Keywords:Robust control, Lyapunov methods, Identification for control Abstract: Recently, there has been renewed interest in data-driven control, that is, the design of controllers directly from observed data. In the case of linear time-invariant (LTI) systems, several approaches have been proposed that lead to tractable optimization problems. On the other hand, the case of non-linear dynamics is considerably less developed, with existing approaches limited to at most rational dynamics and requiring the solution to a computationally expensive Sum of Squares (SoS) optimization. Since SoS problems typically scale combinatorially with the size of the problem, these approaches are limited to relatively low order systems. In this paper, we propose an alternative, based on the use of state-dependent representations. This idea allows for synthesizing data-driven controllers by solving at each time step an on-line optimization problem whose complexity is comparable to the LTI case. Further, the proposed approach is not limited to rational dynamics. The main result of the paper shows that the feasibility of this on-line optimization problem guarantees that the proposed controller renders the origin a globally asymptotically stable equilibrium point of the closed-loop system. These results are illustrated with some simple examples. The paper concludes by briefly discussing the prospects for adding performance criteria and for extending these results to continuous time systems.

Keywords:Learning, Optimal control, Control of networks Abstract: While classic controller design methods rely on a model of the underlying dynamics, data-driven methods allow to compute controllers leveraging solely a set of previously recorded input-output trajectories, with relatively mild assumptions. Assuming knowledge of the dynamics is especially unrealistic in decentralized systems, since information is typically localized by design. In this paper we investigate a decentralized data-driven approach to learn quadratically-optimal controls for interconnected linear systems. Our main result is a distributed algorithm that computes a control input to reach a desired target configuration with provable, and tunable, suboptimality guarantees. Our distributed procedure converges after a finite number of iterations and the suboptimality gap can be characterized analytically in terms of the data properties. Our algorithm relies on a new set of closed-form data-driven expressions of quadratically-optimal controls, which complement the existing literature on data-driven linear-quadratic control. We complement and validate our theoretical analysis by means of numerical simulations with different interconnected systems.

Keywords:Learning, Identification for control, LMIs Abstract: In a recent paper it was shown how a matrix S-lemma can be applied to construct controllers from noisy data. The current paper complements these results by proving a matrix version of the classical Finsler's lemma. This matrix Finsler's lemma provides a tractable condition under which all matrix solutions to a quadratic equality also satisfy a quadratic inequality. We will apply this result to bridge known data-driven control design techniques for both exact and noisy data, thereby revealing a more general theory. The result is also applied to data-driven control of Lur'e systems.

Keywords:Optimization, Linear systems, Output regulation Abstract: This paper proposes a data-driven framework to solve time-varying optimization problems associated with unknown linear dynamical systems. Making online control decisions to regulate a dynamical system to the solution of an optimization problem is a central goal in many modern engineering applications. Yet, the available methods critically rely on a precise knowledge of the system dynamics, thus mandating a preliminary system identification phase before a controller can be designed. In this work, we leverage results from behavioral theory to show that the steady-state transfer function of a linear system can be computed from data samples without any knowledge or estimation of the system model. We then use this data-driven representation to design a controller, inspired by a gradient-descent optimization method, that regulates the system to the solution of a convex optimization problem, without requiring any knowledge of the time-varying disturbances affecting the model equation. Results are tailored to cost functions satisfy the Polyak-Łojasiewicz inequality.

Keywords:Machine learning, Adaptive control, Stability of nonlinear systems Abstract: It was shown, in recent work by the authors, that it is possible to learn an asymptotically stabilizing controller from a small number of demonstrations performed by an expert on a feedback linearizable system. These results rely on knowledge of the plant dynamics to assemble the learned controller from the demonstrations. In this paper we show how to leverage recent results on data-driven control to dispense with the need to use the plant model. By bringing these two methodologies --- learning from demonstrations and data-driven control --- together, this paper provides a technique that enables the control of unknown nonlinear feedback linearizable systems solely based on a small number of expert demonstrations.

Keywords:Learning, Sampled-data control, Robust control Abstract: Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems were obtained by rewriting them as an interconnection of a linear time-invariant system and a delay operator, and subsequently, performing a robust stability analysis using a known bound on the gain of this operator. In this paper, we refine this approach: First, we show that the delay operator is input-feedforward passive and second, we compute its gain exactly. Based on these findings, we derive improved stability conditions both in case of full model knowledge and in case only data are available. In the latter, we require only a finite-length and potentially noisy state-input trajectory of the unknown system. In two examples, we illustrate the reduced conservativeness of the proposed stability conditions over existing ones.

Keywords:Algebraic/geometric methods, Nonlinear systems, Chaotic systems Abstract: The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a growing interest in applications of these compounds, and their generalizations, in systems and control theory.

This tutorial paper provides a gentle introduction to these topics with an emphasis on the geometric interpretation of the compounds, and surveys some of their recent applications.

Keywords:Algebraic/geometric methods, Nonlinear systems, Feedback linearization Abstract: In this paper, we propose a constructive algorithm to dynamically linearize two-input control systems via successive one-fold prolongations of a control that has to be suitably chosen at each step of the algorithm. Contrary to the case of static feedback linearization, for linearization via successive one-fold prolongations, the linearizability distributions need not be involutive but the first noninvolutive one has to contain a sufficiently large involutive subdistribution. The main idea of the algorithm is, at each new step, to prolong the system in such a way that the first noninvolutive distribution is replaced by its largest involutive subdistribution, thus for the prolonged system we gain at least one new involutive distribution. Our algorithm is constructive, gives sufficient conditions for flatness, and can be seen as the dual of the dynamic feedback linearization algorithm of Battilotti and Califano (2004, 2005), which is also based on prolongations, but for which the to-be-prolonged control is identified with the help of the last noninvolutive linearizability distribution.

Keywords:Algebraic/geometric methods, Stochastic systems, Robotics Abstract: Stochastic differential equations (SDEs) evolving on a sphere have numerous applications in Science and Engineering. For ordinary differential equations (ODEs) evolving in a sphere, numerical schemes are reasonably well established. But there is little work on numerical SDEs schemes for motion on a sphere. Here we specialize recent work to develop such a scheme and we illustrate its comparative performance with simulations. But the main contribution is a convergence analysis establishing the mean square order of convergence. While such results are well established for Euclidean SDEs they barely exist for geometric SDEs.

Keywords:Numerical algorithms Abstract: The problems of matrix spectral factorization and J-spectral factorization appear to be important for practical use in many MIMO control systems. We propose a numerical algorithm for J–spectral factorization which extends Janashia–Lagvilava matrix spectral factorization method to the indefinite case. The algorithm can be applied to matrices that have constant signatures for all leading principle submatrices. A numerical example is presented for illustrative purposes.

Keywords:Linear systems, Network analysis and control, Networked control systems Abstract: In this paper we investigate a relaxed concept of controllability, known in the literature as herdability, namely the capability of a system to be driven towards the (interior of the) positive orthant. Specifically, we investigate herdability for linear time-invariant systems, both from an algebraic perspective and based on the graph representing the systems interactions. In addition, we focus on linear state-space models corresponding to matrix pairs (A,B) in which the matrix B is a selection matrix that determines the leaders in the network, and we show that the weights that followers give to the leaders do not affect the herdability of the system. We then focus on the herdability problem for systems with a single leader in which interactions are symmetric and the network topology is acyclic, in which case an algorithm for the leader selection is provided. In this context, under some additional conditions on the mutual distances, necessary and sufficient conditions for the herdability of the overall system are given.

Keywords:Nonlinear systems, Algebraic/geometric methods, Distributed parameter systems Abstract: The evoluted set at time T is the union of all images of an initial set A via the flow at times t in the interval (0,T). Its regularity is for interest for control, being the attainable set in several relevant examples.

We first show that it is not sufficient for A to have negligible boundary (i.e. zero Lebesgue measure) to ensure that the evoluted set has negligible boundary too. Instead, we prove that such property holds when A is a C^{1,1} domain.

Keywords:Hierarchical control, Iterative learning control, Optimization Abstract: For many emerging repetitive control applications such as wind and marine energy generation systems, gait-cycle following in legged locomotion, remote sensing, surveillance, and reconnaissance, the primary objective for repetitive control (RC) is optimization of a cycle cost such as the lap-averaged power generated and metabolic cost of locomotion, as opposed to the classical requirement of tracking a known reference trajectory by the system output. For this newer class of applications, only a range of reference trajectories suitable for cyclic operation is known a priori, the range potentially encapsulating various operational constraints, and as part of repetitive control, it is desired that over a number of operation cycles, the cycle cost, or the economic metric, is optimized. With this underlying motivation, a hierarchical solution is presented, wherein the inner loop includes a classical repetitive controller that tracks a reference trajectory of known period, and the outer loop iteratively learns the desired reference trajectory using a combination of the system and cost function models and the measured cycle cost. This approach results in optimum steady-state cyclic operation. A steepest descent type algorithm is used in the outer loop, and via Lyapunov-like arguments, the existence of tuning parameters resulting in robust and optimal steady-state cyclic operation is discussed. Appropriate guidelines for parameter tuning are presented, and the proposed method is numerically validated using an example of an inverted pendulum.

Keywords:Iterative learning control, Learning, Optimal control Abstract: For systems that execute tasks repetitively, learning control strategies such as iterative learning control and repetitive control have proven to be useful tools for mitigating the effects of model uncertainty to improve system performance. While such strategies have been used to solve the point-to-point motion tracking problem, existing techniques require either that the reference positions are tracked at the same time within each iteration, or that the initial conditions are reset between each iteration of the task. This paper aims to relax these assumptions through the development of a two stage repetitive control framework that drives the system to periodically track a sequence of temporally-varying reference positions by using minimal control effort. Here, the first stage updates the control signal such that the system accurately tracks the reference positions, while the second stage modifies the tracking time requirements of the reference positions to minimize the applied control effort. The effectiveness of the control strategy is demonstrated via simulated application of the algorithm on a mass-spring-damper system.

Keywords:Iterative learning control, Learning, Optimization Abstract: This paper presents a new iterative learning control (ILC) methodology, termed emph{library-based norm-optimal ILC}, which optimally accounts for variations in measurable disturbances and plant parameters from one iteration to the next. In this formulation, previous iteration-varying disturbance and/or plant parameters, along with the corresponding control and error sequences, are intelligently maintained in a dynamically evolving library. The library is then referenced at each iteration, in order to base the new control sequence on the most relevant prior iterations, according to an optimization metric. In contrast with the limited number of library-based ILC methodologies pursued in the literature, the present work (i) selects provably optimal interpolation weights, (ii) presents methods for starting with an empty library and intelligently truncating the library when it becomes too large, and (iii) demonstrates convergence to an optimal performance value. To demonstrate the effectiveness of our new methodology, we simulate our library-based norm-optimal ILC method on a linear time-varying model of a micro-robotic deposition system.

Keywords:Iterative learning control, Linear systems, Learning Abstract: Many control problems are naturally expressed in continuous time. Yet, in Iterative Learning Control of linear systems, sampling the output signal has proven to be a convenient strategy to simplify the learning process while sacrificing only marginally the overall performance. In this context, the control action is similarly discretized through zero-order hold - thus leading to a discrete-time system. With this paper, we want to investigate an alternative strategy, which is to track sampled outputs without masking the continuous nature of the input. Instead, we look at the whole input evolution as an element of a functional subspace. We show how standard results in linear Iterative Learning Control naturally extend to this context. As a result, we can leverage the infinite-dimensional nature of functional spaces to achieve exact tracking of strongly non-square systems (number of inputs less than outputs). We also show that constraints - like those imposed by intermittent control - can be naturally integrated within this framework.

Keywords:Iterative learning control, Linear systems, Optimization Abstract: Multi-stage actuators are becoming more common in practice as the desire for larger work areas is combined with demands for higher precision. Many of these practical systems can be found in manufacturing and digital process environments which perform repetitive tasks. Iterative learning control (ILC) is a control strategy suited for such repetitive tasks. However, complex systems like these often exhibit coupling between individual stages. This work presents a series-hierarchical ILC strategy (SH-ILC) that employs similar coupling between individual ILC algorithms to improve tracking performance in each stage of actuation. A numerical example of a dual-stage actuator (DSA) is provided, and simulation results demonstrate that the proposed SH-ILC achieves improved reference tracking performance.

Keywords:Iterative learning control, LMIs, Linear systems Abstract: This paper considers the design of iterative learning control laws for discrete-time linear time-invariant systems with polytopic uncertainty. To avoid state feedback or using an observer, the control law uses static output feedback. These systems’ control law design problem is reformulated in the repetitive process setting to ensure robust stability along the trial property. Hence, monotonic convergence in the trial-to-trial direction is guaranteed over the whole uncertainty domain. This approach results in a linear matrix inequality-based design, and an illustrative example is given.

Keywords:Filtering, Compartmental and Positive systems, LMIs Abstract: The problems of reduced order H-2 and H-infinity positive filter design for positive uncertain discrete-time linear systems are investigated in this paper. Due to the positivity constraint on the matrices of the filter, optimal H-2 and H-infinity filters cannot be obtained through standard linear matrix inequality (LMI) methods, even in the context of full order filtering for precisely known systems. Therefore, new sufficient LMI conditions are proposed for H-2 and H-infinity positive filter design for positive discrete-time linear systems, having as main advantage the fact that the filter matrices are variables of the problem. In this case, no structural constraints on the optimization variables (source of conservativeness) are needed to ensure positivity. Thanks to a relaxation in the stability of the filter, an iterative algorithm with a feasible initial condition is proposed, allowing the search for positive filters that assure an H-2 or H-infinity guaranteed attenuation level for the filtered system. The conditions can deal with full or reduced order filtering, polytopic type uncertainty and structural constraints. Examples inspired on models borrowed from the literature illustrate the results.

Keywords:Filtering, Networked control systems, Distributed parameter systems Abstract: Filtering is an essential operation in a variety of applications, such as Internet-of-Things and network localization and navigation. Distributed filtering in networked systems is a challenging problem due to the constraints on both the sensing and the communication capabilities of the system. In this paper, we investigate distributed filtering for a two-node system in discrete-time scenarios. In particular, each node is associated with an unknown state and obtains an observation of the two states at each time. One of the two nodes transmits encoded messages to the other node via a Gaussian channel with feedback. The receiver node infers its unknown state in real-time based on its observations and the received messages. We design an encoding strategy for generating transmitted messages and show that it optimizes the distributed filtering performance when certain conditions on the observation model are satisfied. Numerical results quantify the advantage of the designed encoding strategy compared to reference techniques.

Keywords:Filtering, Nonlinear systems, Stochastic systems Abstract: This paper deals with the state estimation of the nonlinear stochastic models with continuous dynamics and discrete measurement. Namely, the numerical solution to the Fokker-Planck equation, representing the estimator time update, is explored. Unlike the classical approaches, which use the finite difference method and operate on a standard rectangular grid, this paper utilizes finite volume method on the logically rectangular grid. In particular, the circular grid is chosen, which better approximates an estimated conditional probability density function support and improves time update accuracy without any impact on the its computational complexity. The benefits of the proposed solution are illustrated in a numerical example.

Keywords:Filtering, Stochastic systems, Estimation Abstract: We present a new uncertainty principle for risk-aware statistical estimation, effectively quantifying the inherent trade-off between mean squared error (mse) and risk, the latter measured by the associated average predictive squared error variance (sev), for every admissible estimator of choice. Our uncertainty principle has a familiar form and resembles fundamental and classical results arising in several other areas, such as the Heisenberg principle in statistical and quantum mechanics, and the Gabor limit (time-scale trade-offs) in harmonic analysis. In particular, we prove that, provided a joint generative model of states and observables, the product between mse and sev is bounded from below by a computable model-dependent constant, which is explicitly related to the Pareto frontier of a recently studied sev-constrained minimum mse (MMSE) estimation problem. Further, we show that the aforementioned constant is inherently connected to an intuitive new and rigorously topologically grounded statistical measure of distribution skewness in multiple dimensions, consistent with Pearson's moment coefficient of skewness for variables on the line. Our results are also illustrated via numerical simulations.

Keywords:Filtering, Algebraic/geometric methods, Estimation Abstract: This paper proposes a symbolic-numeric Bayesian filtering method for a class of discrete-time nonlinear stochastic systems to achieve high accuracy with a relatively small online computational cost. The proposed method is based on the holonomic gradient method (HGM), which is a symbolic-numeric method to evaluate integrals efficiently depending on several parameters. By approximating the posterior probability density function (PDF) of the state as a Gaussian PDF, the update process of its mean and variance can be formulated as evaluations of several integrals that exactly take into account the nonlinearity of the system dynamics. An integral transform is used to evaluate these integrals more efficiently using the HGM compared to our previous method. Further, a numerical example is provided to demonstrate the efficiency of the proposed method over other existing methods.

Keywords:Sampled-data control, Observers for nonlinear systems, Filtering Abstract: In this paper, a semi-implicit Euler approximation scheme is proposed for a second-order homogeneous differentiator. Compared to an explicit Euler approximation, it is well-known that implicit Euler approximation scheme offers better performances like reducing high frequency oscillations. However, the implicit Euler approximation scheme works well only when dealing with classical sliding mode differentiator. In order to keep advantages of implicit Euler approximation, when this approximation is applied in case of homogeneous differentiators, a semi-implicit Euler approximation is proposed for a second-order system. Validation on real data is conducted to highlight the well-founded of the proposed differentiation strategy.

Keywords:Stability of linear systems, Stochastic systems, Robust control Abstract: Robust stability and stochastic stability have separately seen intense study in control theory since its inception. In this work we establish relations between these properties for discrete-time systems. Specifically, we examine a robustness framework which models the inherent uncertainty and variation in the system dynamics which arise in model-based learning control methods such as adaptive control and reinforcement learning. We provide results which guarantee mean-square stability margins in terms of multiplicative noises which affect the nominal dynamics, as well as connections to prior work which together imply that robust stability and mean-square stability are, in a certain sense, equivalent.

Keywords:Stochastic systems, Lyapunov methods, Uncertain systems Abstract: Control barrier functions have been widely used for synthesizing safety-critical controls, often via solving quadratic programs. However, the existence of Gaussian-type noise may lead to unsafe actions and result in severe consequences. In this paper, we study systems modeled by stochastic differential equations (SDEs) driven by Brownian motions. We propose a notion of stochastic control barrier functions (SCBFs) and show that SCBFs can significantly reduce the control efforts, especially in the presence of noise, compared to stochastic reciprocal control barrier functions (SRCBFs), and offer a less conservative estimation of safety probability, compared to stochastic zeroing control barrier functions (SZCBFs). Based on this less conservative probabilistic estimation for the proposed notion of SCBFs, we further extend the results to handle high relative degree safety constraints using high-order SCBFs. We demonstrate that the proposed SCBFs achieve good trade-offs of performance and control efforts, both through theoretical analysis and numerical simulations.

Keywords:Stochastic systems, Agents-based systems Abstract: Multi-agent Markov Decision Processes (MMDPs) arise in a variety of applications including target tracking, control of multi-robot swarms, and multiplayer games. A key challenge in MMDPs occurs when the state and action spaces grow exponentially in the number of agents, making computation of an optimal policy computationally intractable for medium- to large-scale problems. One property that has been exploited to mitigate this complexity is transition independence, in which each agent’s transition probabilities are independent of the states and actions of other agents. Transition independence enables factorization of the MMDP and computation of local agent policies but does not hold for arbitrary MMDPs. In this paper, we propose an approximate transition dependence property, called delta-transition dependence and develop a metric for quantifying how far an MMDP deviates from transition independence. Our definition of delta-transition dependence recovers transition independence as a special case when delta is zero. We develop a polynomial time algorithm in the number of agents that achieves a provable bound on the global optimum when the reward functions are monotone increasing and submodular in the agent actions. We evaluate our approach on two case studies, namely, multi-robot control and multi-agent patrolling example.

