Keywords: Autonomous robots, Agents-based systems, Air traffic management
Abstract: This paper addresses trajectory planning in a multi-agent cooperative setting, where n agents are moving in the same region and need to coordinate so as to maintain a certain pairwise safety distance, while avoiding obstacles. We introduce a decentralized strategy that is based on an iterative (re)plan-compare-assign process. The key features of the proposed strategy are that coordination is obtained via the compare-assign phase in at most n iterations (including the initialization), and (re)planning is performed by the agents using a single-agent planner, considering the tentative trajectories of the others fixed, and without sharing with them their tracking capabilities and adopted cost criterion. In the proposed implementation, each agent uses a dynamic Rapidly exploring Random Tree star (RRT*) planner that integrates a new prune and graft feature to avoid rebuilding a new tree from its root each time replanning is needed. The resulting Multi-RRT* algorithm is tested in 2D scenarios and shows promising results.

Keywords: Autonomous robots, Autonomous systems, Robotics
Abstract: In this paper, we propose a new model predictive control (MPC) formulation for autonomous driving. The novelty of our MPC stems from the following results. Firstly, we adopt an alternating minimization approach wherein linear velocities and angular accelerations are alternately optimized. We show that in contrast to the joint optimization, the alternating minimization better exploits the structure of the problem, which in turn translates to reduction in computation time. Secondly, our MPC explicitly incorporates the time dependent non-linear actuator dynamics that captures the transient response of the vehicle for a given commanded velocity. This added complexity improves the predictive component of MPC resulting in improved margin of inter-vehicle distance during maneuvers like overtaking, lane-change, etc. Although, past works have also incorporated actuator dynamics within MPC, there has been very few attempts towards coupling actuator dynamics to collision avoidance constraints through the non-holonomic motion model of the vehicle and analyzing the resulting behavior. We use a high fidelity simulator to benchmark our actuator dynamics augmented MPC with other related approaches in terms of metrics like inter-vehicle distance, trajectory smoothness, and velocity overshoot.

Keywords: Autonomous robots, Cooperative control
Abstract: In this paper we present a reformulation–framed as a constrained optimization problem–of multi-robot tasks which are encoded through a cost function that is to be minimized. The advantages of this approach are multiple. The constraint-based formulation provides a natural way of enabling long-term robot autonomy applications, where resilience and adaptability to changing environmental conditions are essential. Moreover, under certain assumptions on the cost function, the resulting controller is guaranteed to be decentralized. Furthermore, finite-time convergence can be achieved, while using local information only, and therefore preserving the decentralized nature of the algorithm. The developed control framework has been tested on a team of ground mobile robots implementing long-term environmental monitoring.

Keywords: Autonomous robots, Estimation
Abstract: To empower an autonomous robot to perform long-term navigation in a given area, a concurrent localization and map update algorithm is required. In this paper, we tackle this problem by providing both theoretical analysis and algorithm design for robotic systems equipped with 2D laser range finders. The first key contribution of this paper is that we propose a hybrid signed distance field (SDF) framework for laser based localization. The proposed hybrid SDF integrates two methods with complementary characteristics, namely Euclidean SDF (ESDF) and Truncated SDF (TSDF). With our framework, accurate pose estimation and fast map update can be performed simultaneously. Moreover, we introduce a novel sliding window estimator which attains better accuracy by consistently utilizing sensor and map information with both frame-to-frame and frame-to-map data association. Real-world experimental results demonstrate that the proposed algorithm can be used for commercial robots in various environments with long-term usage. Experiments also show that our approach outperforms competing approaches by a wide margin.

