of a black-box extremum seeking scheme. The analysis reveals that, under proper tuning, the extremum seeking controller converges to the extremum of an average map. A multiplexed extremum seeking framework that estimates the mapping between the extremum point and the disturbance signal is then proposed. The approach is demonstrated via simulation to achieve a finer estimation of the extremum map.

Keywords:Adaptive control, Robotics, Fault tolerant systems Abstract: This paper develops an adaptive actuator failure compensation control scheme for a parallel manipulator robotic system. The adaptive control design uses an integration of multiple failure compensator controllers designed for each actuator failure pattern. Such a design effectively utilizes the actuation redundancy in the unique structure of parallel manipulator systems to compensate for possible actuator failures with no knowledge of actuator failure pattern, failure time instant and failure values. With complete parameterization of system and actuator failure uncertainties and direct adaptation of controller parameters, the adaptive control scheme guarantees desired closed-loop stability and asymptotic output tracking, despite certain actuator failures. Simulation results verify the desired control system performance for a 2-DOF redundantly actuated parallel manipulator.

Keywords:Adaptive control, Robust adaptive control, Robotics Abstract: Abstract A novel method to improve the transient performance of the adaptive tracking control system for robot manipulators is proposed. In short, an exponential convergence to a predetermined residual set of tracking error in the closed-loop system can be guaranteed for the robot manipulator system. In addition, the tracking error converges to zero asymptotically thereafter. The proposed controller utilize the attracting immersed manifold in the system state space, which is introduced in the non-certainty equivalent (NCE) adaptive control framework. In order to guarantee the exponential convergence of the closed-loop tracking error to the predetermined residual set, the additional stabilizing signal is designed to boost the convergence rate on top of the NCE adaptive controller. As a result, the transient response of the adaptive tracking control system is maintained to decay exponentially to the residual set whose size can be regulated. A rigorous proof for the exponential convergence of the closed-loop adaptive control system is presented in contrast to the asymptotic convergence of the conventional model reference adaptive control (MRAC) framework. Numerical simulations are performed for the demonstration of the proposed control method.

Keywords:Adaptive control, Robust control, Uncertain systems Abstract: An extension to the L1 adaptive control theory in a discrete-time framework is proposed. The extension addresses discrete-time systems with unknown time varying parameters, which include input disturbances, unknown input gain and system uncertainties. Sufficient stability conditions and performance bounds are derived. The proposed structure is applied to Rohrs’ example to illustrate its stability and robustness features.

Keywords:Adaptive control, Flight control, Direct adaptive control Abstract: In this paper, we present an adaptive output feedback controller using feedthrough components. This controller consists of an observer-based baseline controller with integral action and a closed-loop reference model and is shown to stabilize a class of linear plants with uncertain parameters including nonzero feedthrough matrices. The presence of direct feedthrough is addressed through the use of suitable feedback gains in the closed-loop reference model. The performance of the adaptive controller is illustrated using simulation studies of a model of an agile aircraft. The results show that a better performance with improved robustness can be obtained with the proposed adaptive controller. These results have important implications on aircraft problems where acceleration measurements are available.

Keywords:Adaptive control, Stability of linear systems Abstract: It is well known that vibrations in oilwell system affect the drilling directions and may be inherent for drilling systems. Further, the environment complexity requires a minimum number of sensor variables. In this paper, for an oilwell drilling system, we present an adaptive observer design for a second-order Partial Differential Equation (PDE) with the usually neglected damping term. The design relies on the top boundary measurements only. From the Lyapunov theory and the backstepping technique, we develop an observer based control law for the one dimension wave PDE. We show an exponentially vibration stability of the partially equipped oilwell drilling system. The simulation results confirm the effectiveness of the proposed PDE observer based controller.

Keywords:Fault detection, Sensor networks Abstract: The paper addresses the problem of detecting attacks on distributed estimator networks that aim to intentionally bias process estimates produced by the network. It provides a sufficient condition, in terms of the feasibility of certain linear matrix inequalities, which guarantees distributed input attack detection using an H∞ approach.

Keywords:Fault diagnosis, Fault detection, Identification for control Abstract: This paper describes a novel approach to sensor and actuator integrity monitoring. Multiple sensor and actuator faults can be detected and isolated. Most importantly, fault magnitudes can be correctly estimated. Our approach is robust to disturbance and does not require additional sensors.

Keywords:Fault diagnosis, Fault detection, Learning Abstract: In this paper, a novel solution to the active fault diagnosis problem for stochastic linear Markovian switching systems on the infinite-time horizon is proposed. The imperfect state information problem of designing an active fault detector that minimizes a general detection cost criterion is reformulated as the perfect state information problem using sufficient statistics. The reformulation decreases theoretical complexity and enables to find a suboptimal solution by dynamic programming. However, classical approaches are computationally complex or fail to identify the most representative states of the system. This paper combines the active fault detection, state estimation, and reinforcement learning. In the proposed algorithm, temporal difference learning is used to train the active fault detector based on input-output data from the system simulation. The designed detector can be then used online. A numerical example is presented to verify the proposed algorithm.

Univ. of Science and Tech. Beijing, Beijing, P.R. Chin

Keywords:Fault diagnosis, Fault detection Abstract: The recent explosion in different statistics for fault detection has meant that the practitioner is faced with the unenviable job of determining which to use in a given situation. Thus, this paper seeks to investigate the different test statistics that can be applied to detect multiplicative faults for multivariate Gaussian-distributed processes in order to provide the practitioner with some guidance. Three groups of methods are: traditional methods (emph{e.g.}, T^2 and Q statistics) and their extensions; the Wishart distribution-based methods; and those methods that are created in information and communication fields to describe the characteristics of measurement variance and covariance (emph{e.g.}, mutual information and Kullback-Leibler divergence). Then, greater details on their interconnections and comparisons are presented and their performance for detecting multiplicative faults is evaluated and demonstrated using numerical simulations.

Keywords:Fault tolerant systems, Estimation, Linear parameter-varying systems Abstract: This paper presents a fault-tolerant sensor reconciliation scheme for systems equipped with a redundant number of possibly faulty "physical" sensors. The reconciliator is in charge to discover on-line, at each time instant, the possibly faulty physical sensors and exclude their measures from the generation of the "virtual" sensors, which, on the contrary, are supposed to be always healthy and suitably usable for control purposes without requiring the reconfiguration of the nominal control law. Amongst many, the solution proposed here is based on the use of a Linear Parameter Varying Unknown Input Observers (LPV-UIO) coupled with an "ad-hoc" parameter estimator used to identify on-line the current sensor reconciliation matrix. The latter is therefore used to hide the faulty measures from the pool of physical outputs in the generation of the virtual outputs. For simplicity, the sensor faults here considered are limited to variation of sensors’ gain and offset values. The scheme is fully described and all of its properties investigated and proved. Finally, a simulation example is reported in details to show the effectiveness of the scheme.

Keywords:Fault tolerant systems, Fault diagnosis, Decentralized control Abstract: This paper deals with a decentralized fault-tolerant control methodology based on an Active Fault Diagnosis approach. The proposed technique addresses the important problem of monitoring interconn