Keywords:Stochastic systems, Healthcare and medical systems, Network analysis and control Abstract: The COVID-19 pandemic began nearly two years ago, yet schools, businesses, and other organizations are still struggling to keep the risk of disease outbreak low while returning to (near) normal functionality. Observations from this past year suggest that this goal can be achieved through the right balance of mitigation strategies, which may include some combination of mask use, vaccinations, viral testing, and contact tracing. The choice of mitigation measures will be uniquely based on the needs and available resources of each organization. This article presents practical guidance for creating these policies based on an analytical model of disease spread that captures the combined effects of each of these interventions. The resulting guidance is tested through simulation across a wide range of parameters and through synthesis of infection case data on college campuses.

Keywords:Stochastic systems, Nonlinear systems, Lyapunov methods Abstract: In this paper, we investigate the role of Lyapunov functions in evaluating nonlinear-nonquadratic cost functionals for Itô-type nonlinear stochastic difference equations. Specifically, it is shown that the cost functional can be evaluated in closed-form as long as the cost functional is related in a specific way to an underlying Lyapunov function that guarantees asymptotic stability in probability. This result is then used to analyze discrete-time linear stochastic systems as well as nonlinear stochastic dynamical systems with polynomial and multilinear cost functionals.

Keywords:Stochastic systems, Optimization, Filtering Abstract: The joint nonanticipative rate distortion function (NRDF) for a tuple of random processes with individual fidelity criteria is considered. Structural properties of optimal test channel distributions are derived. For the application example of the joint NRDF of a tuple of jointly multivariate Gaussian Markov process with individual square-error fidelity criteria, a realization of the reproduction processes which induces the optimal test channel distribution is derived, and the corresponding joint NRDF is characterized. The analysis of the simplest example, of a tuple of scalar correlated Markov processes, illustrates many of the challenging aspects of such problems.

Keywords:Cooperative control, Autonomous robots, Differential-algebraic systems Abstract: This paper presents a nonlinear and discontinuous control scheme for two-dimensional (2-D) multi-agent multi-swarm navigation that resolves deadlocks, without heuristics, by agents reacting purely to their constrained dynamics. The method is based on extensions of Gauss’s Principle of Least Constraint that dynamically identify, incorporate, and stabilize time-varying sets of constraints and also integrate actuator saturation and delay. The deadlocks are naturally resolved by formulating the 2-D leader following and collision avoidance requirements as decomposed inequality constraints along the X and Y axes and by asymmetrically assigning zero collision avoidance constraint value to a specific branch. Numerical results are presented for two agents and two 15-agent swarms resolving nominal deadlocks at a computation time order of 10 microseconds, demonstrating the efficacy and efficiency of the proposed approach.

Keywords:Cooperative control, Autonomous systems, Lyapunov methods Abstract: This paper presents a time-coordination algorithm for multiple UAVs executing cooperative missions. Unlike previous algorithms, it does not rely on the assumption that the communication between UAVs is bidirectional. Thus, the topology of the inter-UAV information flow can be characterized by digraphs. To achieve coordination with weak connectivity, we design a switching law that orchestrates switching between jointly connected digraph topologies. In accordance with the law, the UAVs with a transmitter switch the topology of their coordination information flow. A Lyapunov analysis shows that a decentralized coordination controller steers coordination errors to a neighborhood of zero. Simulation results illustrate that the algorithm attains coordination objectives with significantly reduced inter-UAV communication compared to previous work.

Keywords:Cooperative control, Distributed control, Constrained control Abstract: Control barrier functions have been widely studied and applied to safety-critical systems, including multi-agent obstacle avoidance problems. In this work, we apply control barrier functions to a collaborative transportation problem involving two unmanned aerial vehicles (UAVs) moving a payload around obstacles as they deliver it to a target location. We develop a target-tracking controller for the UAVs, which is constrained to meet the requirements of payload dynamics and obstacle avoidance. We also present simulation results to demonstrate the benefits of the proposed problem formulation for a multi-obstacle environment.

Keywords:Cooperative control, Learning, Sensor networks Abstract: In this paper we propose two novel distributed consensus-based temporal-difference algorithms for multi-agent off-policy learning of linear approximation of the value function in Markov decision processes. The algorithms are composed of: 1) local parameter updates based on single-agent off-policy algorithms TD(lambda) and ETD(lambda), and 2) a linear dynamic consensus scheme. The algorithms are completely decentralized, allowing: 1) efficient parallelization and 2) applications in which all the agents may have completely different behavior policies and different initial state distributions while evaluating a single target policy. Starting from the properties of the underlying Feller-Markov processes, we show that, under nonrestrictive assumptions, the algorithms weakly converge to a unique consensus point. A discussion is given on the asymptotic parameter values at consensus, including estimation bias and variance. The algorithms' properties are illustrated by characteristic simulation results.

Keywords:Cooperative control, LMIs, Distributed control Abstract: For interconnections of vehicles with complex dynamics, it is commonly suggested to design controllers locally at agents so that agents track the trajectories generated by simplified dynamics. We analyze the performance of such a decoupled control architecture by considering the l_{infty} norm of the local tracking error, which allows to quantify the deviation of the actual system from the simplified system and either provide a justification for the decoupled architecture or show a need to consider instead a coupled architecture. Specifically, we consider first-order protocols as the interaction mechanism among agents and general discrete-time Linear Time-Invariant (LTI) dynamics as agent models which track the trajectories generated by the first-order protocols. For the analysis and synthesis of first-order protocols, we do not assume textit{a priori} knowledge of the connectivity of the graph or the spectrum of the Laplacian matrix, but use results on positive systems to obtain conditions that can scale linearly with network size. We provide bounds on the loss in performance due to imperfect tracking of first order dynamics by higher order agent dynamics and due to disturbances acting locally on agents. Numerical simulations involving generic second order vehicle models with damping illustrate the applicability of the results.

Keywords:Cooperative control, Stability of nonlinear systems Abstract: In this paper, novel dissensus algorithms based on the Oja principal component analysis (PCA) flow are proposed to model opinion dynamics on the unit sphere. The information of the covariance formed by the opinion state of each agent is used to achieve a dissensus equilibrium on unsigned graphs. This differs from most of the existing work where antagonistic interactions represented by negative weights in signed graphs are used to achieve a dissensus equilibrium. The nonlinear algorithm is analyzed under both constant covariance and time varying covariance leading to different behaviors. Stability analysis for the unstable consensus and stable dissensus equilibria is provided under various conditions. The performance of the algorithm is illustrated through a simulation experiment of a multi-agent system.

Keywords:Optimal control, Machine learning, Agents-based systems Abstract: We address the problem of model-free distributed stabilization of heterogeneous multi-agent systems using reinforcement learning (RL). Two algorithms are developed. The first algorithm solves a centralized linear quadratic regulator (LQR) problem without knowing any initial stabilizing gain in advance. The second algorithm builds upon the results of the first algorithm, and extends it to distributed stabilization of multi-agent systems with predefined interaction graphs. Rigorous proofs are provided to show that the proposed algorithms achieve guaranteed convergence if specific conditions hold. A simulation example is presented to demonstrate the theoretical results.

Keywords:Optimal control, Nonlinear systems, Control applications Abstract: We provide a sufficient condition to avoid Lavrentiev phenomena for a general optimal control problem subject to endpoint and state constraints. This condition is expressed in terms of a nonsmooth constrained version of the Pontryagin Maximum Principle. In particular, we prove that, in the absence of abnormal feasible extremals, any process which is locally optimal in the set of original (strict sense) processes must also be locally optimal in a larger set of relaxed extended processes. Our relaxed extended problem includes as special cases both the classical extension by convex relaxation of the velocities set and the impulsive extension of control-polynomial systems with unbounded controls.

Keywords:Optimal control, Nonlinear systems Abstract: To investigate solutions of (near-)optimal control problems, we extend and exploit a notion of homogeneity recently proposed in the literature for discrete-time systems. Assuming the plant dynamics is homogeneous, we first derive a scaling property of its solutions along rays provided the sequence of inputs is suitably modified. We then consider homogeneous cost functions and reveal how the optimal value function scales along rays. This result can be used to construct (near-)optimal inputs on the whole state space by only solving the original problem on a given compact manifold of a smaller dimension. Compared to the related works of the literature, we impose no conditions on the homogeneity degrees. We demonstrate the strength of this new result by presenting a new approximate scheme for value iteration, which is one of the pillars of dynamic programming. The new algorithm provides guaranteed lower and upper estimates of the true value function at any iteration and has several appealing features in terms of reduced computation.

Keywords:Optimal control, Nonlinear systems Abstract: The controller of an input-affine system is determined through minimizing a time-varying objective function, where stabilization is ensured via a Lyapunov function decay condition as constraint. This constraint is incorporated into the objective function via a barrier function. The time-varying minimum of the resulting relaxed cost function is determined by a tracking system. This system is constructed using derivatives up to second order of the relaxed cost function and improves the existing approaches in time-varying optimization. Under some mild assumptions, the tracking system yields a solution which is feasible for all times, and it converges to the optimal solution of the relaxed objective function in a user-defined fixed-time. The effectiveness of these results in comparison to exponential convergence is demonstrated in a case study.

Keywords:Optimal control, Optimization algorithms Abstract: This article is concerned with a recently proposed switching cost aware rounding (SCARP) strategy in the combinatorial integral approximation for mixed-integer optimal control problems (MIOCPs). We consider the case of a control variable that is discrete-valued and distributed on a two-dimensional domain.

While the theoretical results from the one-dimensional case directly apply to the multidimensional setting, the structure of the cost function in the graph-based rounding computation is significantly more involved in the two-dimensional case.

We describe a set up of the computational graph and the traversal algorithm underlying the SCARP strategy that enable a transfer to the two-dimensional setting. We demonstrate the SCARP strategy in this two-dimensional setting using the example of a MIOCP from topology optimization. We compare the graph-based approach to a ground truth computation using an integer linear programming (ILP) solver. The graph-based approach becomes computationally intractable for medium grid sizes. We show that the one-dimensional SCARP algorithm can be employed on a serialization of the grid cells in these cases and still provides an efficient heuristic that yields superior performance compared with that of other rounding heuristics such as sum-up rounding (SUR).

Keywords:Optimal control, Predictive control for linear systems, Autonomous systems Abstract: This paper is concerned with designing a risk-aware controller in an unknown and dynamic environment. In our method, the evolution of the environment state is learned using observational data via Gaussian process regression (GPR). Unfortunately, these learning results provide imperfect distribution information about the environment. To address such distribution errors, we propose a risk-constrained model predictive control (MPC) method that exploits techniques from modern distributionally robust optimization (DRO). To resolve the infinite dimensionality issue inherent in DRO, we derive a tractable semidefinite programming (SDP) problem that upper-bounds the original MPC problem. Furthermore, the SDP problem is reduced to a quadratic program when the constraint function has a decomposable form. The performance and the utility of our method are demonstrated through an autonomous driving problem, and the results show that our controller preserves safety despite errors in learning the behaviors of surrounding vehicles.

Keywords:Stability of nonlinear systems, Lyapunov methods, LMIs Abstract: We consider the absolute stability of discrete-time Lurye systems with SISO/MIMO (non-repeated SISO) nonlinearities that are sector bounded and slope restricted. For this class of systems, we present a parametrization of Lyapunov-Lurye functional (LLF) that is the time-domain equivalence to finite impulse response (FIR) Zames-Falb multipliers. As searches over FIR Zames-Falb multipliers provide the best-known results in the literature, the parametrization here provides the best-known Lyapunov function for absolute stability. A motivation of this alternative is making it easy to analyze the system in the time domain, especially when the frequency domain expression of the system is not straightforward. In this letter, we show the equivalence between the proposed LLF and FIR multipliers theoretically and numerically.

Keywords:Stability of nonlinear systems, Lyapunov methods, LMIs Abstract: This paper concerns the stability problem of neural networks with time-varying delay through the Lyapunov-Krasovskii (L-K) functional method. Appropriate the L-K functionals were constructed with an augmented vector of state term and its derivative term. A novel generalized integral inequality based on free matrices is utilized to estimate the tight upper bound of single integral terms of the L-K functional derivative term. Besides, zero equalities between state term and delayed state term are introduced to reduce conservatism of the stability criterion. To verify the superiority of the proposed method, three well-known examples are given.

Keywords:Flexible structures, Stability of nonlinear systems, LMIs Abstract: A systematic approach to maximise estimates on the region of attraction in the exponential stabilisation of geometrically exact (nonlinear) beam models via boundary feedback is presented. Starting from recently established stability results based on Lyapunov arguments, the main contribution of the presented work is to maximise the analytically found bounds on the initial datum, for which local exponential stability is guaranteed, via search of (optimal) polynomial Lyapunov functionals using an iterative semi-definite programming approach.

Keywords:Stability of nonlinear systems, Lyapunov methods, LMIs Abstract: This paper addresses the problem of stabilization of discrete-time piecewise affine (PWA) systems. The design of a piecewise affine state feedback control law is studied using an implicit representation based on ramp functions. LMI-based stability conditions, obtained from a piecewise quadratic Lyapunov function and the implicit representation, are stated to assess the global exponential stability of the origin of the closed-loop PWA system. Through appropriate congruence transformations and some structural assumptions, a method to design the control law parameters using semidefinite programming is then proposed.

Keywords:Stability of nonlinear systems, Lyapunov methods, Nonlinear systems Abstract: The paper provides a sufficient condition to ensure robust finite-time stability of homogeneous generalized Persidskii systems. The proposed condition is formulated using linear matrix inequalities and it allows to obtain settling time estimates. The results are supported with numerical examples.

Keywords:Stochastic systems, Time-varying systems, LMIs Abstract: In this paper we present some new sufficient conditions for the annular stochastic finite-time stability of a class of stochastic linear time-varying systems. These new conditions are obtained adopting time-varying piecewise quadratic Lyapunov functions rather than the classical quadratic ones. The proposed approach allows us to extend the class of consider domains, which are typically limited to ellipsoidal domains. The proposed finite-time stability conditions can be converted into a feasibility problem based on a set of differential linear matrix inequalities. Two numerical examples are considered to perform a comparison with the previous results, and they show that the new proposed conditions are less conservative than the previous ones.

Keywords:Sampled-data control, Lyapunov methods, Feedback linearization Abstract: Controller design for nonlinear systems with Control Lyapunov Function (CLF) based quadratic programs has recently been successfully applied to a diverse set of difficult control tasks. These existing formulations do not address the gap between design with continuous time models and the discrete time sampled implementation of the resulting controllers, often leading to poor performance on hardware platforms. We propose an approach to close this gap by synthesizing sampled-data counterparts to these CLF-based controllers, specified as quadratically constrained quadratic programs (QCQPs). Assuming feedback linearizability and stable zero-dynamics of a system's continuous time model, we derive practical stability guarantees for the resulting sampled-data system. We demonstrate improved performance of the proposed approach over continuous time counterparts in simulation.

Keywords:Sampled-data control, Adaptive control, Delay systems Abstract: This paper proposes a constructive approach for sampled-data delayed extremum seeking (ES) by using two time-delay approaches: one to averaging and another one to sampled-data control. We first investigate the continuous-time ES with square wave dithers and then expand the proposed time-delay method to its sampled-data implementation with constant delay. By transforming the ES system to a time-delay system, we have developed an improved stability analysis via a novel Lyapunov-Krasovskii functional (LKF). We derive the practical stability conditions in terms of linear matrix inequalities (LMIs) for the resulting time-delay system. Under the assumption of some known bounds on the extremum value of the map and its Hessian, the time-delay approach offers a quantitative calculation on the upper bounds of the dither-sampling period and the constant delays that the ES system is able to tolerate, as well as the ultimate bound of the extremum seeking error. The proposed method also provides a bound on the initial deviation starting from which the solution is ultimately bounded.

Keywords:Sampled-data control, Networked control systems, Linear systems Abstract: This paper studies the attainable performance in the discrete-time H2 optimization under process-independent irregular information transmission between sensor- and actuator-side parts of the controller. In particular, we are concerned with effects of the variability of the sampling rate on the attainable optimal cost. Tight upper and lower bounds on the cost are derived for fixed maximal and average sampling intervals. These bounds are shown to correspond to the maximal and minimal possible variances of sampling intervals. Further insight into the dependence of the performance on properties of the sampling sequence is provided in several special cases.

Keywords:Sampled-data control, Hybrid systems, Networked control systems Abstract: In this paper, we show that: if the Krasovskii regularization of a hybrid system H has complete and discrete solutions, then H has solutions with arbitrarily small separation between jumps under the influence of admissible state perturbations; if H is nominally well-posed and does not have complete discrete solutions, then it does not have solutions with vanishing time between jumps (such as Zeno solutions); if, in addition, there exists a compact set A such that all maximal solutions to H from A are complete, discrete and remain in A, then all solutions converging to A have vanishing time between jumps. The results in this paper demonstrate that a good practice to avoid solutions with arbitrarily fast sampling in Event-Triggered Control (ETC) is to ensure that the closed-loop system is nominally well-posed and that it does not have complete discrete solutions.

Keywords:Sampled-data control, Constrained control, Autonomous systems Abstract: This paper presents conditions for ensuring forward invariance of safe sets under sampled-data system dynamics with piecewise-constant controllers and fixed time-steps. First, we introduce two different metrics to compare the conservativeness of sufficient conditions on forward invariance under piecewise-constant controllers. Then, we propose three approaches for guaranteeing forward invariance, two motivated by continuous-time barrier functions, and one motivated by discrete-time barrier functions. All proposed conditions are control affine, and thus can be incorporated into quadratic programs for control synthesis. We show that the proposed conditions are less conservative than those in earlier studies, and show via simulation how this enables the use of barrier functions that are impossible to implement with the desired time-step using existing methods.

Keywords:Sampled-data control, Constrained control, Stability of linear systems Abstract: The stabilization problem of aperiodic sampled-data linear systems subject to input constraints is dealt with. A state feedback control law is designed to optimize the size of a polyhedral estimate of the region of attraction of the origin (RAO) of the closed-loop system. The control law is derived from the computation of a controlled contractive polytope for the dynamics between two successive sampling instants. The polytope is of low complexity as its number of vertices is fixed a priori. As shown in the numerical example, the polyhedral estimate of the RAO associated with the proposed feedback control is larger than the ones obtained with other approaches in the literature.

Keywords:Autonomous systems, Nonlinear systems, Algebraic/geometric methods Abstract: Control systems often must satisfy strict safety requirements over an extended operating lifetime. Control Barrier Functions (CBFs) are a promising recent approach to constructing simple and safe control policies. This paper proposes a framework for verifying that a CBF guarantees safety for all time and synthesizing CBFs with verifiable safety in polynomial control systems. Our approach is to show that safety of CBFs is equivalent to the non-existence of solutions to a family of polynomial equations, and then prove that this non-existence is equivalent to a pair of sum-of-squares constraints via the Positivstellensatz of algebraic geometry. We develop this Positivstellensatz to verify CBFs, as well as generalization to high-degree systems and multiple CBF constraints. We then propose a set of heuristics for CBF synthesis, including a general alternating-descent heuristic, a specialized approach for compact safe regions, and an approach for convex unsafe regions. Our approach is illustrated on two numerical examples.

Keywords:Constrained control, Aerospace, Autonomous vehicles Abstract: This paper introduces the notion of an Input Constrained Control Barrier Function (ICCBF), as a method to synthesize safety-critical controllers for nonlinear control-affine systems with input constraints. The method identifies a subset of the safe set of states, and constructs a controller to render the subset forward invariant. The feedback controller is represented as the solution to a quadratic program, which can be solved efficiently for real-time implementation. Furthermore, we show that ICCBFs are a generalization of Higher Order Control Barrier Functions, and thus are applicable to systems of non-uniform relative degree. Simulation results are presented for the adaptive cruise control problem, and a spacecraft rendezvous problem.