Keywords: Autonomous robots, Flight control, Robust control
Abstract: This paper provides insights on the tilt-rotor quadcopters being a fully actuated system. The tilt-rotor quadcopters are a novel class of quadcopters with the capability of rotating each arm/rotor of the quadcopter to an angle using a servo motor. With the additional servo control inputs, the tilt-rotor quadcopters are fully actuated systems and hence can even hover at any desired orientation. The dynamics of the tilt-rotor quadcopters are derived based on hardware developed in the laboratory with minimal assumptions. A novel non-linear sliding mode controller is designed that provides the controller input values to achieve any orientation and position as desired. Computational Fluid Dynamic (CFD) simulations were performed on a CAD model of the tilt-rotor quadcopter to obtain real time drag forces for various wind velocities. The robustness of the sliding mode controller is demonstrated under various wind disturbance scenarios while the quadcopter is hovering at a desired position and attitude.

Keywords: Autonomous robots, Maritime control, Constrained control
Abstract: This paper addresses the swimming dynamics and control of a flexible fish-inspired robot based on closed-loop control of an internal reaction wheel. Previous studies have shown that the dynamics of a rigid swimming robot are analogous to the canonical Chaplygin sleigh, due to the nonholonomic constraint imposed by the Kutta condition applied to the fish-like tail. The Chaplygin-sleigh dynamics are used here to design a propulsion and steering controller for a flexible swimming robot using state feedback. The desired average heading angle is achieved using a torque calculated from the instantaneous heading angle and rate. This feedback law stabilizes a limit cycle about the desired heading angle and produces forward swimming motion. Analysis of a global bifurcation in the dynamics under feedback control reveals the set of control gains that yield the desired limit cycle. Simulations illustrate planar swimming motion and preliminary experimental results are provided.

Keywords: Traffic control
Abstract: The scientific, technological, social and economic impact of successful research in road traffic control is very significant, with immediate effects on safety, quality of life, environment, use of energy resources, and transportation costs. Yet, the development of effective methods and algorithms for road traffic management has to face notable methodological challenges. In addition, the type of traffic control strategies developed so far, the “classical approaches”, need now to be updated and adapted to take into account the fast development in automotive technologies, traffic sensors, data processing, and communications. This Tutorial Session will address all these aspects, starting from an overview of classical traffic control concepts to arrive at encompassing emerging research trends at different scales: from the management of very large and complex traffic networks to the control of individual connected automated vehicles, also including heavy-duty vehicles, in order to have a beneficial influence on traffic dynamics. The major classical and emerging topics in road traffic control will be introduced in a tutorial style in this leading presentation, while they will be discussed in more details in the subsequent presentations.

Keywords: Traffic control
Abstract: This talk discusses some of our recent advancements in management and estimation of traffic road networks. Traffic congestion is a major source of world-wide inefficiency, with one study estimating that, in 2014, delays due to congestion cost 7 billion hours and 160B in the US alone. However, mitigating congestion through management techniques is difficult, as traffic congestion exists in a confluence of complex phenomena, such as nonlinear shockwaves, emergent macroscopic network effects from multiple agents, and low system observability and controllability. Growth of traffic demand shows no sign of decreasing, so continued infrastructure expansion must be combined with continued development of traffic control engineering to abate these societal costs. Some of today's traffic control efforts make use of novel formulations of these nonlinear systems and new sources of data provided by the connected and autonomous vehicles now entering the fleet. In this talk I will describe a set of modeling and simulation tools for traffic operations planning to provide quick and quantitative assessments of the benefits that transportation management center control policies can provide on freeway corridors, in order to decrease congestion. In addition to describing some basic controllability and observability properties of traffic dynamics, I will briefly describe a set of parameter calibration, ramp flow estimation and sensor fault detection algorithms that were developed in order to achieve reliable simulation of freeway traffic. Subsequently, I will focus on traffic management.

Keywords: Traffic control
Abstract: This talk will discuss traffic control strategies for freeway networks aimed at improving the overall sustainability of such systems. This means that the proposed traffic management and control strategies are designed not only for maximally exploiting the road capacity and preventing congestion phenomena, but also to reduce pollutant emissions, fuel consumptions, and accidents. This, in turn, is also tied to the possibility of improving safety on freeway traffic systems. By focusing on feedback predictive controllers, regulation schemes for freeway networks will be presented, defined by optimizing objective functions considering traffic related performance, emissions reduction and safety improvement. The considered control schemes are, then, based on multi-objective optimization in which several, possibly conflicting cost functions, are present and explicitly analyzed. Moreover, the considered controllers have a multi-class nature, meaning that different classes of vehicles are explicitly considered and dedicated control actions are determined for each class.