Keywords:Constrained control, Autonomous systems, Aerospace Abstract: This paper presents methodologies for ensuring forward invariance of sublevel sets of constraint functions with high-relative-degree with respect to the system dynamics and in the presence of input constraints. We show that such constraint functions can be converted into special Zeroing Control Barrier Functions (ZCBFs), which, by construction, generate sufficient conditions for rendering the state always inside a sublevel set of the constraint function in the presence of input constraints. We present a general form for one such ZCBF, as well as a special case applicable to a specific class of systems. We conclude with a comparison of system trajectories under the two ZCBFs developed and prior literature, and a case study for an asteroid observation problem using quadratic-program based controllers to enforce the ZCBF condition.

Keywords:Constrained control, Robotics, Nonlinear systems Abstract: Task-space Passivity-Based Control (PBC) for manipulation has numerous appealing properties, including robustness to modeling error and safety for human-robot interaction. Existing methods perform poorly in singular configurations, however, such as when all the robot's joints are fully extended. Additionally, standard methods for constrained task-space PBC guarantee passivity only when constrains are not active. We propose a convex optimization-based control scheme which provides guarantees of singularity avoidance, passivity, and feasibility. This work paves the way for PBC with passivity guarantees under other types of constraints as well, including joint limits and contact/friction constraints. The proposed methods are validated in simulation experiments on a 7 degree-of-freedom manipulator.

Keywords:Constrained control, Stability of nonlinear systems, Robotics Abstract: This paper presents an approach to deal with safety of dynamical systems in presence of multiple non-convex unsafe sets. While optimal control and model predictive control strategies can be employed in these scenarios, they suffer from high computational complexity in case of general nonlinear systems. Leveraging control barrier functions, on the other hand, results in computationally efficient control algorithms. Nevertheless, when safety guarantees have to be enforced alongside stability objectives, undesired asymptotically stable equilibrium points have been shown to arise. We propose a computationally efficient optimization-based approach which allows us to ensure safety of dynamical systems without introducing undesired equilibria even in presence of multiple non-convex unsafe sets. The developed control algorithm is showcased in simulation and in a real robot navigation application.

Keywords:Optimal control, Optimization, Predictive control for nonlinear systems Abstract: Safety is one of the fundamental problems in robotics. Recently, one-step or multi-step optimal control problems for discrete-time nonlinear dynamical system were formulated to offer tracking stability using control Lyapunov functions (CLFs) while subject to input constraints as well as safety-critical constraints using control barrier functions (CBFs). The limitations of these existing approaches are mainly about feasibility and safety. In the existing approaches, the feasibility of the optimization and the system safety cannot be enhanced at the same time theoretically. In this paper, we propose two formulations that unifies CLFs and CBFs under the framework of nonlinear model predictive control (NMPC). In the proposed formulations, safety criteria is commonly formulated as CBF constraints and stability performance is ensured with either a terminal cost function or CLF constraints. Relaxing variables are introduced on the CBF constraints to resolve the tradeoff between feasibility and safety so that they can be enhanced at the same. The advantages about feasibility and safety of proposed formulations compared with existing methods are analyzed theoretically and validated with numerical results.

Keywords:LMIs, Observers for nonlinear systems, Fuzzy systems Abstract: In this paper, a 3D point feature depth and camera focal length estimation is proposed, using a partially calibrated low cost monocular camera. The camera intrinsic parameters are known, except for the focal length, which may vary across different views. The camera perspective projection model is augmented using dynamic extension approach, then decomposed into two interconnected subsystems. The subsystems are described as quasi-Linear Parameter Varying (qLPV) systems with unmeasured premise variables for which an interconnected fuzzy observer is designed. Necessary and sufficient conditions to ensure the observer existence are presented. The error convergence analysis is performed based on Lyapunov theory associated with Lipchitz condition. Gains that guarantee the asymptotic stability of the estimation error are computed in terms of Linear Matrix Inequalities (LMI) with eigenvalues clustering in LMI region to improve the estimation performance.

King Abdullah University of Science and Technology (KAUST)

Keywords:LMIs, Observers for nonlinear systems, Nonlinear systems Abstract: This paper deals with the observer design for a class of nonlinear Lipschitz systems via Linear Matrix Inequalities~(LMIs) based approach. Using some mathematical matrix decompositions, general LMI conditions ensuring the exponential convergence of the estimation error are provided. Thanks to linear and/or nonlinear transformations, these LMIs are enhanced from feasibility viewpoint.

Keywords:Sensor fusion, Observers for nonlinear systems, Estimation Abstract: In this work we solve the position-aided 3D navigation problem using a nonlinear estimation scheme. More precisely, we propose a nonlinear observer to estimate the full state of the vehicle (position, velocity, orientation and gyro bias) from IMU and position measurements. The proposed observer does not introduce additional auxiliary states and is shown to guarantee semi-global exponential stability. The performance of the observer is shown, through simulation, to overcome the state-of-the-art approach that assumes negligible accelerations.

Keywords:Observers for nonlinear systems, Estimation, Nonlinear systems Abstract: This work deals with the problem of designing observers for the estimation of a single function of the states for discrete–time nonlinear systems. Necessary and sufficient conditions for the existence of lower order functional observers with linear dynamics and linear output map are derived. The results provide a direct generalization to Luenberger’s linear theory of functional observers. The design methodology is tested on a non-isothermal CSTR case study.

Keywords:Observers for nonlinear systems, Estimation, Nonlinear systems Abstract: This paper proposes novel set-theoretic approaches for recursive state estimation in bounded-error discrete-time nonlinear systems subject to nonlinear observations/constraints. By transforming the polytopes that are characterized as zonotope bundles (ZB) and/or constrained zonotopes (CZ), from the state space to the space of the generators of ZB/CZ, we leverage a recent result on the remainder-form mixed-monotone decomposition functions to compute the propagated set, i.e., a ZB/CZ that is guaranteed to enclose the set of the state trajectories of the considered system. Further, by applying the remainder-form decomposition functions to the nonlinear observation function, we derive the updated set, i.e., an enclosing ZB/CZ of the intersection of the propagated set and the set of states that are compatible/consistent with the observations/constraints. In addition, we show that the mean value extension result in [1] for computing propagated sets can also be extended to compute the updated set when the observation function is nonlinear.

Keywords:Observers for nonlinear systems, Kalman filtering, Filtering Abstract: Attitude estimation is a core problem in many rigid body systems. The scientific literature proposed a lot of filters and algorithms to estimate pose and velocity of such rigid body systems. In this paper we compare the extended Kalman filter, that represents a generalization of the standard Kalman filter for non-linear systems, and a second-order-optimal minimum-energy filter on the matrix Lie group TSE(2). Optimality refers to a cost function in the unknown model error and measurement error. The measurement system consists of a GPS-like, that provides the position of two antennas on the vehicle, and an INS unit, that provides the linear and angular velocity.

Keywords:Nonlinear systems, Distributed parameter systems Abstract: We investigate abstract nonlinear infinite dimensional systems of the form: dot{x}(t) in Ax(t)-M(x(t))+Bu(t). These are obtained by subtracting a nonlinear maximal monotone (possibly multi-valued) operator M from the semigroup generator A of a linear system. While the linear system may have unbounded linear damping (for instance, boundary damping), the operator M is "bounded" in the sense that it is defined on the whole state space. We show that under some assumptions, such nonlinear infinite dimensional systems have unique classical and generalized solutions. Moreover, these solutions are Lipschitz continuous on any finite time interval and right differentiable. Our approach uses the theory of maximal monotone operators and the Crandall-Pazy theorem about nonlinear contraction semigroups, which we apply to a Lax-Phillips type nonlinear semigroup that represents the entire system, with states and input signals.

Keywords:Distributed parameter systems, Stability of linear systems, Flexible structures Abstract: We investigate the stability of the wave equation with spatial dependent coefficients on a bounded multidimensional domain. The system is stabilized via a scattering passive feedback law. We formulate the wave equation in a port-Hamiltonian fashion and show that the system is semi-uniform stable, which is a stability concept between exponential stability and strong stability. Hence, this also implies strong stability of the system. In particular, classical solutions are uniformly stable. This will be achieved by showing that the spectrum of the port-Hamiltonian operator is contained in the left half plane mathbb{C}_{-} and the port-Hamiltonian operator generates a contraction semigroup. Moreover, we show that the spectrum consists of eigenvalues only and the port-Hamiltonian operator has a compact resolvent.

Keywords:Stability of linear systems, Distributed parameter systems, Fluid flow systems Abstract: We consider the strong stabilization of a gravity-capillary water waves in a rectangular tank. The control acts on one lateral boundary, by producing the horizontal acceleration of the water, as a multiple of a scalar input function u, times a given function h of the height along the active boundary. We first establish the well-posedness of the whole water waves system by formulating this system as an abstract linear control system with the state z given in terms of the water level zeta. Then we show that for suitable functions h, there exists a functional F such that the closed-loop system, with the state feedback u=Fz, is strongly stable. Moreover, for the initial data in the domain of the semigroup generator, the energy of the control system decays like (1+t)^{-frac{3}{2}}. Our approach is based on a detailed construction of the Dirichlet to Neumann and Neumann to Neumann operators associated with certain edges of the domain, as well as a general non-uniform stabilization result by Ammari and Tucsnak (2001).

Keywords:Distributed parameter systems, Lyapunov methods, Simulation Abstract: In this paper, we consider the stabilization of a clamped beam with torque and force actuation on a mass situated at the other side of the beam. We show how to derive the model starting from the Principle of Least Action and we rewrite it as the interconnection between two port-Hamiltonian systems: an infinite dimensional system and a finite dimensional one. Therefore, we propose a control law that allows to exponentially stabilize the origin of the closed-loop system. Further, we show how to explicitly compute, from the system and control parameters, the exponential decreasing rate of the system’s norm along time. For a sake of conciseness, we only sketch the theoretical proofs. Finally, we provide some numerical simulations illustrating the closed-loop performances with different choices of the control parameters.

Keywords:Fluid flow systems, Stability of nonlinear systems, LMIs Abstract: This paper considers the stability analysis of fluid flows in 2D channels. By representing the dynamics of the flow as the feedback interconnection of a linear system with a memoryless and lossless nonlinearity, passivity theory is used to bound the critical Reynolds number governing the transition from laminar to turbulent flow. The main result shows how the introduction of a loop transformation into the feedback system can increase the critical energy Reynolds number for 2D channel flow from 87.7 to 190.0 whilst still using the system's kinetic energy as the Lyapunov function.

Keywords:Lyapunov methods, Fluid flow systems, Stability of nonlinear systems Abstract: This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the nonlinearity on elliptical sets. This approach reduces conservatism and improves estimates for regions of attraction and bounds on permissible perturbation amplitudes over related methods that employ quadratic constraints on spherical sets. We present and investigate two algorithms for performing the analysis: an iterative method that refines the analysis by solving a sequence of semi-definite programs, and another based on solving a generalized eigenvalue problem with lower computational complexity, but at the cost of some precision in the final solution. The proposed algorithms are demonstrated on low-order mechanistic models of transitional flows. We further compare accuracy and computational complexity with analysis based on sum-of-squares optimization and direct-adjoint looping methods.

Keywords:Networked control systems, Constrained control, Control over communications Abstract: In this work we consider the problem of remote control over lossy networks for systems subject to constraints. The objective is to devise a strategy for tracking reference signals while satisfying constraints under any network condition. We consider a remote Model Predictive Controller (MPC) and a local smart actuator able to stabilize the system when needed, in combination with a suitable mechanism to tackle packet losses. We show that the proposed algorithm allows us to enforce constraints without any assumption on the network, while we prove the convergence to constant desired references under mild assumptions. Simulations with real Wi-Fi communication data show the benefits of the algorithm with respect to other networked MPCs. The proposed solution is useful to combine high performances of advanced control technologies that cannot be implemented on-board and safety of locally controlled systems.

Keywords:Networked control systems, Control of networks, Control over communications Abstract: In this paper, we study the prioritized transmission schemes for event-triggered wireless networked control systems (WNCSs) with smart (i.e., with computational power) or conventional (i.e., without computational power) sensors. When considering conventional sensors, the estimated state available to the controller is based on the intermittently received raw measurements. We show that the priority measure is associated with the statistical properties of the observations conforming with the cost of information loss (CoIL). Next, we consider the case of smart sensors, and despite the fact that CoIL can also be deployed, we deduce that it is more beneficial to use the available measurements as suggested by the value of information (VoI). The derived VoI incorporates the channel conditions and is compatible with distributed implementation. The impact of adopting each priority measure on the performance is evaluated via simulations.

Keywords:Networked control systems, Game theory, Decentralized control Abstract: In stochastic control, information structure arguments have been crucial for stochastic analysis. Such an approach is often called static reduction in dynamic team theory (or decentralized stochastic control) and has been an effective method for establishing existence and approximation results for optimal policies. In this paper, we classify such static reductions into three categories: (i) those that are policy-independent (introduced by Witsenhausen), (ii) those that are policy-dependent (introduced by Ho and Chu for partially nested dynamic teams), and (iii) static measurement with control-sharing reduction (where the measurements become static although control actions are shared according to the partially nested information structure). For these reductions, while there exist bijection relationships between globally optimal solutions of dynamic teams and their reductions, in general there is no bijection for person-by-person optimal policies. We also establish a similar result (but not identical) concerning stationary solutions. We present sufficient conditions under which bijection relationships hold. Under static measurement with control-sharing reduction, connections between optimality concepts can be established under relaxed conditions. An implication is a convexity characterization of dynamic teams under static measurement with control-sharing reduction. Some counterparts for stochastic games are also discussed.

Keywords:Networked control systems, Delay systems, Modeling Abstract: We study modeling for a class of random delay and packet drop channels, that are almost ubiquitous in networked control systems. Such a class of random channels are temporally correlated, assumed to admit a Markovian description in the known literature, and thus the theory of Markov jump linear systems can be applied for design of the stabilizing and optimal or robust controllers. However, why and how such a Markov channel model is derived remained to be unclear. Based on some simple and reasonable hypothesis on the channel, we show that the class of random delay and packet drop channels can indeed be modeled by finite state discrete Markov chains, thereby enabling application of the theory of Markov jump linear systems to design of the networked control system over such a class of random channels. On the other hand, the channel model presented in this paper differs from the existing one in that it not only includes the derivation of the channel states and transition probability matrix but also mitigates several modeling issues of the existing work, thereby providing a solid footing to the new Markov channel model obtained in this paper.

Keywords:Networked control systems, Control over communications, Optimization algorithms Abstract: This paper considers the problem of task-dependent (top-down) attention allocation for vision-based autonomous navigation using known landmarks. Unlike the existing paradigm in which landmark selection is formulated as a combinatorial optimization problem, we model it as a resource allocation problem where the decision-maker (DM) is granted extra freedom to control the degree of attention to each landmark. The total resource available to DM is expressed in terms of the capacity limit of the in-take information flow, which is quantified by the directed information from the state of the environment to the DM’s observation. We consider a receding horizon implementation of such a controlled sensing scheme in the Linear-Quadratic-Gaussian (LQG) regime. The convex-concave procedure is applied in each time step, whose time complexity is shown to be linear in the horizon length if the alternating direction method of multipliers (ADMM) is used. Numerical studies show that the proposed formulation is sparsity-promoting in the sense that it tends to allocate zero data rate to uninformative landmarks.

Keywords:Networked control systems, Control of networks, Optimal control Abstract: In this paper, we propose a formation maneuver control strategy to steer a triangulated formation from two dimensional (2D) space to three dimensional (3D) space, while maintaining the shape of each triangle during the transition. To describe the desired 3D formation shape, we adopt a weak rigidity function containing both distance and angle constraints, together with a sign function. The local shapes are preserved by restricting agents' motions to the null-space of the distance rigidity function. Furthermore, we formulate this formation maneuver control as an optimal control problem to minimize the control efforts subject to system dynamics, local shape-preserving constraints, initial and terminal boundary conditions, which can be solved via a nonlinear programming solver. In the end, two simulation examples are provided to show the effectiveness of our formation control strategy.

Keywords:Agents-based systems, Estimation, Autonomous systems Abstract: In this paper, we propose a distributed protocol for multi-agent systems to estimate and track changes to the diameter, and radius of a network with time-varying topology, as well as the eccentricity of each agent within it.

The main strengths of the proposed protocol are its finite-time convergence and robustness to re-initialization, i.e., if there are changes in the network topology or in the agents' states during the protocol execution then it does not need to be re-initialized to converge to the correct estimation at the steady-state.

The expected estimation error of the protocol can be traded-off by increasing the size of locally exchanged messages.

We provide a theoretical characterization of the expected steady-state error and some numerical simulations.

Keywords:Large-scale systems, Network analysis and control Abstract: In this paper, we consider the terminal behaviour of resistive electrical networks that are subject to changes or re-design. Specifically, we study the robustness of the effective resistance as a measure of this terminal behaviour. We give an explicit expression of how the effective resistance changes as a result of network perturbations, e.g., the addition/deletion of edges or changes in the conductance value. This expression has a clear interpretation and allows for efficient numerical evaluation. We extend this result to the total effective resistance, which can be regarded as a performance measure of consensus networks. In addition, these results are used to derive a graph theoretical characterisation of the effective resistance.

Keywords:Adaptive control, Decentralized control, Stability of nonlinear systems Abstract: Flow and storage volume regulation is essential for the adequate transport and management of energy resources in district heating systems. In this letter, we propose a novel and suitably tailored---decentralized---adaptive control scheme addressing this problem whilst offering closed-loop stability guarantees. We focus on a system configuration comprising multiple heat producers, consumers and storage tanks exchanging energy through a common distribution network, which are features of modern and prospective district heating installations. The proposed controller is based on passivity, backstepping and (indirect) adaptive control theory.

Keywords:Optimization algorithms, Quantized systems, Large-scale systems Abstract: In this paper we analyze the problem of optimal task scheduling for data centers. Given the available resources and tasks, we propose a fast distributed iterative algorithm which operates over a large scale network of nodes and allows each of the interconnected nodes to reach agreement to an optimal solution in a finite number of time steps. More specifically, the algorithm (i) is guaranteed to converge to the exact optimal scheduling plan in a finite number of time steps and, (ii) once the goal of task scheduling is achieved, it exhibits distributed stopping capabilities (i.e., it allows the nodes to distributely determine whether they can terminate the operation of the algorithm). Furthermore, the proposed algorithm operates exclusively with quantized values (i.e., the information stored, processed and exchanged between neighboring agents is subject to deterministic uniform quantization) and relies on event-driven updates (e.g., to reduce energy consumption, communication bandwidth, network congestion, and/or processor usage). We also provide examples to illustrate the operation, performance, and potential advantages of the proposed algorithm. Finally, by using extensive empirical evaluations through simulations we show that the operation of our proposed algorithm is suitable for large scale networks such as data centers.

Keywords:Optimization algorithms, Large-scale systems, Distributed control Abstract: In this paper we consider a distributed stochastic optimization framework in which agents in a network aim to cooperatively learn an optimal network-wide policy. The goal is to compute local functions to minimize the expected value of a given cost, subject to individual constraints and average coupling constraints. In order to handle the challenges of the distributed stochastic context, we resort to a Lagrangian duality approach that allows us to derive an associated stochastic dual problem with a separable structure. Thus, we propose a distributed algorithm, without a central coordinator, that exploits consensus iterations and stochastic approximation to find an optimal solution to the problem, with attractive scalability properties. We demonstrate convergence of the proposed scheme and validate its behavior through simulations.

Keywords:Control of networks, Distributed control, Optimization algorithms Abstract: This paper deals with linear algebraic equations where the global coefficient matrix and constant vector are given respectively, by the summation of the coefficient matrices and constant vectors of the individual agents. Our approach is based on reformulating the original problem as an unconstrained optimization. Based on this exact reformulation, we first provide a gradient-based, centralized algorithm which serves as a reference for the ensuing design of distributed algorithms. We propose two sets of exponentially stable continuous-time distributed algorithms that do not require the individual agent matrices to be invertible, and are based on estimating non-distributed terms in the centralized algorithm using dynamic average consensus. The first algorithm works for time-varying weight-balanced directed networks, and the second algorithm works for general directed networks for which the communication graphs might not be balanced. Numerical simulations illustrate our results.

Keywords:Aerospace, Lyapunov methods, Control applications Abstract: Prior results on target localization and circumnavigation with bearing measurements in R2 are extended with integral action, resulting in a control system that is robust to bounded load disturbances on the control inputs. Such disturbances may arise in practice due to modeling errors and need to be considered to ensure small tracking errors. The control inputs are modeled as the system velocities in the bearing and orthogonal bearing directions, facilitating an implementation on both aerial and ground vehicles. This is demonstrated in a simulation example, followed by an experimental application with ground-based vehicle circumnavigation, highlighting the performance and importance of using the proposed controllers.

Keywords:Aerospace, Numerical algorithms, Uncertain systems Abstract: Computing long-term collision probability in space encounters is usually based on integration of a multivariate Gaussian distribution over the volume of initial conditions which generate collisions in the considered time interval. As this collision set is very difficult to determine analytically, for practical computation various simplifications are made in the literature. We present a new method for computing the collision probability based on two steps. Firstly, a higher-order outer-approximation of the swept-volume by a polynomial superlevel set is obtained as an optimal solution of a polynomial optimization problem. This has the advantage of providing approximate closed-form descriptions of the collision-prone states which can then be effectively used for long-term and repeated conjunctions analysis. From a computational viewpoint, one has to solve a hierarchy of linear matrix inequality problems of increasing size, which provide approximations (i) of increasing accuracy and (ii) convergent in volume to the original set. Secondly, once such a polynomial representation is computed, a high-order quadrature scheme for volumes implicitly defined by a polynomial superlevel sets is employed. Finally, the method is illustrated on some numerical examples borrowed from the literature.

Keywords:Flight control, Aerospace, Optimization Abstract: Trajectory tracking control for winged eVTOL aircraft is complicated by the high-angle-of-attack aerodynamics experienced during navigational flight occurring immediately after takeoff and immediately before landing. The total energy use of the vehicle can be reduced and the control performance can be improved by appropriately considering the pitch angle of the vehicle in varying flight conditions. We present a review of high-angle-of-attack aerodynamic models as well as an algorithm for finding the optimal pitch and thrust of a winged eVTOL throughout its flight regime. We show simulation results demonstrating a 75% reduction in tracking error over our previous work while maintaining a similar average thrust and an 85% reduction in tracking error over using a multirotor-like controller.

Keywords:Optimal control, Aerospace Abstract: This paper studies the problem of vertical powered landing through a non-negligible density atmosphere. Several constraints are considered, one of them prevents hovering flight. The findings of the paper extend the results from the literature on atmosphere-free problems. The main contribution establishes the nature of the fuel-optimal control sequence. Sufficient and necessary conditions are provided that guarantee the Min-Max nature of the normal extremals. Abnormal extremals are also shown to be either Min or Max.

Keywords:Modeling, Aerospace Abstract: In this paper, we propose a Koopman operator based approach to describe the nonlinear dynamics of a quadrotor on SE(3) in terms of an infinite-dimensional linear system which evolves in the space of observable functions (lifted space) and which is more appropriate for control design purposes. The major challenge when using the Koopman operator is the characterization of a set of observable functions that can span the lifted space. Recent methods either use tools from machine learning to learn the observable functions or guess a suitable set of observables that best describes the nonlinear dynamics. Instead of guessing or learning the observables, in this work we derive them in a systematic way for the quadrotor dynamics on SE(3). In addition, we prove that the proposed sequence of observable functions converges pointwise to the zero function, which allows us to select only a finite set of observable functions to form (an approximation of) the lifted space. Our theoretical analysis is also confirmed by numerical simulations which demonstrate that by increasing the dimension of the lifted space, the derived linear state space model can approximate the nonlinear quadrotor dynamics more accurately.

Keywords:Neural networks, Machine learning, Formal Verification/Synthesis Abstract: Learning-based methods could provide solutions to many of the long-standing challenges in control. However, the neural networks (NNs) commonly used in modern learning approaches present substantial challenges for analyzing the resulting control systems' safety properties. Fortunately, a new body of literature could provide tractable methods for analysis and verification of these high dimensional, highly nonlinear representations. This tutorial first introduces and unifies recent techniques (many of which originated in the computer vision and machine learning communities) for verifying robustness properties of NNs. The techniques are then extended to provide formal guarantees of neural feedback loops (e.g., closed-loop system with NN control policy). The provided tools are shown to enable closed-loop reachability analysis and robust deep reinforcement learning.

Keywords:Neural networks, LMIs, Robust control Abstract: Neural networks have become increasingly effective at many difficult machine learning tasks. However, the nonlinear and large-scale nature of neural networks makes them hard to analyze, and, therefore, they are mostly used as black-box models without formal guarantees. This issue becomes even more complicated when neural networks are used in learning-enabled closed-loop systems, where a small perturbation can substantially impact the system being controlled. Therefore, it is of utmost importance to develop tools that can provide useful certificates of stability, safety, and robustness for neural network-driven systems.

In this overview, we present a convex optimization framework for the analysis of neural networks. The main idea is to abstract hard-to-analyze components of a neural network (e.g., the nonlinear activation functions) with the formalism of quadratic constraints. This abstraction allows us to reason about various properties of neural networks (safety, robustness, generalization, stability in closed-loop settings, etc.) via semidefinite programming.

Keywords:Power systems, Predictive control for nonlinear systems, Smart grid Abstract: Control systems dedicated to manage power transmission networks are facing deisgn and deployment problems due to uncertainties and input time-delays, which may affect the overall system's performance and stability. To face situations due to the violations of the power lines thermal limits, transmission system operators (TSOs) as the French RTE aim to focus on splitting the entire system in sub-transmission areas (zones), and operate optimal management of battery devices and renewable production curtailments. The target of the present paper is to describe a time-delay model-based control approach for managing the electric power flow in sub-transmission zones dealing with model uncertainties while ensuring problem feasibility. Simulations on a case study of industrial interest validate the proposed method.

Keywords:Automotive systems, Modeling, Predictive control for nonlinear systems Abstract: Fuel cell systems that utilize anode recirculation generally require a purge process to remove accumulated gaseous impurities from the anode recirculation system. Especially the accumulation of nitrogen leads to a decrease of the cell voltage and therefore a reduced stack efficiency. However, unconsumed hydrogen is lost during the purge process, resulting in a decrease of hydrogen utilization. Therefore, an optimal purge control can help to maximize the overall system efficiency.

In order to determine and predict the influence of the purge valve opening on the system efficiency with respect to the hydrogen utilization and the stack efficiency we develop a control-oriented model of a PEMFC anode recirculation system. We then set up a model predictive purge controller and compare its performance to two standard purge strategies using the NEDC vehicle test cycle.

Keywords:Learning, Smart grid, Predictive control for nonlinear systems Abstract: The cost of the power distribution infrastructures is driven by the peak power encountered in the system. At the local level, consumers are connected to a common transformer, which must be sized to withstand the peak power. With the electrification of our society, this issue is becoming more severe, and the distribution network operators consider billing consumers in the function of their power peak demand. The ideal peak power cost ought to be charged in function of the peak power at the infrastructure level (typ. transformers), and leave it to the consumers to manage their collective power peak. This management is, however, not trivial. In this paper, we consider a multi-agent residential smart grid system, where each agent has local renewable energy production and energy storage, and all agents are connected to a local transformer. The objective is to develop an optimal policy that minimizes the economic cost consisting of both the spot-market cost for each consumer and the collective peak-power cost of the agents. We propose to use a parametric Model Predictive Control (MPC)-scheme to approximate the optimal policy. The optimality of this policy is limited by its finite horizon and inaccurate forecasts of the local power production-consumption. A Deterministic Policy Gradient (DPG) method is deployed to adjust the MPC parameters and improve the MPC policy. Our simulations show that the proposed MPC-based Reinforcement Learning (RL) method is effective at decreasing the long-term economic cost for this smart grid problem.

Keywords:Predictive control for nonlinear systems, Smart grid, Distributed control Abstract: This paper proposes a distributed Model Predictive Control (MPC) approach to coordinate flexible resources as a virtual storage plant (VSP) for delivering ancillary services to the power network with high renewable penetration. We consider VSPs comprising battery systems and Heating, Ventilation and Air Conditioning (HVAC) systems acting as storages. The proposed control framework is based on stochastic MPC and an alternating direction method of multipliers (ADMM)-based fully distributed algorithm. The main control objective is to timely track a time-varying automatic generation control signal from the area control center of the electric grid by optimally coordinating an arbitrary number of HVAC and battery units. The uncertainty is handled by randomized techniques, with a number of scenarios guaranteeing a robust constraint satisfaction of the stochastic convexified problem formulation. The effectiveness of the MPC scheme is tested through a numerical case study, where the proposed MPC framework can systematically deal with the system constraints and technical service requirements, and the procured nearly real-time unit dispatch can compensate for the impact of renewables on the network operation.

Keywords:Smart grid, Machine learning, Optimal control Abstract: Many electrical loads seek to maintain a measurement, such as a temperature, pressure, flow rate, fluid level or charge state, near a setpoint. In some cases, setpoints can be adjusted slightly without noticeably affecting quality of service. Small setpoint adjustments have an indirect effect on power use that, when aggregated over a large number of loads, can be significant. This paper develops a framework to provide services to the power grid by adjusting device setpoints. The framework has several practical advantages: it scales to very large load aggregations; accommodates a wide variety of loads, including those with nonlinear behavior; and requires little sensing or communication and no private information. The framework involves (1) learning a model to predict aggregate power under baseline operation, (2) exciting the system to identify a model relating setpoint perturbations to aggregate power perturbations, and (3) embedding baseline predictions and the perturbation model in load-shifting optimization. Simulations of a 50,000-load, 115-MW aggregation in the Texas storms of February, 2021, suggest that this framework can reduce peak demand, arbitrage dynamic energy prices or carbon intensities, and provide utility demand response or wholesale ancillary services.

Keywords:Smart grid, Output regulation, Robust control Abstract: This paper tackles the problem of robust output set-point tracking for a power flow controller (PFC) for meshed DC micro-grids. The PFC is a power electronics device used to control the power (or current) flow in the lines of the grid and act as a DC circuit breaker. The state-space model of this system is bilinear with uncertain dynamics and a polynomial output. In the proposed design, the plant is first extend with an integral action on the tracking error. The cascade model composed by the plant and the integrator is then stabilized by means of a state-feedback law, with a forwarding approach. If the plant parameters are sufficiently close to their nominal value, robust regulation is then achieved. Simulations are given to validate the results.

Keywords:Variable-structure/sliding-mode control, Constrained control Abstract: The design of sliding-mode controllers with continuous control signals in the presence of saturated actuators is a challenging task. This paper analyzes existing formal assumptions required by such designs, and proposes a new controller design that is applicable for a large class of linear time-invariant plants. The proposed design is based on the suitable selection of a sliding surface, to which the conditioned super-twisting algorithm is then applied. Stability conditions for the closed loop in presence of perturbations with bounded amplitude and slope are given. Simulation results obtained with the model of a continuous flow heater for silicon wafer processing illustrate the presented approach.

Keywords:Variable-structure/sliding-mode control, Lyapunov methods, Nonlinear systems Abstract: A discrete-time implementation of a continuous-time adaptive gain sliding mode control law for a system with matched disturbance is presented. The discrete-time control algorithm is derived from the solution of the nominal continuous-time closed-loop dynamics. This approach ensures elimination of discretization chattering as well as proper disturbance rejection. Slight modifications of the resulting discrete-time control law are proposed to guarantee ultimate boundedness of the sliding variable and the adaptive gain which is formally proven by means of Lyapunov arguments. Prevention of discretization chattering and disturbance attenuation properties are validated in a simulation and compared to other approaches.

Keywords:Variable-structure/sliding-mode control, Nonlinear output feedback, Sampled-data control Abstract: A new chattering-mitigation method is proposed for discontinuous dynamics discretization. Its application to feedback and output-feedback homogeneous sliding-modes significantly diminishes the control chattering in the absence of noises, while preserving the system accuracy in their presence. Numeric experiments illustrate the approach efficacy.

Keywords:Variable-structure/sliding-mode control, Observers for nonlinear systems, Uncertain systems Abstract: This paper proposes global sliding mode observers for a class of one-degree-of-freedom mechanical systems. For the observer design, besides the usual Coriolis and centrifugal forces, we consider uncertain dry frictions and disturbances. Moreover, the system is not required to be bounded-input bounded-state stable, rendering the observer design problem challenging. The observer design exploits the specific relationships between the inertia and Coriolis terms providing a sliding-mode observer, with global theoretically exact finite-time and fixed-time convergence to the velocities of the mechanical system. The efficiency of the proposed observer is validated through simulations on an inverted pendulum.

Keywords:Variable-structure/sliding-mode control, Robust adaptive control, Nonlinear systems Abstract: In this paper, an eigenvalue-based discretization scheme is applied to a novel adaptive super-twisting-algorithm. Following the proposed procedure the discretization chattering effect is avoided entirely. An attractive property of the adaptation law is the insensitivity of the closed-loop system to overly large gains which in existing laws potentially leads to instability. Using Lyapunov's direct method the stability of the feedback loop is shown. Numerical examples underline the beneficial properties of the proposed methodology.

Keywords:Variable-structure/sliding-mode control, Robust control, Constrained control Abstract: Terminal sliding mode (TSM) control algorithm and its non-singular refinement have been elaborated for two decades and belong, since then, to a broader class of the finite-time controllers, which are known to be robust against the matched perturbations. While TSM manifold allows for different forms of the sliding variable, which are satisfying the q/p power ratio for the measurable output state, we demonstrate that q/p=0.5 is the optimal one for the second-order Newton's motion dynamics with a bounded control action. The paper analyzes the time-optimal sliding surface and, based thereupon, claims the optimal TSM control for the second-order motion systems. It is stressed that the optimal TSM control is fully inline with the Fuller's problem of optimal switching which minimizes the settling time, i.e. with time-optimal control of an unperturbed double-integrator. It is also shown that for the given plant characteristics, i.e. the overall inertia and the maximal control magnitude, there is no need for any additional control parameters. The single design parameter of the surface might (but not necessarily need to) be used for either driving the system on a boundary layer of the twisting mode, or for forcing it into robust terminal sliding mode. Additional insight is given into the finite-time convergence of TSM and robustness against the bounded perturbations. Numerical examples with different upper-bounded perturbations are demonstrated.

Keywords:Agents-based systems, Algebraic/geometric methods Abstract: This work establishes properties of the normalized rigidity matrix in two- and three-dimensional spaces. The upper bounds of the normalized rigidity matrix singular values are derived for minimally and infinitesimally rigid frameworks in two- and three-dimensional spaces. We prove that the transformation of a framework does not affect the normalized rigidity matrix properties. The largest minimum singular value of the normalized rigidity matrix for a rigid framework of three agents in two-dimensional space is given as well as necessary and sufficient conditions to reach that value. These results can be used in stability analysis and control design of a distance-based formation control. The numerical simulation for multi-agent systems in two-dimensional space illustrates the theoretical results. Moreover, a simulation in a robot simulator demonstrates the spectral properties of the normalized rigidity matrix.

Keywords:Agents-based systems, Autonomous robots, Distributed control Abstract: This paper proposes a novel distributed technique to induce collective motions in affine formation control. Instead of the traditional leader-follower strategy, we propose modifying the original weights that build the Laplacian matrix so that a designed steady-state motion of the desired shape emerges from the agents' local interactions. The proposed technique allows a rich collection of collective motions such as rotations around the centroid, translations, scalings, and shearings of a reference shape. These motions can be applied in useful collective behaviors such as shaped consensus (the rendezvous with a particular shape), escorting one of the team agents, or area coverage. We prove the global stability and effectiveness of our proposed technique rigorously, and we provide some illustrative numerical simulations.

Keywords:Nonholonomic systems, Robotics, Nonlinear output feedback Abstract: We address the full-consensus problem for multiagent nonholonomic systems via output feedback. That is, consensus both in position and orientation considering the latter as the measured output. The controller is dynamic, but it does not rely on a velocity estimator, it relies on a dynamic extension that has a clear physical interpretation, as a mechanical system itself. Roughly speaking, it is showed that the consensus problem may be solved indirectly, by achieving consensus of the controllers themselves and, then, coupling each of these to each vehicle, via a virtual spring. Simulation tests are provided in the present manuscript to show the performance of our proposal.

Keywords:Cooperative control, Distributed control, Autonomous robots Abstract: This paper addresses a formation control problem of mechanical multi-agent systems. The state of each agent is governed by an Euler-Lagrange system, defined in a heterogeneous configuration space. In contrast, a formation task is carried out in a task space common to all the agents with their end-effectors. The coordinate transformation between the configuration and task spaces is defined with a mapping. Each agent can measure its state in the configuration space and the coordinates of other agents in the task space over its own local frames. We design a distributed controller with local measurements with which the task is achieved. As a typical example, the developed method is applied to a group of robotic manipulators with heterogeneous numbers of links.

Keywords:Autonomous vehicles, Agents-based systems, Control applications Abstract: This work proposes a formation control law for multi-agent systems whose components are heterogeneous in terms of actuation capabilities, but at the same time are all able to retrieve bearing information w.r.t. some neighbors in the group. The designed controller exploits the results of the bearing rigidity theory deriving from the modeling of heterogeneous formations as generalized frameworks. The outlined solution is compared with a leader-follower combination of existing rigidity based homogeneous formation controllers in order to highlight the easy tuning, the flexibility w.r.t. the formation composition, and the increased efficiency of the new proposed control approach. A sufficient condition ensuring the convergence of the designed controller is also given.

Keywords:Autonomous vehicles, Agents-based systems, Estimation Abstract: We propose a distributed estimation and control strategy to balance a multi-agent system along a closed-curve. Each agent in the formation has a limited sensing range, such that a noisy measurement of the Euclidean distance from its neighbors is collected only when they are sufficiently close. We frame this problem in the challenging setting in which, when the formation is balanced, no measurement can be further obtained. An additional hurdle for control is that, even when the Euclidean distance between a pair of agent is measured, this may correspond to infinite distances along the curve, if the latter is not circular. To cope with these challenges, we make a synergistic design of the estimation and control law, and formally prove that a balanced formation is achieved. The analysis is complemented by numerical simulations demonstrating the performance of the proposed control scheme.

Keywords:Nonlinear systems identification, Neural networks, Network analysis and control Abstract: This paper studies the reconstruction from data of firing rate dynamics in linear-threshold network models of brain activity. Instead of identifying the system parameters directly, which would lead to a large number of variables and a highly non-convex objective function, the novelty of our approach stems from reformulating the identification problem as a scalar variable optimization of a discontinuous, nonconvex objective function. We formally show that the reformulated optimization problem has a unique solution and establish that it leads to the identification of all the desired system parameters. These results form the basis for the introduction of an algorithm to find the optimizer that identifies the different regions in the domain of definition of the objective function. The results not only validate the system identifiability but also provide the foundation for further research on data-driven control of firing rate dynamics. We demonstrate the algorithm effectiveness in simulation.