Keywords: Traffic control
Abstract: A tutorial-style presentation will be made on a decentralized framework for optimally controlling Connected Automated Vehicles (CAVs) at conflict points of a transportation system: road merging, signal-free intersections, automated passing in highways, and no-stop crossing at signaled intersections. The objective is set to minimize convex combinations of travel times over designated road segments and of energy and passenger comfort metrics. At the same time, hard safety constraints are guaranteed, along with speed and acceleration limits. We will describe how to check for feasible solutions and how to obtain complete analytical solutions of these decentralized optimization problems. Simulation examples will be included to demonstrate the on-line computational feasibility of the proposed framework, as well as its benefits by allowing CAVs to conserve momentum and energy while also improving travel times and ensuring safety passenger comfort.

Keywords: Traffic control
Abstract: Automated and connected road vehicles enable large-scale control and optimisation of the transport system with the potential to radically improve energy efficiency, decrease the environmental footprint, and enhance safety. In this talk we will focus on automated heavy-duty vehicle platooning, which is currently being implemented and evaluated by several truck manufacturers world-wide. We will discuss how to deploy feedback control of individual platoons utilising the cellular communication infrastructure and how such controlled platoons can be used improve overall traffic conditions. It will be argued that the average total variation of traffic density can be reduced and thereby creating incentives for platooning beyond fuel savings and driver support.

Keywords: Traffic control
Abstract: Panel Discussion

Keywords: Cooperative control, Adaptive control, Spacecraft control
Abstract: The leader-following consensus problem of multiple uncertain rigid body systems subject to static networks has been studied by a distributed adaptive control law utilizing the distributed observer for the leader system. In this paper, we extend this result to jointly connected switching networks. This extension needs to overcome the discontinuity of some variables caused by the switching network. Additionally, we remove the assumption that every follower knows the system matrix of the leader system by employing an adaptive distributed observer for the leader system.

Keywords: Cooperative control, Aerospace, Multivehicle systems
Abstract: This paper experimentally evaluates continuum deformation cooperative control for the first time. Theoretical results are expanded to place a bounding triangle on the leader-follower system such that the team is contained despite nontrivial tracking error. Flight tests were conducted with custom quadrotors running a modified version of ArduPilot on a BeagleBone Blue in M-Air, an outdoor netted flight facility. Motion capture and an onboard inertial measurement unit were used for state estimation. Position error was characterized in single vehicle tests using quintic spline trajectories and different reference velocities. Five-quadrotor leader trajectories were generated, and followers executed the continuum deformation control law in-flight. Flight tests successfully demonstrated continuum deformation; future work in characterizing error propagation from leaders to followers is discussed.

Keywords: Cooperative control, Agents-based systems, Decentralized control
Abstract: We consider the optimal multi-agent persistent monitoring problem defined by a team of cooperating agents visiting a set of nodes (targets) on a graph with the objective of minimizing a measure of overall node state uncertainty. The solution to this problem involves agent trajectories defined both by the sequence of nodes to be visited by each agent and the amount of time spent at each node. We propose a class of distributed threshold-based parametric controllers through which agent transitions from one node to the next are controlled by thresholds on the node uncertainty. The resulting behavior of the agent-target system is described by a hybrid dynamic system. This enables the use of Infinitesimal Perturbation Analysis (IPA) to determine on-line optimal threshold parameters through gradient descent and thus obtain optimal controllers within this family of threshold-based policies. Simulations are included to illustrate our results and compare them to optimal solutions derived through dynamic programming.