Keywords:Lyapunov methods, Robust control, Uncertain systems Abstract: Modern nonlinear control theory seeks to endow systems with properties such as stability and safety, and has been deployed successfully across various domains. Despite this success, model uncertainty remains a significant challenge in ensuring that model-based controllers transfer to real world systems. This paper develops a data-driven approach to robust control synthesis in the presence of model uncertainty using Control Certificate Functions (CCFs), resulting in a convex optimization based controller for achieving properties like stability and safety. An important benefit of our framework is nuanced data-dependent guarantees, which in principle can yield sample-efficient data collection approaches that need not fully determine the input-to-state relationship. This work serves as a starting point for addressing important questions at the intersection of nonlinear control theory and non-parametric learning, both theoretical and in application. We demonstrate the efficiency of the proposed method with respect to input data in simulation with an inverted pendulum in multiple experimental settings.

Keywords:Stability of nonlinear systems, Lyapunov methods, Uncertain systems Abstract: Estimating the region of attraction (ROA) of general nonlinear autonomous systems remains a challenging problem and requires a case-by-case analysis. Leveraging the universal approximation property of neural networks, in this paper, we propose a counterexample-guided method to estimate the ROA of general nonlinear dynamical systems provided that they can be approximated by piecewise linear neural networks and that the approximation error can be bounded. Specifically, our method searches for robust Lyapunov functions using counterexamples, i.e., the states at which the Lyapunov conditions fail. We generate the counterexamples using Mixed-Integer Quadratic Programming. Our method is guaranteed to find a robust Lyapunov function in the parameterized function class, if exists, after collecting a finite number of counterexamples. We illustrate our method through numerical examples.

Keywords:Identification for control, Linear systems Abstract: Willems' fundamental lemma asserts that all trajectories of a linear time-invariant system can be obtained from a finite number of measured ones, assuming that controllability and a persistency of excitation condition hold. We show that these two conditions can be relaxed. First, we prove that the controllability condition can be replaced by a condition on the controllable subspace, unobservable subspace, and a certain subspace associated with the measured trajectories. Second, we prove that the persistency of excitation requirement can be relaxed if the degree of a certain minimal polynomial is tightly bounded. Our results show that data-driven predictive control using online data is equivalent to model predictive control, even for uncontrollable systems. Moreover, our results significantly reduce the amount of data needed in identifying homogeneous multi-agent systems.

Keywords:Learning, Estimation, Optimal control Abstract: Data-driven control of nonlinear dynamical systems is a largely open problem. In this paper, building upon the theory of Koopman operators and exploiting ideas from policy gradient methods in reinforcement learning, a novel approach for data-driven optimal control of unknown non-linear dynamical systems is introduced.

Keywords:Autonomous systems, Optimization, Information theory and control Abstract: This paper is concerned with the problem of designing agents able to dynamically select information from multiple data sources in order to tackle tasks that involve tracking a target behavior while optimizing a reward. We formulate this problem as a data-driven optimal control problem with integer decision variables and give an explicit expression for its solution. The solution determines how (and when) the data from the sources should be used by the agent. We also formalize a notion of agent's regret and, by relaxing the problem, give a regret upper bound. Simulations complement the results.

Keywords:LMIs, Model/Controller reduction, Agents-based systems Abstract: In this paper, we propose a novel method to find matrices that satisfy sparsity and LMI (linear matrix inequality) constraints at the same time. This problem appears in sparse control design such as sparse representation of the state feedback gain, sparse graph representation with fastest mixing, and sparse FIR (finite impulse response) filter design, to name a few. We propose an efficient algorithm for the solution based on Dykstra's projection algorithm. We then prove a convergence theorem of the proposed algorithm, and show some control examples to illustrate merits and demerits of the proposed method.

Keywords:Computational methods, Numerical algorithms, Linear systems Abstract: This paper shows that every simple but non-trivial continuous-time, linear time-invariant (LTI) system shows a complexity blowup if its output is simulated on a digital computer. This means that for a given LTI system, a Turing machine can compute a low-complexity input signal in polynomial-time but which yields a corresponding output signal which has high complexity in the sense that the computation time for determining an approximation up to n significant digits grows faster than any polynomial in n. A similar complexity blowup is observed for the calculation of Fourier series approximations and the Fourier transform.

Keywords:Computational methods Abstract: Computational uncertainty (also called numerical or algorithmic) is the discrepancy between a mathematical result and its implementation in a computer. In control engineering, computational uncertainty is usually either neglected or considered submerged into some other type of uncertainty, such as system noise, and addressed within robust control. However, even robust control methods may be compromised when the mathematical objects involved in the respective algorithms fail to exist in exact form and subsequently fail to satisfy the required properties. For instance, in general stabilization using a control Lyapunov function, computational uncertainty may distort stability certificates or even destabilize the system despite robustness of the stabilization routine with regards to system, actuator and measurement noise. Such observations indicate that computational uncertainty should indeed be addressed explicitly in controller synthesis and system analysis. There is a number of relatively recent works which aim at this goal, and a brief survey of them is given in the current paper. The major contribution is the presentation of a fairly general framework for proof techniques in analysis and synthesis of control systems based on constructive analysis which explicitly states that every computation be doable only up to a finite precision. A series of previous works is overviewed, including constructive system stability and stabilization, approximate optimal controls, eigenvalue problems, Caratheodory trajectories, measurable selectors. Additionally, a new constructive version of the Danskin's theorem, which is crucial in adversarial defense, is presented.

Energy Systems Division, Argonne National Laboratory, Argonne, I

Keywords:Energy systems, Computational methods Abstract: Simulation and control of many dynamic systems involve solving partial differential equations (PDE). This letter proposes a semi-analytical solution (SAS) approach for fast and high-quality solution of first-order PDEs. The region of interest of the studied PDE is divided into a grid, and an SAS is derived for each grid cell in the form of the multivariate polynomials, of which the coefficients are identified using initial value and boundary value conditions. The solutions are solved in a "time-stepping" manner, i.e. within one time step, the coefficients of the SAS are identified and the initial value of the next time step is evaluated. This approach achieves a significantly larger grid cell than the widely used finite difference method, and thus enhances the computational efficiency significantly. The simulation result on the natural gas pipeline model demonstrates the advantages of SAS in accuracy and computational efficiency.

Keywords:Optimization, Lyapunov methods, Optimization algorithms Abstract: This paper considers the problem of designing a dynamical system to solve constrained nonlinear optimization problems such that the feasible set is forward invariant and asymptotically stable. The invariance of the feasible set makes the dynamics anytime, when viewed as an algorithm, meaning that it is guaranteed to return a feasible solution regardless of when it is terminated. Such property is of critical importance in feedback control since controllers are often implemented as solutions to constrained programs that must be solved in real time. The proposed design builds on the basic insight of following the gradient flow of the objective function while keeping the state evolution within the feasible set using techniques from the theory of control barrier functions. We show that the resulting closed-loop system can be interpreted as a continuous approximation of the projected gradient flow, establish the monotonic decrease of the objective function along the feasible set, and characterize the asymptotic convergence properties to the set of critical points. Various examples illustrate our results.

Keywords:Optimization, Numerical algorithms, Computational methods Abstract: Dynamical systems approaches to constrained optimization often rely on a penalization term to reach feasible points, at the cost of slower convergence. However, we show one can construct a discrete-time system that maintains the same convergence guarantees without requiring such penalization term. We demonstrate that the sequential homotopy method, namely taking projected backward Euler steps on a projected gradient/anti-gradient augmented Lagrangian flow, matches with the classical augmented Lagrangian method without the multiplier estimate update. Then, we introduce a time-scaled flow and provide an interpretation of augmented Lagrangian methods as discrete-time dynamical systems. This approach inspires a simple yet effective method for nonlinear programming. We report on numerical results for equality-constrained problems.

Keywords:Iterative learning control, Nonlinear systems, Machine learning Abstract: Model-free learning-based control methods have seen great success recently. However, such methods typically suffer from poor sample complexity and limited convergence guarantees. This is in sharp contrast to classical model-based control, which has a rich theory but typically requires strong modeling assumptions. In this paper, we combine the two approaches. We consider a dynamical system with both linear and non-linear components and use the linear model to define a warm start for a model-free, policy gradient method. We show this hybrid approach outperforms the model-based controller while avoiding the convergence issues associated with model-free approaches via both numerical experiments and theoretical analyses, in which we derive sufficient conditions on the non-linear component such that our approach is guaranteed to converge to the (nearly) global optimal controller.

Keywords:Iterative learning control, Robust control, Uncertain systems Abstract: This paper presents a higher-order spatial iterative learning control (HO-SILC) framework for heightmap tracking of 3D structures that are fabricated by additive manufacturing (AM) technology. In the literature, first-order spatial ILC (FO-SILC) has been used in conjunction with additive processes to regulate single-layer structures. However, ILC has undeveloped potential to regulate AM structures that are fabricated by the repetitive addition of material in a layer-by-layer manner. Estimating the appropriate feedforward signal in these structures can be challenging due to iteration varying system parameters. In this paper, HO-SILC is used to iteratively construct the feedforward signal to improve device quality of 3D structures. To have a more realistic representation of the additive process, iteration varying uncertainties in the plant dynamics and non-repetitive noise in the input signal are included. We leverage the existing FO-SILC models in the literature and extend them to a HO-SILC framework that incorporates data available from a previously printed device, as well as multiple previously printed layers to enhance the overall performance. Subsequently, the monotonic and asymptotic stability conditions for the nominal HO-SILC algorithm are illustrated.

Keywords:Iterative learning control Abstract: High performance formation control problem working repetitively has found important applications in various areas. Recent design uses iterative learning control (ILC) to achieve the high performance requirements, since ILC does not require a highly accurate model required by traditional control methods. This paper considers a previously unexplored problem in formation control problem, which aims at achieving the high performance requirement while guaranteeing individual input energy cost using only local information. We propose two novel ILC algorithms to solve the above problem. The proposed algorithms are suitable for both homogeneous and heterogeneous networks, as well as non-minimum phase systems, which are appealing in practice. Distributed implementations using the alternating direction method of multiplies are provided, allowing the proposed algorithms to be applied to large scale networked dynamical systems. Convergence properties of the algorithms are analysed rigorously and numerical examples are presented to demonstrate their effectiveness.

Keywords:Learning, Iterative learning control, Agents-based systems Abstract: We study the problem of learning safe control policies that are also effective; i.e., maximizing the probability of satisfying a linear temporal logic (LTL) specification of a task, and the discounted reward capturing the (classic) control performance. We consider unknown environments modeled as Markov decision processes. We propose a model-free reinforcement learning algorithm that learns a policy that first maximizes the probability of ensuring safety, then the probability of satisfying the given LTL specification and lastly, the sum of discounted Quality of Control rewards. Finally, we illustrate applicability of our RL-based approach.

Keywords:Mechatronics, Learning, Iterative learning control Abstract: The performance increase up to the sensor resolution in repetitive control (RC) invalidates the standard assumption in RC that data is available at equidistant time instances, e.g., in systems with package loss or when exploiting timestamped data from optical encoders. The aim of this paper is to develop an intermittent sampling RC framework for non-equidistant measurements. Sufficient stability conditions are derived that can be verified using non-parametric frequency response function data. This results in a frequency domain design procedure to explicitly address uncertainty. The RC framework is validated on an industrial printbelt setup for which exact non-equidistant measurement data is available.

Keywords:Iterative learning control, Linear systems, Switched systems Abstract: A reference trajectory is specified for systems that repetitively execute the same finite duration task in iterative learning control. In many current designs, the reference signal remains the same, but in others, it is desirable to allow the reference trajectory to change during the system's overall operation. This paper develops a control law design method for linear dynamics where the measured signals are noise corrupted, random disturbances are present, and the reference trajectory is allowed to change during operation. The new design is based on the recently developed stochastic stability theory for repetitive processes, a class of 2D systems, and uses vector Lyapunov functions and their divergence properties. It also shows how to eliminate the transient error that results from a switch of the reference trajectory. A numerical case study demonstrates the applicability of the new design.

Keywords:Kalman filtering, Estimation, Sensor networks Abstract: The optimal fusion of estimates in a Distributed Kalman Filter (DKF) requires tracking of the complete network error covariance, problematic in terms of memory and communication. A scalable alternative is to fuse estimates under unknown correlations, doing the update by solving an optimisation problem. Unfortunately, this problem is NP-hard, forcing relaxations that lose optimality guarantees. Motivated by this, we present the first Certifiable Optimal DKF (CO-DKF). Using only information from one-hop neighbours, CO-DKF solves the optimal fusion of estimates under unknown correlations by a particular tight Semidefinite Programming (SDP) relaxation which allows to certify, locally and in real time, if the relaxed solution is the actual optimum. In that case, we prove optimality in the Mean Square Error (MSE) sense. Additionally, we demonstrate the global asymptotic stability of the estimator. CO-DKF outperforms other state-of-the-art DKF algorithms, specially in sparse, highly noisy setups.

Keywords:Kalman filtering, Stochastic systems, Control system architecture Abstract: A real-time, recursive, multivariate estimation algorithm for time-invariant and time-varying linear systems with modelled Cauchy noises is developed. When previously compared to the Kalman Filter, the Multivariate Cauchy Estimator was shown to be robust against impulsive disturbances in the process or measurement functions, but proved computationally intractable for real-time estimation applications. Two significant insights allow for a reformulation of the Multivariate Cauchy Estimator to possess a streamlined recursive and computationally reduced characteristic function of the conditional probability density function of the system state-vector given the measurement sequence. This characteristic function is represented by a sum of terms, expanding with each measurement. First, we show that a cell-enumeration matrix can be computed for each hyperplane arrangement embedded within each term of the characteristic function of the Cauchy Estimator. We then show that functions used to formulate the terms of this characteristic function can be expressed as a vector of parameters operating on basis functions constructed from this enumeration matrix. This vector is obtained by solving an under-determined system of equations. We demonstrate that our reformulation allows all terms with equal hyperplane arrangements to be reduced into a unique set. Secondly, we take advantage of advances in parallel processing to exploit the inherent parallelism found in the characteristic function of the Cauchy Estimator. A three state time-invariant system example is used to illustrate the performance of the Cauchy Estimator against the Kalman Filter when subjected to Gaussian and Cauchy noises. We report computational savings of over 99% when compared to the previous formulation. Furthermore, we discuss the real-time architecture of the Cauchy Estimator and report the execution speeds for a three-state system implemented on a single NVIDIA GeForce GTX 1060 graphics processing unit (GPU).

Keywords:Estimation, Cyber-Physical Security, Kalman filtering Abstract: We consider the problem of estimating the state of a linear Gaussian system in the presence of integrity attacks. The attacker can compromise p out of m sensors, the set of which is fixed and unknown to the system operator, and manipulate the measurements arbitrarily. Under the assumption that all the eigenvalues of system matrix A have geometric multiplicity 1 (A is non-derogatory), we propose a secure estimation scheme that is resilient to integrity attack as long as the system is 2p-sparse observable. In the absence of attack, the proposed estimation coincides with Kalman estimation with a certain probability that can be adjusted. Furthermore, our proposed estimator is computational efficient during the security condition checking in the designing phase and during the estimation computing in the online operating phase. A numerical example is provided to corroborate the results and illustrate the performance of the proposed estimator.

Keywords:Filtering, Distributed parameter systems, Kalman filtering Abstract: In this work we adopt a novel formulation of the distributed parameters recursive filter for discrete-time systems evolving in L_2 spaces to widen the class of systems that can be processed by a state estimation algorithm. Starting from a rigorous definition of Kronecker algebra on L_2 spaces that involves both elements and bounded operators of L_2, we provide a computationally efficient solution in the case of linear systems with multiplicative noises. We illustrate the potential application of the approach by developing a case-study concerning the conceptual design of a distributed thermo-couple in the presence of the Nyquist–Johnson noise.

Keywords:Estimation, Kalman filtering, Stochastic systems Abstract: This paper studies the state estimation of nonlinear dynamical systems using stochastically forced linearized dynamics, where the stochastic input models the effect of process noise and the uncertainty caused by excluding nonlinear terms from the linearized model. The statistics of the input stochastic forcing greatly influence the design of estimation gains and can lead to the undesirable performance of state estimators. When the process noise is colored-in-time, conventional methods can fail to provide reasonable estimates of second-order statistics that are of interest in many feedback control applications. To address this problem, we utilize a recently developed framework for the dynamical modeling of input disturbances that provides statistical consistency at the level of second-order statistics with the underlying nonlinear dynamics. We demonstrate the efficacy of linear innovations models that result from this approach for the ensemble Kalman filtering of colored noise processes.

Keywords:Filtering, Kalman filtering, Estimation Abstract: The ensemble Kalman filter (EnKF) is well-established for discrete state-space models. In this paper, we provide the methodology of applying the EnKF to continuous-discrete (CD) state-space models. The proposed CD EnKF algorithm is a bank of the CD extended Kalman filters for the time update. Then, the observation update is formulated using the Gaussian-sum distributed predicted state probability density function (PDF). We also provide the observation update based on the Dirac's delta mixture predicted state PDF. The numerical simulation using a benchmark filtering problem called the satellite reentry is conducted to investigate the performance of the CD EnKFs. The performance comparison with the EnKF applied to the discretized model is also made.

Keywords:Stochastic systems, Optimization, Learning Abstract: In this paper, we consider a variant of the cascade model of customer behavior, where the customer browses through a multi-page menu, scanning each page from top to the bottom predominantly. Each page is assigned items belonging to a specific class out of a set of classes. He/she adopts the first most attractive content, which generates some revenue. We aim at maximizing the total revenue by finding an optimal index-based policy for ranking the content when the customer preferences and patience levels are known. When we have no prior information about the customer, we design the Online Greedy Algorithm (OGA) which we prove to be asymptotically converging to the optimal solution with probability one. We also provide high probability finite-time convergence bounds for the same.

Keywords:Stochastic systems, Predictive control for linear systems, Aerospace Abstract: We propose a tractable approach to generate abort-safe trajectories for spacecraft rendezvous that guarantees safety, i.e., the spacecraft does not enter a keep-out set defined around the rendezvous target. We guarantee safety of the rendezvous trajectory even in the event of propulsion failure and in the presence of stochastic uncertainty in actuation and navigation. We use a combination of stochastic reachability, computational geometry, and optimization to synthesize a nominal rendezvous trajectory and its associated controller. The designed trajectory is such that safe recovery, in the event of a propulsion failure, is guaranteed with pre-specified, sufficiently high probability. The recovery controllers are available when needed via an offline pre-computation, which significantly reduces the online computational effort. Numerical experiments show the efficacy of the proposed approach.

Keywords:Stochastic systems, Statistical learning, Machine learning Abstract: In this paper we derive a PAC-Bayesian error bound for autonomous stochastic LTI state-space models. The motivation for deriving such error bounds is that they will allow deriving similar error bounds for more general dynamical systems, including recurrent neural networks. In turn, PACBayesian error bounds are known to be useful for analyzing machine learning algorithms and for deriving new ones.

Keywords:Stochastic systems, Uncertain systems, Optimization Abstract: This study investigates an optimal control problem of discrete-time finite-state Markov chains with application in the operation of car-sharing services. The optimal control of probability distributions is the object of focus to ensure that the controlled distributions are as close as possible to the given ones. The problem is formulated using Wasserstein distances, which allows us to measure the difference among probability distributions and is suitable for the objective of this study. For the control problem, we provide a necessary condition for optimality in the control inputs and develop an algorithm for obtaining optimal control inputs. The developed algorithm is then applied to the probability distribution control of a one-way car-sharing service, which provides a rebalancing strategy to resolve car unevenness.

Keywords:Robust control, Autonomous systems, Stochastic systems Abstract: Accurate quantification of safety is essential for the design of autonomous systems. In this paper, we present a methodology to characterize the exact probabilities associated with invariance and recovery in safe control. We consider a stochastic control system where control barrier functions, gradient-based methods, and barrier certificates are used to constrain control actions and validate safety. We derive the probability distributions of the minimum and maximum barrier function values during any time interval and the first entry and exit times to and from any super level sets of the barrier function. These distributions are characterized by deterministic convection-diffusion equations, and the approach used is generalizable to other safe control methods based on barrier functions. These distributions can be used to characterize various quantities associated with invariance and recovery, such as the safety margin, the probability of entering and recovering from safe and unsafe regions, and the mean and tail distributions of failure and recovery times.