Keywords: Cooperative control, Agents-based systems, Networked control systems
Abstract: In this paper, we consider the regional consensus problem for a group of identical systems, each represented by a linear differential inclusion, over an undirected communication topology. Each vertex system of the linear differential inclusion is represented by a general linear system subject to input saturation, and hence only regional consensus can be achieved. For given saturated distributed linear control protocols, we establish a set of conditions under which these control protocols achieve regional consensus and a level set of a Laplacian quadratic function can be used as an estimate of the domain of consensus. These conditions are given in the form of matrix inequalities and involve the properties of the communication topology. Based on these matrix inequalities, we formulate a linear matrix inequalities based optimization problem for obtaining as large an estimate of the domain of consensus as possible. By viewing the gain matrix in the consensus algorithms as an additional variable, this optimization problem can be adapted for the design of the consensus protocols. Simulation results illustrate the effectiveness of our proposed approach.

Keywords: Cooperative control, Agents-based systems, Networked control systems
Abstract: This paper addresses the formation control problem of a group of Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicles (UAVs) under directed and dynamically-changing interconnection graphs. Based on the hierarchical control design framework, we present a distributed algorithm that steers the vehicles to a desired geometric shape using only local interaction between the vehicles. The proposed algorithm is based on instrumental dynamic systems that ensure a singularity-free operation of each vehicle and achieve our control objective under a directed graph containing a spanning tree frequently enough. A numerical example is given to illustrate the effectiveness of the proposed approach.

Keywords: Control of networks, Linear systems, Large-scale systems
Abstract: The notion of strong structural controllability (s- controllability) allows for determining controllability properties of large linear time-invariant systems even when numerical values of the system parameters are not known a priori. The s-controllability guarantees controllability for all numerical realizations of the system parameters. We address the optimization problem of minimal cardinality input selection for s-controllability. Previous work shows that not only the optimization problem is NP-hard, but finding an approximate solution is also hard. We propose a randomized algorithm using the notion of zero forcing sets to obtain an optimal solution with high probability. We compare the performance of the proposed algorithm with a known heuristic [1] for synthetic random systems and three real-world networks, viz. IEEE 39-bus system, protein-protein interaction network, and US airport network. It is found that our algorithm performs much better than the heuristic in each of these cases.

Keywords: Control of networks, Stochastic optimal control, Markov processes
Abstract: As the size of the Internet of Things (IoT) grows, so does its vulnerability to malicious attacks. When such an attack occurs, one of the only means of defense available to a system controller before a patch is developed is resetting devices to a known malware-free state. In this paper, we study the design of reset strategies which optimize the network’s performance when under a malware attack. In particular, we show that under mild assumptions, the problem of optimizing the network’s performance can be posed as an optimal control problem for a Markov chain with a number of states and actions which grows polynomially with respect to the size of the network. We investigate our results with simulation.

Keywords: Control of networks, Stability of nonlinear systems, Communication networks
Abstract: A cyber security problem is considered in a networked system formulated as a resilient graph problem based on a game theoretic approach. The connectivity of the underlying graph of the network system is reduced by an attacker who removes some of the edges whereas the defender attempts to recover them. Both players are subject to energy constraints so that their actions are restricted and cannot be performed continuously. We provide a subgame perfect equilibrium analysis and fully characterize the optimal strategies for the attacker and the defender in terms of edge connectivity and the number of connected components of the graph. The resilient graph game is then applied to the multi-agent consensus problem. We study how the attacks and the recovery on the edges affect the consensus process.

Keywords: Control of networks, Observers for Linear systems, Estimation
Abstract: The design of local state-feedback control systems in dynamical networks to block observability at remote nodes is studied, in the context of a canonical linear network synchronization model. A general design algorithm is presented first, which can be used to ensure unobservability at any group of m nodes using m+1 local controllers. The algorithm is based on a method for joint eigenvalue-eigenvector assignment, and serves to prevent observability while leaving all eigenvalues and all but one eigenvector of the open loop unchanged. Next, the topological structure of the network is exploited to reduce the number of controllers required for blocking observability; the result is based on blocking observability on node cutsets separating the actuation locations and nodes that must be made unobservable. The results are illustrated with a numerical example.

Keywords: Control of networks, Network analysis and control, Cooperative control
Abstract: In this paper, we study the relationship between two crucial properties in linear dynamical networks of diffusively coupled agents, that is controllability and robustness to noise and structural changes in the network. In particular, for any given network size and diameter, we identify networks that are maximally robust and then analyze their strong structural controllability. We do so by determining the minimum number of leaders to make such networks completely controllable with arbitrary coupling weights between agents. Similarly, we design networks with the same given parameters that are completely controllable independent of coupling weights through a minimum number of leaders, and then also analyze their robustness. We utilize the notion of Kirchhoff index to measure network robustness to noise and structural changes. Our controllability analysis is based on novel graph-theoretic methods that offer insights on the important connection between network robustness and strong structural controllability in such networks.

Keywords: Control of networks, Agents-based systems, Linear systems
Abstract: Composite systems are large complex systems consisting of interconnected agents (subsystems). Agents in a composite system interact with each other towards performing an intended goal. Controllability is essential to achieve desired system performance in linear time-invariant composite systems. Agents in a composite system are often uncontrollable individually, further, only a few agents receive input. In such a case, the agents share/communicate their private state information with pre-specified neighboring agents so as to achieve controllability. Our objective in this paper is to identify an optimal network topology, optimal in the sense of minimum cardinality information transfer between agents to guarantee the controllability of the composite system when the possible neighbor set of each agent is pre-specified. We focus on graph-theoretic analysis referred to as structural controllability as numerical entries of system matrices in complex systems are mostly unknown. We first prove that given a set of agents and the possible set of neighbors, finding a minimum cardinality set of information (interconnections) that must be shared to accomplish structural controllability of the composite system is NP-hard. Subsequently, we present a polynomial-time algorithm that finds a 2-optimal solution to this NP-hard problem. Our algorithm combines a minimum weight bipartite matching algorithm and a minimum spanning tree algorithm and gives a subset of interconnections which when established guarantees structural controllability, such that the worst-case performance is 2-optimal. Finally, we show that our approach directly extends to weighted constrained optimal network topology design problem and constrained optimal network topology design problem in switched linear systems.

Keywords: Chaotic systems, Lyapunov methods, Optimization
Abstract: In this paper we show that Sum-of-Squares optimization can be used to find optimal semialgebraic representations of sets. These sets may be explicitly defined, as in the case of discrete points or unions of sets; or implicitly defined, as in the case of attractors of nonlinear systems. We define optimality in the sense of minimum volume, while satisfying constraints that can include set containment, convexity, or Lyapunov stability conditions. Our admittedly heuristic approach to volume minimization is based on the use of a determinant like objective function. We provide numerical examples for the Lorenz attractor and the Van der Pol limit cycle.

Keywords: Queueing systems, Stochastic systems, Optimization
Abstract: This paper considers the optimization of static and dynamic appointments for a sequence of customers with random processing times served by a single agent. In the static case, the problem is to find the appointment times for the customers that minimize the expected weighted sum of idle time of the agent, waiting time of the customers, and overtime of the agent. The dynamic formulation is original. It limits cascading delays by using warning times, which are defined relative to the start of a previous job, to tell customers when to arrive for their job. The problem in this formulation is to find the warning times which minimize the aforementioned objective. We outline an algorithmic framework based on infinitesimal perturbation analysis (IPA) and stochastic gradient descent (SGD) that can be used to solve both problems. For the static case, we show that the SGD method converges to a global minimizer with no assumptions on the joint distribution of the processing durations. For the dynamic case, we construct a warning time schedule which provably outperforms the static scheme under certain conditions. We give empirical evidence of the efficacy of both approaches using both synthetic data as well as data collected from a year of elective surgeries at a local hospital. Our results suggest the validity of the dynamic formulation as a more cost-efficient solution than the static formulation to the appointment scheduling problem.