Keywords:Stochastic systems, Markov processes, Stability of nonlinear systems Abstract: In this paper, we address finite time stability in probability of discrete-time stochastic dynamical systems. Specifically, a stochastic comparison lemma is constructed along with a scalar system involving a generalized deadzone function to establish almost sure convergence and finite time stability in probability. This result is used to provide Lyapunov theorems for finite time stability in probability for Ito-type stationary nonlinear stochastic difference equations involving conditions on the minimum of the Lyapunov function itself along with a fractional power of the Lyapunov function. In addition, we establish sufficient conditions for almost sure lower semicontinuity of the stochastic settling-time capturing the average settling time behavior of the discrete-time nonlinear stochastic dynamical system.

Keywords:Control system architecture, Cooperative control, LMIs Abstract: This paper studies distributed edge weight synthesis of a cooperative system for a fixed topology to improve H_{infty} performance, considering that disturbances are injected at interconnection channels. This problem is cast into a linear matrix inequality problem by replacing the original cooperative system with an equivalent ideal cooperative system. The proposed method relies on a dissipative system framework and provides an upper bound for the induced mathcal{L}_{2} norm of the original lumped cooperative system while reducing the computation time. A comparison for computation time illustrates the advantage of the proposed method against the lumped counterpart.

Air Force Research Laboratory, AFRL/RISC, Rome, NY

Keywords:Cooperative control, Adaptive systems, Numerical algorithms Abstract: In this paper, we consider the cooperative control problem for a class of discrete-time nonlinear multiagent systems with the objective of minimizing a group cost functional. A multiagent Hamilton-Jacobi-Bellman (HJB) equation is first derived and then a new consensus-based value iteration algorithm is proposed to seek the online approximate solution to multiagent HJB. Neural networks are employed to parameterize the state value functions for individual agents, and a novel adaptive law for updating neural network weights is proposed based on the estimation of several global terms. The proposed local information based cooperative control is based on the minimization of the overall cost functional which is the sum of all individual agents' cost functionals. Numerical simulations show the effectiveness of the proposed design.

Keywords:Cooperative control, Agents-based systems Abstract: In this paper, the consensus problem is studied for double-integrator multi-agent systems with edge-based event-triggered communication. More specifically, two agents connected by an edge mutually sample the relative state information when a designed triggering condition is satisfied. The triggering mechanism is introduced to reduce the communication frequency. To make the triggering mechanism implementable, a positive minimum inter-event time is guaranteed in all communication links in the network. All designs use only local neighborhood information. Based on Lyapunov analysis, the proposed algorithm makes all the agents converge to a consensus trajectory asymptotically.

Keywords:Cooperative control, Autonomous robots Abstract: We propose a consensus-based artificial potential field (CAPF) approach for swarm control. The CAPF approach enables a swarm to accomplish different complex tasks including task allocation. The artificial potential field (APF) approach provides an efficient control law for different types of swarm control, such as consensus control, formation control, and coverage control. In the APF approach, the control inputs of robots are determined on the basis of a potential field, that is, a gradient of the potential function. In the existing swarm controls, the potential field for each robot depends on only local information such as the robot's own state and states of nearby robots. A swarm cannot accomplish complex tasks with the existing APF approach because of this restriction on the potential function. In our CAPF approach, in contrast, the potential function does not have this restriction and the potential field is calculated on the basis of a consensus filter that requires only local communication. We show that, by using the CAPF approach, a state of a swarm converges to a local minimum of the potential function. Moreover, we apply the CAPF approach to a multi-robot task allocation (MRTA) problem.

Pontifical Catholic University of Rio Grande Do Sul

Keywords:Cooperative control, Nonlinear systems, LMIs Abstract: In this paper we propose a new systematic methodology for the cooperative output feedback control design such that exponential consensus is achieved in a dual agent homogeneous nonlinear system network with additive control inputs. Our design approach ensures that all system trajectories are bounded and exponentially synchronize within a minimum and maximum decay-rate range. Our results are derived by using a combination of two quasi-Linear Parameter Varying representations: one for the synchronization error dynamics and other for the absolute network dynamics. This way, we derive matrix inequality conditions that ensure both exponential consensus and absolute boundedness, which are used to design distributed controllers via convex optimization problems. The Lorenz Attractor is considered as a numerical example in order to illustrate the application of the proposed method.

Keywords:Network analysis and control, Control of networks, Cooperative control Abstract: In this paper, we consider a network of agents with Laplacian dynamics, and study the problem of improving network robustness by adding maximum number of edges within the network while preserving a lower bound on its strong structural controllability (SSC). Edge augmentation increases network's robustness to noise and structural changes, however, it could also deteriorate network controllability. By exploiting relationship between network controllability and distances between nodes in graphs, we formulate an edge augmentation problem with a constraint to preserve distances between certain node pairs, which in turn guarantees that a lower bound on SSC is maintained even after adding edges. In this direction, first we choose a node pair and maximally add edges while maintaining the distance between selected nodes. We show that an optimal solution belongs to a certain class of graphs called clique chains. Then, we present and analyze two algorithms to add edges while preserving distances between a certain collection of nodes. Finally, we evaluate our results on various networks.

Keywords:Optimal control, Queueing systems, Optimization Abstract: We consider the problem of online job scheduling on a single machine with general job-dependent cost functions. In this model, each job j has a processing requirement (length) v_{j} and arrives with a nonnegative nondecreasing cost function g_{j}(t), and this information is revealed to the system upon arrival of job j at time r_j. The goal is to schedule the jobs preemptively on the machine in an online fashion so as to minimize the generalized completion time sum_{j}g_{j}(C_j), where C_j is the completion time of job j on the machine. It is assumed that the machine has a unit processing speed that can work on a single job at any time instance. In particular, we are interested in finding an online scheduling policy whose objective cost is competitive with respect to a slower optimal offline benchmark, i.e., the one that knows all the job specifications a priori and is slower than the online algorithm. Under some mild assumptions, we provide a speed-augmented competitive algorithm for general nondecreasing cost functions g_j(t) by utilizing a novel optimal control framework.

Keywords:Optimal control, Stability of nonlinear systems, Lyapunov methods Abstract: A new approach to feedback control design based on optimal control is proposed. Instead of expensive computations of the value function for different penalties on the states and inputs, we use a control Lyapunov function that amounts to be a value function of an optimal control problem with suitable cost design and then study combinations of input and state penalty that are compatible with this value function. This drastically simplifies the role of the Hamilton-Jacobi-Bellman equation, since it is no longer a partial differential equation to be solved, but an algebraic relationship between different terms of the cost. The paper illustrates this idea in different examples, including H_infty control and optimal control of coupled oscillators.

Keywords:Optimal control, Stability of nonlinear systems Abstract: The problem of finite-time stabilization of a linear plant with an optimization of both a settling time and an weighted/averaged control energy is studied using the concept of generalized homogeneity. It is shown that the optimal finite-time stabilizing control in this case can be designed solving a simple linear algebraic equation. Some issues of a practical applicability and a robustness of the obtained control law are studied.

Keywords:Optimal control, Uncertain systems, Nonlinear systems Abstract: A controlled system subject to dynamics with unknown but bounded parameters is considered. The control is defined as the solution of an optimal control problem, which induces hybrid dynamics. A method to enclose all optimal trajectories of this system is proposed. Using interval and zonotope based validated simulation and Pontryagin’s Maximum Principle, a characterization of optimal trajectories, a conservative enclosure is constructed. The usual validated simulation framework is modified so that possible trajectories are enclosed with spatio-temporal zonotopes that simplify simulation through events. Then optimality conditions are propagated backward in time and added as constraints on the previously computed enclosure. The obtained constrained zonotopes form a thin enclosure of all optimal trajectories that is less susceptible to accumulation of error. This algorithm is applied on Goddard’s problem, an aerospace problem with a bang-bang control.

Keywords:Optimization algorithms, Robust control, Optimal control Abstract: We propose an algorithm for solving tube-based robust nonlinear optimal control problems based on the approximate propagation of ellipsoidal uncertainty tubes. Crucially, the algorithm does not only optimize the nominal control trajectory, but the decision variables include linear feedback gains for each time step. In consequence, the resulting trajectories do not suffer from the unrealistically large uncertainty sets of open-loop robust trajectories, but are able to approximately capture the feedback behavior implicit to model predictive control. The proposed algorithm iterates by alternatingly performing a Riccati recursion and solving a perturbed nominal optimal control problem. We provide a theoretical analysis of the local convergence behavior and demonstrate its basic applicability on the example problem of controlling a towing kite.

Keywords:Optimization algorithms, Optimal control, Stability of nonlinear systems Abstract: This paper presents a fast and flexible projected primal-dual method for solving linear quadratic optimal control problems with box constraints. Using a specific preconditioning, the algorithm achieves dead-beat convergence for unconstrained problems and has fast convergence for constrained problems. Accelerated convergence is obtained by applying a heavy-ball method to accelerate the projected primal-dual algorithm. In order to avoid missing critical points due to high momentum, an adaptive restarting procedure is used to slow the algorithm down if the solution diverges. Furthermore, convergence is proven by representing the algorithm as a Lur'e-type dynamic system and applying LaSalle's invariance principle to show the fixed point is asymptotically stable. The resulting algorithm is simple, while also achieving competitive computational times.

Keywords:Uncertain systems, LMIs, Robust control Abstract: The computation of the minimum sensitivity of uncertain Linear Time Invariant (LTI) systems is presented in the paper. The system interconnection is given by a generic Linear Fractional Transformation (LFT) of a nominal model and an uncertain block, where the input-output behavior of the latter is described by Integral Quadratic Constraints (IQC). The extension of the Minimum Gain Lemma is presented for such interconnections, resulting in a convex optimization problem subject to Linear Matrix Inequality (LMI) constraints. With the aim of the Generalized-KYP (GKYP) lemma the minimum gain/sensitivity is computed over a certain finite frequency range. Connection with the already existing literature is highlighted, providing an insight on the obtained results. A numerical example is given to illustrate and validate the proposed methodology.

Keywords:Uncertain systems, Chemical process control Abstract: This paper proposes a new class of real-time optimization schemes to overcome system-model mismatch of uncertain processes. This work's novelty lies on integrating derivative-free optimization schemes and multi-fidelity Gaussian processes within a Bayesian optimization framework. The proposed scheme uses two Gaussian processes for the stochastic system, one emulates the (known) process model, and another, the true system though measurements. In this way, low fidelity samples can be obtained via a model, while high fidelity samples are obtained through measurements of the system. This framework captures the system's behavior in a non-parametric fashion, while driving exploration through acquisition functions. The benefit of using a Gaussian process to represent the system is the ability to perform uncertainty quantification in real-time and allow for chance constraints to be satisfied with high confidence. This results in a practical approach that is illustrated in numerical case studies, including a semi-batch photobioreactor optimization problem.

Keywords:Uncertain systems, Optimization, Identification Abstract: Sliced distributions enable the characterization of multivariate data as both a vector of continuous and possibly dependent random variables, or as a semi-algebraic, tightly enclosing set. Sliced distributions inject the physical space into a higher-dimensional feature space using a polynomial mapping. This paper introduces the Sliced-Exponential (SE) subclass of distributions, proposes a suitable data-based polynomial basis for it, and compares its performance against that of the Sliced-Normal (SN) subclass. The key advantage of the SEs over the SNs is that their maximum likelihood estimate results from solving a convex optimization program in a number of decision variables that grows linearly with the dimension of feature space. This is in sharp contrast to the SNs which, as all other Sum of Squares (SOS) methods, have a number of decision variables that increases exponentially with such a dimension thereby limiting their applicability. In addition, SEs have greater versatility since they are not restricted to the space of SOS polynomials. However, this enhanced versatility when coupled with an inaccurate estimation of the normalization constant might yield spurious distributions. This paper presents strategies that mitigate these anomalies by restricting the decision space. Furthermore, we use numerical experiments of increasing dimension size to determine practical limitations, and to set good practice guidelines.

LIX, CNRS, École Polytechnique, Institut Polytechnique De Paris

Keywords:Uncertain systems, Time-varying systems, Hybrid systems Abstract: This paper presents an approach to over-approximate the reachable set of states of a system whose uncertainties are arbitrarily time-varying. Most approaches generally assume piecewise continuity or sometimes Riemann-integrability of the uncertainties. In this paper we go one step further, only assuming Lebesgue measurability, which is the weakest meaningful hypothesis. We develop our new technique, based on a decomposition of components as a difference of positive functions, for separable systems, a generalization of control-affine systems. We compare the over-approximation produced by our method with the ones obtained using the tools Flow* and CORA on simple examples, and show that correct outer-approximations of the reachable sets are computable with a high degree of precision even for these general forms of uncertainties.

Keywords:Simulation, Computer-aided control design, Process Control Abstract: We apply Monte Carlo simulation for performance quantification and tuning of controllers in nonlinear closed-loop systems. Computational feasibility of large-scale Monte Carlo simulation is achieved by implementation of a parallelized high-performance Monte Carlo simulation toolbox for closed-loop systems in C for shared memory architectures. The toolbox shows almost linear scale-up on 16 CPU cores on a single NUMA node, and a scale-up of 27.3 on two NUMA nodes with a total of 32 CPU cores. We demonstrate performance quantification and tuning of a PID controller for a bioreactor in fed-batch operation. We perform 30,000 closed-loop simulations of the fed-batch reactor within 1 second. This is approximately a 2300 times computational performance increase compared to a serial reference implementation in Matlab. Additionally, we apply Monte Carlo simulation to perform automatic tuning of the PID controller based on maximizing average produced biomass within 8 seconds.

Keywords:Uncertain systems, Lyapunov methods, Optimization Abstract: Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are popular tools for enforcing safety and stability of a controlled system, respectively. They are commonly utilized to build constraints that can be incorporated in a min-norm quadratic program (CBF-CLF-QP) which solves for a safety-critical control input. However, since these constraints rely on a model of the system, when this model is inaccurate the guarantees of safety and stability can be easily lost. In this paper, we present a Gaussian Process (GP)-based approach to tackle the problem of model uncertainty in safety-critical controllers that use CBFs and CLFs. The considered model uncertainty is affected by both state and control input. We derive probabilistic bounds on the effects that such model uncertainty has on the dynamics of the CBF and CLF. We then use these bounds to build safety and stability chance constraints that can be incorporated in a min-norm convex optimization-based controller, called GP-CBF-CLF-SOCP. As the main theoretical result of the paper, we present necessary and sufficient conditions for pointwise feasibility of the proposed optimization problem. We believe that these conditions could serve as a starting point towards understanding what are the minimal requirements on the distribution of data collected from the real system in order to guarantee safety. Finally, we validate the proposed framework with numerical simulations of an adaptive cruise controller for an automotive system.

Keywords:Hybrid systems, Observers for Linear systems, Sampled-data control Abstract: Observer design for linear systems with aperiodic sampled-data measurements is addressed. To solve this problem, a novel hybrid observer is designed. The main peculiarity of the proposed observer consists of the use two output injection terms, one acting at the sampling instants and one providing an intersample injection. The error dynamics are augmented with a timer variable triggering the arrival of a new measurement and analyzed via hybrid system tools. Using Lyapunov theory, sufficient conditions for the convergence of the observer are provided. Relying on those conditions, an optimal LMI-based design is proposed for the observer gains. The effectiveness of the approach is illustrated in an example.

Keywords:Sampled-data control, Robust adaptive control Abstract: Twisted and Coiled Artificial Muscles (TCAMs) are lightweight actuators providing high power/weight ratio, and can substitute heavy electromagnetic motors and pneumatic artificial muscles in applications that require low weight and high contractile work. In this paper we present a robust and adaptive output feedback control strategy for electro-thermally actuated TCAMs. The controller adjusts the voltage applied to the TCAM in order to match desired muscles contraction/expansion. The proposed controller compensates for disturbances and uncertainties in the TCAM’s dynamic model. The robustness and stability analysis of the controller takes into account a digital implementation of the control algorithms. Performance is derived in terms of the sampling time of the CPU and the sensors available. The efficacy of the controller is validated through experimental tests.

Keywords:Sampled-data control, Stability of nonlinear systems, LMIs Abstract: This paper addresses the stabilization of aperiodic sampled-data Lure systems, where the nonlinearity is assumed to be both sector and slope restricted. Based on a looped-functional and a Lure-type function, this method provides sufficient stabilization conditions in the form of matrix inequalities. It is shown that the proposed conditions guarantee that the Lure-type function is strictly decreasing at the sampling instants, which also implies that the continuous-time trajectories converge asymptotically to the origin. As the derived matrix inequalities are LMIs provided some variables are fixed, we propose a Particle Swarm Optimization (PSO) algorithm to compute a nonlinear sampled-data state feedback control law aiming at maximizing the intersampling interval or the sector bounds for which the global asymptotic stability of the origin of the closed-loop system is guaranteed.

Keywords:Linear systems, Sampled-data control, Stability of linear systems Abstract: This paper is concerned with the sampled-data stabilization problem for a class of linear systems. Different from the input-delay approach that has been widely used in analyzing the stabilization problem of sampled-data systems, an extended form of the celebrated Halanay inequality is developed for sampled-data systems so as to study the stabilization problem of linear systems under aperiodic sampled-data control. Based on the extended Halanay inequality, the stabilization problem is solved for linear sampled-data systems, where it is required that the gain should be strictly less than the decay rate and then the upper bound of the sampling intervals can be estimated. In order to enlarge the upper bound of the sampling intervals, a further extension of the developed Halanay inequality is made. Then some new conditions are derived to ensure the exponential stability of linear sampled-data systems, where the upper bound of the sampling intervals is allowed to violate the condition of the Halanay inequality. Subsequently, the obtained results are applied to deal with the consensus problem of linear multi-agent systems.

Keywords:Networked control systems, Sampled-data control, Decentralized control Abstract: This note studies the consensus problem for in- tegrator agents under intermittent information exchange be- tween connected neighbours at asynchronous sampling time instances. It proposes a novel sampled-data protocol, based on emulating suitable global analog consensus dynamics at each agent and using sampled centroids of these emulators to convey information between agents. We show that the closed-loop dynamics can be divided into centroid and disagreement parts. The former is completely autonomous and evolves according to time-varying discrete consensus dynamics, independent of the sampling intervals. The disagreement part evolves according to conventional analog consensus dynamics for a constant network topology and is driven by the emulator centroids. The system then asymptotically converges to agreement under mild assumptions on the persistency of connectivity and the uniform boundedness of sampling intervals. A substantially simplified implementation under a special emulated topology, namely the complete graph, is also proposed.

Keywords:Uncertain systems, Sampled-data control, Robust control Abstract: In this paper, a robust quantized sampled--data controller is provided for a class of nonlinear systems affected by time--varying uncertainties, actuation disturbances and measurement noises. Sufficient conditions based on linear matrix inequalities and ensuring the existence of the proposed robust quantized sampled--data controller are given. Quantization of both state measurements and input signals is simultaneously considered. Input--to--state stability redesign technique is used in order to attenuate the effects of bounded actuation disturbances and of bounded observation errors. It is proved that, under suitably fast sampling and accurate quantization of the input/output channels, the proposed controller achieves the semi--global practical stability, with arbitrarily small final target ball, of the related quantized sampled--data closed--loop system provided that the observation errors do not affect (or affect marginally) the robustification term added in the controller and, that the bounds of the actuation disturbances as well as of the observation errors are a--priori known. The theory here developed includes also the cases of time--varying sampling intervals and of non--uniform quantization of the input/output channels as well as the stability analysis of the inter--sampling system behaviour. The provided results are validated through an example of one--link manipulator.

Keywords:Nonlinear systems, Uncertain systems Abstract: As the complexity of control systems increases, safety becomes an increasingly important property since safety violations can damage the plant and put the system operator in danger. When the system dynamics are unknown, safety-critical synthesis becomes more challenging. Additionally, modern systems are controlled digitally and hence behave as sampled-data systems, i.e., the system dynamics evolve continuously while the control input is applied at discrete time steps. In this paper, we study the problem of control synthesis for safety-critical sampled-data systems with unknown dynamics. We overcome the challenges introduced by sampled-data implementation and unknown dynamics by constructing a set of control barrier function (CBF)-based constraints. By satisfying the constructed CBF constraint at each sampling time, we guarantee the unknown sampled-data system is safe for all time. We formulate a non-convex program to solve for the control signal at each sampling time. We decompose the non-convex program into two convex sub-problems. We illustrate the proposed approach using a numerical case study.

Keywords:Optimal control, Lyapunov methods, Robust control Abstract: This paper works towards unifying two popular approaches in the safety control community: Hamilton-Jacobi (HJ) reachability and Control Barrier Functions (CBFs). HJ Reachability has methods for direct construction of value functions that provide safety guarantees and safe controllers, however the online implementation can be overly conservative and/or rely on chattering bang-bang control. The CBF community has methods for safe-guarding controllers in the form of point-wise optimization using quadratic programs (CBF-QP), where the CBF-based safety certificate is used as a constraint. However, finding a valid CBF for a general dynamical system is challenging. This paper unifies these two methods by introducing a new reachability formulation inspired by the structure of CBFs to construct a Control Barrier-Value Function (CBVF). We verify that CBVF is a viscosity solution to a novel Hamilton-Jacobi-Isaacs Variational Inequality and preserves the same safety guarantee as the original reachability formulation. Finally, inspired by the CBF-QP, we propose a QP-based online control synthesis for systems affine in control and disturbance, whose solution is always the CBVF's optimal control signal robust to bounded disturbance. We demonstrate the benefit of using the CBVFs for double-integrator and Dubins car systems by comparing it to previous methods.

Keywords:Constrained control, Robotics, Automotive control Abstract: In this paper we consider multi-agent collision avoidance using Control Barrier Functions (CBF). One contribution is a comparison of several CBF-based control policies proposed in the literature and a new one proposed here for completeness. We study tradeoffs between a level of safety guarantee and liveness - the ability to reach a destination in short time without large detours or gridlock - using the centralized controller as the benchmark. The new policy (CCS2) straddles the space between policies with only local control available and a more complex Predictor-Corrector for Collision Avoidance (PCCA) policy and tries to answer how much performance might be lost if the policy does not use estimates or measurements of other agents control actions. Another contribution of the paper is that it establishes feasibility for the centralized, PCCA and CCS2 policies. Monte Carlo simulations show that decentralized, host-only control policies lack liveness compared to the ones that use everyone's control inputs in the calculations (whether they are local copies or not) and that the PCCA policy, which runs with incomplete information, performs equally as well as the centralized.

Keywords:Constrained control, Optimal control, Nonlinear output feedback Abstract: This work proposes an optimal safe controller minimizing an infinite horizon cost functional subject to control barrier functions (CBFs) safety conditions. The constrained optimal control problem is reformulated as a minimization problem of the Hamilton-Jacobi-Bellman (HJB) equation subjected to the safety constraints. By solving the optimization problem, we are able to construct a closed form solution that satisfies optimality and safety conditions. The proposed solution is shown to be continuous and thus it renders the safe set forward invariant while minimizing the given cost. Hence, optimal stabilizability and safety objectives are achieved simultaneously. To synthesize the optimal safe controller, we present a modified Galerkin successive approximation approach which guarantees an optimal safe solution given a stabilizing safe initialization. The proposed algorithm is implemented on a constrained nonlinear system to show its efficacy.

Keywords:Robotics, Constrained control Abstract: The backup control barrier function (CBF) was recently proposed as a tractable formulation that guarantees the feasibility of the CBF quadratic programming (QP) via an implicitly defined control invariant set. The control invariant set is based on a fixed backup policy and evaluated online by forward integrating the dynamics under the backup policy. This paper is intended as a tutorial of the backup CBF approach and a comparative study to some benchmarks. First, the backup CBF approach is presented step by step with the underlying math explained in detail. Second, we prove that the backup CBF always has a relative degree 1 under mild assumptions. Third, the backup CBF approach is compared with benchmarks such as Hamilton Jacobi PDE and Sum-of-Squares on the computation of control invariant sets, which shows that one can obtain a control invariant set close to the maximum control invariant set under a good backup policy for many practical problems.

Keywords:Robust control, Autonomous vehicles Abstract: To bring complex systems into real world environments in a safe manner, they will have to be robust to uncertainties—both in the environment and the system. This paper investigates the safety of control systems under input disturbances, wherein the disturbances can capture uncertain- ties in the system. Safety, framed as forward invariance of sets in the state space, is ensured with the framework of control barrier functions (CBFs). Concretely, the definition of input to state safety (ISSf) is generalized to allow the synthesis of non-conservative, tunable controllers that are provably safe under varying disturbances. This is achieved by formulating the concept of tunable input to state safe control barrier functions (TISSf-CBFs) which guarantee safety for disturbances that vary with state and, therefore, provide less conservative means of accommodating uncertainty. The theoretical results are demonstrated with a simple control system with input disturbance and also applied to design a safe connected cruise controller for a heavy duty truck.

Keywords:Fault detection, Autonomous systems, Nonlinear systems Abstract: In this paper, we consider the problem of de-signing a model discrimination algorithm for partially known systems, where only sampled data of the unknown dynamics are available. Leveraging data-driven abstraction methods to over-approximate the unknown dynamics and an incremental abstraction approach, we propose a method to find a pair of piecewise affine functions that “includes” all possible trajectories of the original unknown dynamics which further simplify the data-driven abstraction and can scale well for high dimensional systems. Then, using the models from the abstraction method, we analyze the detectability of models from noisy, finite data as well as design a model discrimination algorithm to rule out models that are inconsistent with a newly observed output trajectory by checking the feasibility of mixed-integer linear programs. Moreover, we investigate the trade-off among the accuracy of abstraction models, the computational cost for obtaining reduced models and the guaranteed detection time T for distinguishing the models. Finally, we evaluate the effectiveness of our approach on a vehicle intent estimation example using the highD dataset of naturalistic vehicle trajectories recorded on German highways.

Keywords:Fault detection, Nonlinear systems identification, Control applications Abstract: The Koopman operator is a novel approach to embed nonlinear dynamics into linear models. This work shows its successful application for fault detection to a large-scale facility with challenging real-time requirements: the European XFEL, which is the worldwide largest linear particle accelerator. We concentrate on the superconducting radio-frequency cavities, from which 808 exist and whose effective operation directly influences the performance of the whole facility. Thus, a proper fault detection scheme is desired. While a nonlinear state-space description of the cavity dynamics is well-known, its usage along with an unscented Kalman filter is not able to cope with the challenging online implementation requirements. Therefore, in this paper, we apply the Koopman operator technique to identify a finite-dimensional linear approximation of the nonlinear system. For the data-driven identification, the model knowledge is exploited by choosing physically motivated basis functions. With the linear approximation at hand, a linear Kalman filter can be applied. Results are presented for real experimental data. Compared to the unscented Kalman filter, the same detection capability but a speed-up of three orders of magnitude in calculation time can be achieved with the Koopman-based Kalman filter, which enables its implementation to the real facility.

Keywords:Fault detection, Variable-structure/sliding-mode control, Delay systems Abstract: This paper proposes a first order sliding mode observer for the purpose of simultaneously estimating the unknown input time delay and reconstructing the loss of effectiveness in a model of an actuator. The adaptive algorithm is driven by the `equivalent output error injection' signal associated with the sliding motion. Sufficient conditions are given to ensure finite time convergence of the state estimation error system, ensuring both the time delay estimation error and the estimation error associated with the actuator fault converge to a small region around zero. The efficacy of the approach has been evaluated via both a numerical simulation and flight data validation.

Keywords:Fault diagnosis, Discrete event systems, Automata Abstract: In this paper, we characterize diagnosability for a labeled weighted automaton mathcal{A}^{mathbb{Q}} over the monoid (mathbb{Q},+,0). By developing a notion of concurrent composition, under a mild assumption that no observable transition is instantaneous, we prove that diagnosability of automaton mathcal{A}^{mathbb{Q}} can be verified in coNP. On the other hand, we prove that the problem of verifying diagnosability of a deterministic, deadlock-free automaton mathcal{A}^mathbb{N}} is coNP-hard, where mathcal{A}^{mathbb{N}} denotes a labeled weighted automaton over the monoid (mathbb{N},+,0).

Keywords:Fault diagnosis, Estimation, Nonlinear systems Abstract: In this paper a novel hybrid-degree dual cubature-based nonlinear filtering methodology is proposed for fault diagnosis of nonlinear systems subject to multiplicative component faults. Distinct from conventional dual estimation schemes, the nonlinear functions are approximated with cubature rules to achieve a designated and case-dependent degree of accuracy. Our methodology is motivated from two primary observations: (i) dynamic characteristics of system states and parameters generally are distinct and posses different degrees of complexities, and (ii) performance of cubature rules depend on the system dynamics and vary when approximate high-dimensional integrations are utilized. The boundedness of the estimation error covariance and stability analysis are formally investigated in presence of approximation errors due to cubature rules, uncertainties, and noise. The effectiveness of our proposed methodology is evaluated by application to a gas turbine engine for addressing the multi-mode component fault diagnosis problem within an integrated fault detection, isolation and identification framework. Case studies are provided to substantiate the superiority of the proposed methodology when compared with those of other representative filters including the Unscented Kalman Filters (UKF) and Particle Filters (PF).

Keywords:Fault diagnosis, Fault detection, Identification for control Abstract: This letter proposes a threat discrimination methodology for distinguishing between sensor replay attacks and sensor bias faults, based on the specially designed watermark integrated with adaptive estimation. For each threat type, a watermark is designed based on the changes that the threat imposes on the system. Threat discrimination conditions are rigorously investigated to characterize quantitatively the class of attacks and faults that can be discriminated by the proposed scheme. A simulation is presented to illustrate the effectiveness.

Keywords:Reduced order modeling, Differential-algebraic systems, Nonlinear systems Abstract: We extend the Loewner framework for nonlinear input-affine systems to nonlinear descriptor systems possessing a feedforward term. This is accomplished by further generalizing the notion of Loewner functions, which characterize the response of a system when interconnected with two generators. These Loewner functions are used to construct a Loewner equivalent model which yields the same Loewner functions when interconnected with the same generators, thus achieving interpolation in the Loewner sense. Finally, a feedforward term is added to the interpolant, thus providing a parameterization of a family of interpolants.

Keywords:Reduced order modeling, Model/Controller reduction, Linear parameter-varying systems Abstract: We present a novel projection-based model reduction framework for parametric linear time-invariant systems that allows interpolating the transfer function at a given frequency point along parameter-dependent curves as opposed to the standard approach where transfer function interpolation is achieved for a discrete set of parameter and frequency samples. We accomplish this goal by using parameter-dependent projection spaces. Our main result shows that for holomorphic system matrices, the corresponding interpolatory projection spaces are also holomorphic. The coefficients of the power series representation of the projection spaces can be computed iteratively using standard methods. We illustrate the analysis on three numerical examples.

Keywords:Reduced order modeling, Model/Controller reduction, Modeling Abstract: The paper addresses the model reduction problem by least squares moment matching for continuous-time, linear, time-invariant systems. The basic idea behind least squares moment matching is to approximate a transfer function by ensuring that the interpolation conditions imposed by moment matching are satisfied in a least squares sense. This idea is revisited using invariance equations and steady-state responses to provide a new time-domain characterization of least squares moment matching. The characterization, in turn, is then used to obtain a parameterized family of models achieving least squares moment matching. The theory is illustrated by a worked-out numerical example.

Keywords:Reduced order modeling, Simulation Abstract: With the escalating demand for fast simulation of large-scale multi-input multi-output (MIMO) RCS circuits formulated as second-order differential systems, the need arises for more effective decentralized second-order model order reduction (MOR) methods, while providing a desired approximation of the original system. Relative gain array (RGA) has shown promising efficacy in measuring the degree of each loop interaction, which is crucial for decoupling a MIMO system into several multi-input single-output (MISO) subsystems. Although several decentralized MOR methods have been introduced for dimension reduction to linear MIMO networks, hardly has any research explored second-order decentralized MOR methods with regard to MIMO RCS circuits. We develop a second-order block Arnoldi method based on RGA, termed RGA-SOBAR, which enables the extension of the SOAR method to MIMO scenarios. Experimental results on RCS networks show that most input-output interactions are negligible in terms of the magnitude-wise insignificance, and our proposed RGA-SOBAR based reduced systems perform with higher accuracy compared to the PRIMA and the generalized block SOAR methods.

Keywords:Reduced order modeling, Optimization algorithms, LMIs Abstract: This paper proposes an approach to model order reduction of stable linear time-invariant (LTI) models. The proposed approach extends time-domain moment matching by the minimization of the H_infty norm of the error dynamics characterizing the difference between the full-order and reduced-order models given fixed interpolation points. The optimal H_infty moment matching problem is a constrained optimization problem with bilinear constraints. Introducing a novel numerical procedure, we minimize the approximation error, while respecting the constraints and, thereby, find a suboptimal H_infty reduced-order model. The effectiveness of the approach is illustrated in a numerical example.

Keywords:Reduced order modeling, Uncertain systems, Biological systems Abstract: Model reduction methods usually focus on the error performance analysis; however, in presence of uncertainties, it is important to analyze the robustness properties of the error in model reduction as well. In this paper, we give robustness guarantees for structured model reduction of linear and nonlinear dynamical systems under parametric uncertainties. In particular, we consider a model reduction where the states in the reduced model are a strict subset of the states of the full model, and the dynamics for all other states are collapsed to zero (similar to quasi-steady state approximation). We show two approaches to compute a robustness metric for any such model reduction --- a direct linear analysis method for linear dynamics and a sensitivity analysis based approach that also works for nonlinear dynamics. We also prove that for linear systems, both methods give equivalent results.

Keywords:Networked control systems, Healthcare and medical systems, Optimal control Abstract: Modelling large networks is impractical since the difficulty of computation increases combinatorically with every node added. One approach to alleviating these issues is to find a limit object of a corresponding graph sequence called a graphon, which is associated with a limiting adjacency matrix mapped to the unit square. However, graphons can be difficult to use computationally. To this end, a type of random graph called a featured graph is introduced, which is a graph sequence with meaningful vertex attributes. Following this, the convergence of the adjacency matrix as an operator to the featured graphon limit is explored. Convergence is qualitatively demonstrated on an SIR epidemic model generalized to multiple communities.

Keywords:Networked control systems, Linear systems, Distributed control Abstract: In this paper, an event-based consensus of linear multiagent systems (MASs) is considered. By using the concept of condensation graph, some existing works under strongly connected networks are extended to the event-triggered consensus under the general directed network with a directed spanning tree. The extension preserves some advantages of the control law under the original network, which does not lead to Zeno behavior. In addition, the gain matrix in the control law can be designed separately for different strongly connected components. The effectiveness of the extension strategy is verified by a numerical example.

Keywords:Networked control systems, Observers for nonlinear systems, Sensor networks Abstract: We study emulation-based state estimation for non-linear plants that communicate with a remote observer over a shared wireless network subject to packet losses. To reduce bandwidth usage, a stochastic communication protocol is employed to determine which node should be given access to the network. We describe the overall wireless system as a hybrid model, which allows us to capture the behaviour both between and at transmission instants, whilst covering network features such as random transmission instants, packet losses, and stochastic scheduling. Under this setting, we provide sufficient conditions on the transmission rate that guarantee an input-to-state stability property for the corresponding estimation error system. We illustrate our results with an example of Lipschitz non-linear plants.

Keywords:Networked control systems, Switched systems, Stability of linear systems Abstract: This paper deals with the design of scheduling logics for Networked Control Systems (NCSs) whose shared communication networks have limited capacity. We assume that among (N) plants, only (M:(< N)) plants can communicate with their controllers at any time instant. We present an algorithm to allocate the network to the plants periodically such that stability of each plant is preserved. The main apparatus for our analysis is a switched systems representation of the individual plants in an NCS. We rely on multiple Lyapunov-like functions and graph-theoretic arguments to design our scheduling logics. The set of results presented in this paper is a continuous-time counterpart of the results proposed in cite{abc}. We present a set of numerical experiments to demonstrate the performance of our techniques.

Keywords:Networked control systems, Switched systems, Uncertain systems Abstract: This paper focuses on networked control systems with parameter uncertainties in system models under Denial-of-Services (DoS) attacks. The objective is to find the coarsest quantizer for a given quadratic Lyapunov function and still maintain stability while the network for transmitting quantized control signals is disrupted by a class of DoS attacks. Our main result shows that the coarsest quantization can be analytically obtained in the form of logarithmic quantizers whose coarseness is constrained by the unstable system poles and the level of DoS attacks. This result explicitly shows that under more frequent DoS attacks, finer quantization is required to achieve stability. Furthermore, we provide a switching control method for increasing the coarseness while the system operates without much influence of attacks.

Sorbonne Universités, Inria, UPMC Université Paris 06

Keywords:Modeling, Biological systems, Networked control systems Abstract: Controlling human mobility during an epidemic is a fundamental issue faced by policymakers. Such control can only be done optimally if human mobility is adequately modeled at the scale of a city or metropolis. This paper, first, develops a model of human mobility that captures the daily patterns of mobility in an urban environment through time-dependent gating functions, which are controlled by the destination schedules and mobility windows. The epidemic spread process is incorporated at each location that depends on the number of susceptible and infected people present at that location. Then, two optimal control policies are proposed to maximize the economic activity at the destinations while mitigating the epidemic. Precisely, operating capacities and time schedules of destinations are controlled to maximize the economic activity under the constraint that the number of active infected cases remains bounded.

Keywords:Agents-based systems, Game theory, Optimization Abstract: We consider a two-dimensional multi-agent echelon formation, where each agent receives a benefit that depends on its position relative to others, and adjusts its position to increase this benefit. We analyze the selfish case where each agent maximizes its own benefit, leading to a Nash-equilibrium problem, and the collaborative case in which agents maximize the global benefit of the group. We provide conditions on the benefit function under which the echelon formations cannot be Nash equilbriums or group optimums.

We then show that these conditions are satisfied by the conventionally used fixed-wing wake benefit model. This implies that energy saving alone is not sufficient to explain the emergence of the observed migratory formations, based on the fixed-wing model. Hence, either non-aerodynamic aspects or a more accurate model of bird dynamics should be considered to construct such formations.

Keywords:Iterative learning control, Decentralized control, Large-scale systems Abstract: Control of large-scale networked systems often necessitates modeling complex interactions amongst agents. However, as the size of the network increases, modeling these interactions often becomes exponentially expensive in applications. In this paper, we propose a distributed model-free policy iteration algorithm to design a feedback mechanism for large networks of homogeneous systems. We assume that the networked system is built upon an underlying information-exchange graph allowing the distributed controller to synthesize a feedback signal using information from adjacent agents. This model-free approach provides a stabilizing distributed feedback controller through a learning phase. In particular, a data-driven control method is utilized to circumvent model uncertainties by directly synthesizing a controller based on data that is obtained from a relatively small subgraph of the original network. Additionally, a stability margin is learned from data which is then utilized to design a suboptimal distributed controller for the entire network even during the learning phase. We showcase the performance of our methodology by examining distributed control scenarios involving modeling errors.