Keywords: Randomized algorithms, Identification, Optimization
Abstract: This paper proposes an optimization-based framework for the calibration of parametric models according to multi-variate, input-output data. We focus on continuous models whose outputs depend nonlinearly (and possibly implicitly) on the inputs and the parameters. Maximum likelihood and scenario optimization techniques are combined to generate stochastic predictor models having dependent parameters. Nonconvex scenario theory is then used to assess the reliability of the predictor within a distribution-free setting by bounding the probability of future data falling outside the predicted output ranges. By choosing the parameter set from a family of nested sets, this probability can be calculated explicitly. Herein, such a family is comprised of the superlevel sets of the joint density function that maximizes the likelihood of the data. This framework is illustrated by considering modal analysis data drawn from a system having a non-colocated sensor-actuator pair.

Keywords: Control of networks, Optimization, Sensor networks
Abstract: The problem of lifetime maximization and connectivity control in an asymmetric network is considered in this work. It is assumed that the network is modeled by a weighted directed graph, and that the information flow structure is centralized. The generalized algebraic connectivity notion is adopted as the network connectivity measure, and is formulated here as an implicit function of the transmission powers used by the nodes to communicate with their neighbors. An optimization problem is presented to maximize the network lifetime while ensuring that the degree of connectivity of the network is above a prespecified threshold and that transmission powers of the nodes are limited to a predefined range. The mixed interior point-exterior point technique is utilized to convert the problem into a sequential unconstrained optimization. In order to solve each subproblem numerically in the new framework, the subgradient technique with backtracking line search is utilized. It is shown that the proposed solution asymptotically converges to the global optimum of the original optimization problem. Simulations confirm the efficacy of the proposed technique.

Keywords: Energy systems, Optimization, Network analysis and control
Abstract: The critical role of gas fired-plants to compensate renewable generation has increased the operational variability in natural gas networks (GN). Towards developing more reliable and efficient computational tools for GN monitoring, control, and planning, this work considers the task of solving the nonlinear equations governing steady-state flows and pressures in GNs. It is first shown that if the gas flow equations are feasible, they enjoy a unique solution. To the best of our knowledge, this is the first result proving uniqueness of the steady-state gas flow solution over the entire feasible domain of gas injections. To find this solution, we put forth a mixed-integer second-order cone program (MI-SOCP)-based solver relying on a relaxation of the gas flow equations. This relaxation is provably exact under specific network topologies. Unlike existing alternatives, the devised solver does not need proper initialization or knowing the gas flow directions beforehand, and can handle gas networks with compressors. Numerical tests on tree and meshed networks indicate that the relaxation is exact even when the derived conditions are not met.

Keywords: Air traffic management, Optimization, Computational methods
Abstract: The importance of short-term air traffic flow management can never be depreciated due to the associated demand uncertainty which is caused by the dynamicity in the air transportation systems. Ideally, the flight plans require frequent fine-tuning depending on the dynamic network changes such as flight time deviations, weather conditions, etc.. Motivated by this, the paper incorporates the effect of departure time uncertainty and wind uncertainty in short-term flight routing and scheduling. The en route capacities are utilized while ensuring safety in terms of maintaining required in-trail-separation between aircraft, avoiding capacity violations as well as merging conflicts due to uncertainty of demand. The proposed model effectively manages the uncertainty in the network by utilizing short-term planning horizons and further, more accurate real-time wind forecast data are incorporated in optimizing the flight schedules. To generate flight schedules with a less time-complexity, we use a heuristic approach with parallel computation while decomposing the problem into maximum independent sets. The proposed model is experimentally validated for the applicability via realistic air traffic data.

Keywords: Chemical process control, Modeling, Optimization
Abstract: Steam system, which is an important component of utility system of the industrial process, provides power and heat to the process. Operational optimization methods can improve the efficiency of the steam system and increase the economic benefits for industrial plants. Because of the uncertainty in device efficiency, traditional deterministic optimization methods could lead to suboptimal or even infeasible optimization decisions of steam systems. This paper proposes a data-driven adaptive robust optimization approach to deal with the operational optimization under uncertainty for industrial steam systems. Uncertain parameters of the steam system model are derived from the historical process data based on steam turbine models. A robust kernel density estimation method is employed to construct the uncertainty sets. The data-driven uncertainty sets are incorporated into a two-stage adaptive robust mixed-integer linear programming (MILP) framework for steam systems operational optimization to minimize the total operating cost. By applying the affine decision rule, the proposed multi-level optimization model is transformed into a single-level MILP problem. An industrial case study of the steam system from an ethylene plant is presented to demonstrate the effectiveness of the proposed method.