Keywords:Agents-based systems, Distributed control Abstract: This paper studies a distributed multi-armed bandit problem in a network of multiple agents, each of which can communicate only with its neighbors, where neighbor relationships are described by an undirected graph. Each agent makes a sequence of decisions on selecting an arm from a given set of candidates, yet it only has access to local samples of the reward for each action, which is an unknown random variable. All the agents share the same distribution of each arm’s reward. A distributed upper confidence bound (UCB) algorithm is proposed for the agents to cooperatively learn the best arm, which does not require any global information. It is shown that the algorithm achieves a logarithmic regret for each of the agents, even though the graph is disconnected. The derived regret implies that the proposed distributed UCB algorithm enables a faster learning for any agent in the network compared with the classical single-agent UCB algorithm, as long as the agent has at least one neighbor.

Keywords:Control applications, Autonomous systems, Network analysis and control Abstract: In this paper, a deep structured tracking problem is introduced for a large number of decision-makers. The problem is formulated as a linear quadratic deep structured team, where the decision-makers wish to track a global target cooperatively while considering their local targets. For the unconstrained setup, the gauge transformation technique is used to decompose the resultant optimization problem in order to obtain a low-dimensional optimal control strategy in terms of the local and global Riccati equations. For the constrained case, however, the feasible set is not necessarily decomposable by the gauge transformation. To overcome this hurdle, we propose a family of local and global receding horizon control problems, where a carefully constructed linear combination of their solutions provides a feasible solution for the original constrained problem. The salient property of the above solutions is that they are tractable with respect to the number of decision-makers and can be implemented in a distributed manner. In addition, the main results are generalized to cases with multiple sub-populations and multiple features, including leader-follower setup, cohesive cost function and soft structural constraint. Furthermore, a class of cyber-physical attacks is proposed in terms of perturbed influence factors. A numerical example is presented to demonstrate the efficacy of the results.

Keywords:Kalman filtering, Large-scale systems, Linear parameter-varying systems Abstract: In this article, we introduce decentralized Kalman filters for linear quadratic deep structured teams. The agents in deep structured teams are coupled in dynamics, costs and measurements through a set of linear regressions of the states and actions (also called deep states and deep actions). The information structure is decentralized, where every agent observes a noisy measurement of its local state and global deep state. Since the number of agents is often very large in deep structured teams, any naive approach to find an optimal Kalman filter suffers from the curse of dimensionality. Moreover, due to the decentralized nature of information structure, the resultant optimization problem is non-convex, in general, where non-linear strategies can outperform linear ones. However, we prove that the optimal strategy is linear in the local state estimate as well as the deep state estimate, and can be efficiently computed by two scale-free Riccati equations and Kalman filters. To achieve the above result, we propose a bi-level orthogonal approach across both space and time levels based on a gauge transformation technique. We also establish a separation principle between optimal control and optimal estimation. Furthermore, we show that as the number of agents goes to infinity, the Kalman gain associated with the deep state estimate converges to zero at a rate inversely proportional to the number of agents. This leads to a fully decentralized approximate strategy where every agent predicts the deep state by its conditional/unconditional expected value (also known as certainty equivalence/mean-field approximation). To the best of our knowledge, this is the first result establishing a tractable optimal strategy under noisy measurements for a class of large-scale control systems with non-classical information structure, that is neither partially nested nor quadratically invariant.

Keywords:Distributed control, Large-scale systems, Network analysis and control Abstract: We study an optimal control problem for a simple transportation model on a path graph. We give a closed-form solution for the optimal controller, which can also account for planned disturbances using feed-forward. The optimal controller is highly structured, which allows the controller to be implemented using only local communication, conducted through two sweeps through the graph.

Keywords:Supervisory control, Discrete event systems, Automata Abstract: Recently, the problem of model-based synthesis of covert attackers has received a lot of attention in the discrete event systems literature. However, all the existing works assume the model of the supervisor to be available (to the adversary) for the synthesis to be effective, which can be unrealistic in practice. In this work, we consider a much more challenging, but more practical, setup where the model of the supervisor is in general not available. To compensate this lack of knowledge, we assume that the adversary has recorded a (prefix-closed) finite set of observations of the runs of the closed-loop system, which can be used for assisting the synthesis. We present a heuristic algorithm for the synthesis of covert damage-reachable attackers, based on the model of the plant and the (finite) set of observations, by a transformation into solving an instance of the partial-observation supervisor synthesis problem over certain surrogate plant. Due to the over-approximation involved in the surrogate plant, the heuristic is provably sound, but in general it is not complete. For simplicity, in this paper we only consider covert attackers that are able to carry out sensor replacement attacks and actuator disablement attacks.

Keywords:Supervisory control, Discrete event systems, Automata Abstract: The ability to hide sensitive information is important in many contexts such as multi-agent systems' communications, industry 4.0, among others. In this paper, we deal with weak versions of known state-based opacity properties by using synchronizing automata to enforce such properties. A case study is presented in the context of the communication of multi-agent systems, where we aim to hide the leader from an intruder. Using synchronizing automata, initial-state and initial-and-final state opacity are enforced even if the intruder has full observation of the events of the system.

Keywords:Discrete event systems, Formal Verification/Synthesis, Automata Abstract: In this paper, we investigate the problem of synthesizing optimal control policies for stochastic control systems to achieve high-level temporal logic specifications under security constraints. Specifically, we consider a stochastic control system modeled by a finite labeled Markov Decision Process (MDP). We consider a passive intruder (an eavesdropper) that can observe the external output behavior of the system. We assume the system has a secret, modeled as visiting of some secret states, that does not want to be revealed to the intruder. The security constraint is that the intruder can never determine for sure that the system is/was at a secret state for any specific instant of time. The overall objective is to maximize the probability of achieving the temporal logic task while ensuring the information-flow security of the system. An effective algorithm is proposed to solve this problem. Specifically, we show that the security constraints can be handled as a safety requirement over the information-state-space and the optimal control problem can be then solved by leveraging existing results from probabilistic model checking. The proposed approach is also illustrated by a case study for robot task planning.

Keywords:Discrete event systems, Control Systems Privacy, Automata Abstract: This paper studies current-state opacity and initial-state opacity verification of distributed discrete event systems. The distributed system's global model is the parallel composition of multiple local systems: each of which represents a component. We propose sufficient conditions for verifying opacity of the global system model based only on the opacity of the local systems. We also present efficient approaches for the opacity verification problem that only rely on the intruder's observer automata of the local DESs.

Keywords:Discrete event systems, Petri nets, Optimization Abstract: Privacy of distributed cyber-physical systems can be compromised by the presence of information leaks which permit to external intruders to infer the state of the system itself. These systems are built using several off-the-shelf components with communication capabilities that provide a significant level of control, and lower operational costs in comparison to the traditional vendor-specific proprietary and closed-source systems. However, these components expose the control systems to more vulnerabilities and threats. This work focuses on the multi-level intransitive non-interference, a property particularly suitable to tackle privacy problems of control systems under attack. The property is characterized and verified using Petri net models and mathematical programming.

Keywords:Petri nets Abstract: In this paper, we study the problem of non-blockingness verification by tapping into the basis reachability graph (BRG). Non-blockingness is a property that ensures that all pre-specified tasks can be completed, which is a mandatory requirement during the system design stage. We develop a condition of transition partition of a given net such that the corresponding conflict-increase BRG contains sufficient information on verifying non-blockingness of its corresponding Petri net. Thanks to the compactness of the BRG, our approach possesses practical efficiency since the exhaustive enumeration of the state space can be avoided. In particular, our method does not require that the net is deadlock-free.

Keywords:Energy systems, Estimation, Stability of nonlinear systems Abstract: The Immersion and Invariance (I&I) wind speed estimator is a powerful and widely-used technique to estimate the rotor effective wind speed on horizontal axis wind turbines. Anyway, its global convergence proof is rather cumbersome, which hinders the extension of the method and proof to time-delayed and/or uncertain systems. In this letter, we illustrate that the circle criterion can be used as an alternative method to prove the global convergence of the I&I estimator. This also opens up the inclusion of time-delays and uncertainties. First, we demonstrate that the I&I wind speed estimator is equivalent to a torque balance estimator with a proportional correction term. As the nonlinearity in the estimator is sector bounded, the well-known circle criterion is applied to the estimator to guarantee its global convergence for time-delayed systems. By looking at the theoretical framework from this new perspective, this letter further proposes the addition of an integrator to the correction term to improve the estimator performance. Case studies show that the proposed estimator with an additional integral correction term is effective at wind speed estimation. Furthermore, its global convergence can be guaranteed by the circle criterion for time-delayed systems.

Keywords:Energy systems, Estimation Abstract: The temperature distribution in the battery significantly impacts the short-term and long-term performance of battery systems. Therefore, efficient, safe, and reliable battery system operation requires an accurate estimation of the temperature field. The current industry standard for sensors to battery cell ratio is quite frugal. Thus, the problem of sensor placement for accurate temperature estimation becomes non-trivial, especially for large-scale systems. In this paper, we explore a greedy approach for sensor placement suitable for large-scale battery systems. An observer to estimate the thermal field is designed in an H-infinity framework while simultaneously minimizing the sensor precisions, thus lowering the overall thermal management system's economic cost.

Keywords:Energy systems, Fault tolerant systems, Lyapunov methods Abstract: This paper introduces a complete DC-AC conversion system fed by photovoltaic (PV) energy. The system consists of N PV panels, N DC-DC boost converters, N cascaded H-bridge inverters, a DC-link composed of N capacitors and an LCL filter. This work aims at reaching threefold control objectives: i) Extracting the available maximum power by regulating the voltages across the PV panels, ii) Ensuring a unitary power factor, iii) Regulating the DC-link voltage to a desired reference. To achieve the mentioned objectives, a multi-loop regulator is designed. The PV panels are individually controlled to track the maximum power point in order to efficiently operate at either the same or different varying climatic conditions without failures. In addition to the maximum power point tracking (MPPT) controller, two cascaded loops guaranteeing a satisfactory power factor and DC-link voltage regulation are developed. The nonlinear backstepping approach combined with Lyapunov theory are used based on the averaged model for the synthesis of the multi-loop controller. The performance of the studied system is tested via MATLAB / SimPowerSystems environment. The obtained simulation results prove that the proposed controller meets its objectives and demonstrate the efficiency of the chosen control strategy under faulty conditions.

Keywords:Optimization algorithms, Energy systems Abstract: The multi-energy system (MES) takes into account different forms of energy such as electricity, heat, and gas, and coordinate the different processes from the side of supply to demand. It truly realizes the mutual complementation of multiple energy resources and can greatly improve the flexibility and efficiency compared to traditional energy systems. In this paper, we study the economic dispatch (ED) problem in the MES aiming to minimize both generation and pollution cost. A distributed method via the symmetric alternating direction multiplier method (symmetric-ADMM) is proposed to deal with non-convex factors caused by coupling between different energy sources. Through the dynamic consensus mechanism and the variational inequality, we prove that the proposed algorithm has the convergence rate of mathcal{O}( frac{1}{t}). The effectiveness of the proposed algorithm is verified by simulations on the IEEE 24-bus system.

Keywords:Power systems, Energy systems Abstract: The rapid growth of distributed energy resources (DERs) is one of the most significant changes to electricity systems around the world. Examples of DERs include solar panels, small natural gas-fueled generators, combined heat and power plants, etc. Due to the small supply capacities of these DERs, it is impractical for them to participate directly in the wholesale electricity market. We study in this paper an efficient aggregation model where a profit-maximizing aggregator procures electricity from DERs, and sells them in the wholesale market. The interaction between the aggregator and the DER owners is modeled as a Stackelberg game: the aggregator adopts two-part pricing by announcing a participation fee and a per-unit price of procurement for each DER owner, and the DER owner responds by choosing her payoff-maximizing energy supplies. We show that our proposed model preserves full market efficiency, i.e., the social welfare achieved by the aggregation model is the same as that when DERs participate directly in the wholesale market.

Keywords:Variable-structure/sliding-mode control, Robust control Abstract: The presence of chattering i.e. high frequency oscillations with finite amplitude, is unavoidable in systems driven by conventional and higher order sliding mode (HOSM) control. A widely used technique to attenuate chattering is the boundary layer (BL) method, it is based on the approximation of discontinuous terms by a saturation function. However, sliding mode control (SMC) systems with BL approximation still presents chattering due to unmodeled dynamics. Amplitude and frequency of chattering can be estimated applying describing function (DF) and harmonic balance (HB) equation techniques. In this paper, HOSM controllers such as Twisting, Nested second order, and Super Twisting (ST) extension to relative degree two, with BL approximation, are analyzed. The effect of the BL value in the parameters of chattering is studied. When the BL value increments, chattering in systems driven by Twisting and Nested may decrease in amplitude, whereas in the case of ST-extension the variation in amplitude and frequency is minimum. Also, it is included the analysis when the derivative in Twisting and ST-extension algorithms is computed via a linear differentiator. Examples and simulations verifying the results are presented.

Keywords:Variable-structure/sliding-mode control Abstract: This note proposes a novel architecture of integral sliding mode control, in which a special "ideal control" part is introduced. This part incorporates a fairly general form of internal model to deal with regular (i.e., modeled) persistent disturbances. A key property of this architecture is a complete separation of the internal model from the design of the "discontinuous" component of the controller. In particular, the latter component is designed for systems whose dimension coincides with that of the plant, even if the internal model is infinite dimensional.

Keywords:Systems biology, Variable-structure/sliding-mode control, Process Control Abstract: We address the problem of controlling the dilution rate in a chemostat to regulate the ratio between the concentrations of two microbial populations growing in continuous culture. After analyzing the open-loop dynamics of this multicellular system, we present two alternative feedback control strategies, one based on a gain-scheduled state feedback controller, the other on a switching control strategy. We show that both strategies are effective in solving the problem and illustrate the results by a set of representative numerical simulation.

Keywords:Lyapunov methods, Variable-structure/sliding-mode control, Stability of nonlinear systems Abstract: This paper proposes a novel sliding mode control method for a class of electro-mechanical systems using passivity based approach. For mechanical systems, the authors proposed a passivity based sliding mode controller based on the kinetic potential energy shaping method which allows one to obtain a wider class of Lyapunov function candidates. The present paper extends this framework to cope with a class of electro-mechanical systems and gives a new class of energy based Lyapunov function candidates. Based on this technique, a novel sliding mode controller with an explicit energy based Lyapunov function is proposed. It is expected to provide a new basis for a unified control design framework for both passivity based control and sliding mode control. Furthermore, a numerical example demonstrates the effectiveness of the proposed method.

Keywords:Decentralized control, Variable-structure/sliding-mode control, Uncertain systems Abstract: In this paper, a class of nonlinear interconnected systems with matched and unmatched uncertainties is considered. The isolated subsystem dynamics are described by linear systems and a nonlinear component. The matched uncertainties and unmatched unknown interconnection terms are assumed to be bounded by known functions. Based on sliding mode techniques, a state feedback decentralized control scheme is proposed such that the outputs of the controlled interconnected system track given desired signals uniformly ultimately. The desired reference signals are allowed to be time-varying. Using multiple transformations, the considered system is transferred to a new interconnected system with an appropriate structure to facilitate the sliding surface design and the design of a decentralized controller. A set of conditions is proposed to guarantee that the designed controller drives the tracking errors onto the sliding surface. The sliding motion exhibited by the error dynamics is uniformly ultimately bounded. The developed results are applied to a river quality control problem. Simulation results show that the proposed decentralized control strategy is effective and feasible.

Keywords:Fault accomodation, Autonomous vehicles, Fault tolerant systems Abstract: In this paper, an actuator fault accommodation controller is developed to solve the trajectory tracking problem in Quad-Rotors under the effects of faults in multiple actuators and external disturbances. The faults are modeled as partial loss of effectiveness. The proposed fault accommodation approach is composed of a fault identification module and a baseline robust nominal controller. The fault identification module is based on a finite-time sliding-mode observer that provides a set of residuals using only the output information. The fault accommodation strategy uses fault identification to partially compensate the actuator faults allowing the usage of a baseline robust-nominal controller that deals with the external disturbances. Numerical simulations show the performance of the proposed control strategy.

Keywords:Algebraic/geometric methods, Agents-based systems, Nonlinear systems Abstract: Positivity and Perron-Frobenius theory provide an elegant framework for the convergence analysis of linear consensus algorithms. Here we consider a generalization of these ideas to the analysis of nonlinear consensus algorithms on the circle and establish tools for the design of consensus protocols that monotonically converge to target formations on the circle.

Keywords:Agents-based systems, Distributed control, Autonomous systems Abstract: We study the formation control problem for multiple nonholonomic vehicles in 3D space, where vehicles are required to maintain a prescribed pattern and rotate around a target in the target plane, with the direction of rotation along with the normal vector of the target plane. Unlike the most existing works that study formation problems of agents modeled by mass-point in a 2D plane, control of multiple nonholonomic vehicles in 3D space means a grand challenge since both the space and dynamics are complex. We give explicit formulations of the problem and vehicles' dynamics. Then, control laws to solve the problem are proposed and further transformed into the body-fixed frames of vehicles to show that they can be easily implemented using only local measurements and the direction of gravity. Theoretical analysis is presented and simulations show the effectiveness of the proposed laws.

Keywords:Distributed control, Quantized systems, Robotics Abstract: This paper addresses a formation control problem of four-legged robots with discrete-valued inputs. Four-legged robots have the potential for completing tasks on non-flat terrains, while their position control is achieved by switching between specific movements, i.e., discrete-valued signals. This implies that existing results assuming the use of continuous-valued inputs are not available. We present a solution to this control problem by combining conventional formation controllers with dynamic quantization. The resulting feedback system is analyzed based on a performance index describing the difference between the systems with and without quantization. As a result, we can estimate the effects of the quantization on the behavior of the system and guarantee its stability.

Keywords:Distributed control, Linear parameter-varying systems, LMIs Abstract: This paper studies the formation control problem for a group of non-holonomic agents modeled as LPV systems with heterogeneous scheduling. Here we use an approach based on an information flow filter that makes it possible to design the dynamics of the information flow in the network. We propose a synthesis condition in the form of a linear matrix inequality for a distributed control scheme that guarantees stability and a level of mathcal{L}_2 performance. Moreover, by using the framework of decomposable systems, the complexity of the synthesis problem can be made independent of the network size; it corresponds to the size of the synthesis problem for a single agent. The work presented here extends earlier work where a similar scheme was proposed, however restricted by the assumption that the LPV agents are scheduled homogeneously. Whereas in that work the agents were modeled as polytopic LPV models, here the extension to heterogeneously scheduled agents is achieved by using LFT representations of the agents and employing the full-block S-procedure for synthesis. The proposed method is illustrated in simulation by applying it to a formation control problem for a group of dynamic unicycles.

Keywords:Autonomous systems, Cooperative control, Lyapunov methods Abstract: This paper studies the formation tracking control problem in the agents' local co-ordinate frame without any special assumption, such as positive definiteness, on the initial orientation matrix. When follower agents do not have knowledge of their absolute orientation with respect to a global reference frame, formation control is difficult and special assumptions on initial orientation matrix are generally imposed for orientation synchronization. To address this, a distributed fixed time orientation synchronization law is first presented, using only relative orientation measurements, which aligns the co-ordinate frames of agents almost globally in finite time and locally in fixed time. This law is then used in cascade with an acceleration command for formation tracking control in a leader-follower set-up. Global asymptotic convergence of formation tracking error is proved for displacement based formation. For bearing-only formation control, semi-global uniformly asymptotic stability is established. Simulations illustrate the applicability of the results.

Keywords:Formal Verification/Synthesis, Uncertain systems, Agents-based systems Abstract: Collision-free motion planning of formation of robots is an essential property to assess for safety purpose. We propose in this paper a new formal verification method based on abstract interpretation and constraint satisfaction problems to reach this goal. We consider state of the art control algorithms for formation maneuver to generate trajectories for a group of robots. Additionally, bounded uncertainties are considered to represent potential localization and measure errors. The collision-free property is formalized using the constraint satisfaction problem framework.