Keywords: Chemical process control, Modeling, Uncertain systems
Abstract: This paper aims to leverage the big data in shale gas industry for better decision making in optimal design and operations of shale gas supply chains under uncertainty. We propose a two-stage distributionally robust optimization model, where uncertainties associated with both the upstream shale well estimated ultimate recovery and downstream market demand are simultaneously considered. In this model, decisions are classified into first-stage design decisions, which are related to drilling schedule, pipeline installment, and processing plant construction, as well as second-stage operational decisions associated with shale gas production, processing, transportation, and distribution. A data-driven approach is applied to construct the ambiguity set based on principal component analysis and first-order deviation functions. By taking advantage of affine decision rules, a tractable mixed-integer linear programming formulation can be obtained. The applicability of the proposed modeling framework is demonstrated through a case study of Marcellus shale gas supply chain. Comparisons with alternative optimization models are investigated as well.

Keywords: Chemical process control, Predictive control for nonlinear systems
Abstract: Recent work on economic model predictive control (EMPC) has indicated that some processes may be operated in a more economically-optimal fashion under a time-varying operating policy than under a steady-state operating policy. However, a concern for time-varying operation is how such a change in operating policy might impact the equipment within which the processes being controlled are carried out. While under steady-state operation, the operating conditions to which equipment would regularly be exposed can be estimated, this would be more difficult to assess thoroughly textit{a priori} under time-varying operation. It could be explored whether the EMPC could be made aware of any impacts the control actions that it chooses might have on equipment, and then to seek to impose constraints on these impacts. This would require explicit consideration of equipment design, material properties/behavior, and material loading at the EMPC design stage. This work provides an initial exploration of this topic by seeking to extract principles related to the integration of equipment material fidelity considerations and EMPC through an example accounting for a simple preliminary case of thermal stresses in a pipe at equilibrium conditions.

Keywords: Chemical process control, Process Control, Machine learning
Abstract: Process scheduling is one key layer of decision hierarchy for process industries to optimize their production schedule in order to gain the long-term economic viability. A main challenge of process scheduling lies in the treat of uncertainties when approaching the multistage adaptive robust optimization of the scheduling problem. In this work, we introduce the non-parametric Bayesian inference technique to construct the data-driven disjunctive uncertainty set to alleviate the over-conservatism issue faced by most commonly used fixed-shaped uncertainty sets, and utilized the piecewise linear decision rule to generate solutions for the multistage batch scheduling optimization. Based on improvement in uncertainty set construction and decision rule flexibility, we demonstrated with an industrial process case study that the proposed approach with the disjunctive uncertainty set and decision rule is capable of generating usually better process cheduling optimization solutions in comparison to those obtained by conventional adaptive robust optimization approaches.

Keywords: Control applications, Predictive control for nonlinear systems, Chemical process control
Abstract: This work focuses on computational fluid dynamics (CFD) modeling and control of a phthalic anhydride (PA) synthesis in a fixed-bed catalytic reactor. Specifically, a CFD model of a two-dimensional in space fixed-bed catalytic reactor is first developed in ANSYS Fluent with appropriate geometry characteristics and catalyst packing. Subsequently, to regulate the product yield of phthalic anhydride in the reactor outlet and avoid the formation of a hot-spot inside the reactor due to the exothermicity of the PA synthesis reaction, model predictive control is utilized to optimize the outer jacket temperature (manipulated variable) via a data-driven model of the reactor constructed using CFD model data. To implement MPC in real-time within the dynamic CFD simulation of the fixed-bed catalytic reactor, a user-defined function (UDF) of ANSYS Fluent is employed to invoke an MPC solver outside of the CFD modeling environment to obtain the optimized manipulated inputs. The CFD simulation results demonstrate that under MPC, the outlet concentration of phthalic anhydride can be driven to its set-point while the temperature of inner reactor fluid remains below the maximum allowable temperature.

Keywords: Chemical process control, Process Control, Manufacturing systems
Abstract: This article considers the design of plantwide control for a portable modular reconfigurable system for the on-demand continuous-flow production of pharmaceuticals. The existing physical system has a regulatory control layer that is designed to control key states such as reactor temperatures at specified setpoint values, but lacks a higher level control system for the control of plantwide objectives such as overall yield and production rate. This article presents the design of a model predictive control-based plantwide control system, whose online optimization enables on-demand changing of plantwide control objectives while satisfying operational constraints. The controller was applied to a simulated plant based on the physical system. Strong dynamic nonlinearities that arise when operating the system near optimality complicate the design of a model predictive control system based on a linear process model. Two strategies for obtaining linear input-output models for model predictive control design are proposed that provide high-performance control, in spite of the large dynamic nonlinearities between the manipulated and controlled variables.

Keywords: Iterative learning control, Optimization, Control applications
Abstract: Abstract—This paper presents an iterative learning approach for optimizing the crosswind flight path of an energy-harvesting tethered system that executes cyclic spool-in/spool-out motions. Through the combination of high-tension crosswind spool-out motion (made possible through a high-lift wing) and low-tension spool-in motion, net energy is generated at every cycle. Because the net energy generated by the system is highly sensitive to the crosswind flight patterns used on spool-out, and because the motions of the system are repetitive, we use an iterative learning formulation to improve power production from one cycle to the next. Using a medium-fidelity dynamic model, we demonstrate that the iterative learning approach significantly increases the average power generated over each cycle.

Keywords: Spacecraft control, Energy systems, Stability of nonlinear systems
Abstract: We address the problem of generating electrical power through Airborne Wind Energy Systems, using a kite connected to a generator on the ground. We propose a controller to steer the kite to follow a pre-defined eight-shaped path based on a nonlinear guidance logic. The controller has an easy implementable explicit form, has asymptotic stability guarantees and a large domain of attraction. We report simulations of a complete production cycle, including a production phase and a recovery phase. Also, we provide a Lyapunov stability analysis.

Keywords: Emerging control applications, Flight control
Abstract: A control design approach for a hybrid multi-copter/box-wing drone is presented. The drone is designed to be used in an airborne wind energy system, where tethered aircrafts are used to convert wind energy into electricity. It features four propellers and multiple aerodynamic control surfaces, and can operate either as multi-copter or as airplane. An untethered system is considered in this work, and the goal is to achieve fully autonomous take-off, transition to dynamic flight, and landing. A model-based, hierarchical feedback controller is proposed, with linear inner control loops to stabilize the drone's attitude, and an outer nonlinear loop to obtain the desired flight trajectory. A switching strategy is employed to transition from hovering mode (i.e. multi-copter) to dynamic flight mode (i.e. airplane), and vice-versa. Simulation results with a realistic system model indicate that the controller can achieve good performance and robustness in all flight conditions, notwithstanding its simplicity and ease of implementation.

Keywords: Autonomous systems, Control software, Flight control
Abstract: This paper presents the systematic approach and analysis of the flight test verification of a small-scale rigid wing airborne wind energy system. An overview of the model-based design process used to produce the embedded software is provided, together with a description of the simulation “truth” models. Important aspects of sensor modelling that impact the flight control design are highlighted. The control design process is elaborated and a description of the verification methods used to provide assurance that the embedded software is fit for purpose is given. Flight test results for typical flight conditions are presented for launch, power generation, and landing.

Keywords: Flight control, Predictive control for nonlinear systems, Robotics
Abstract: Airborne Wind Energy (AWE) is a new way of harvesting the wind's power via tethered kite systems which has enormous potential, but poses many challenges in practice. One particularly challenging aspect is the control of the kite, or similarly a tethered fixed-wing vehicle. Tethered flight is a highly nonlinear, constrained, and fast dynamic system, requiring careful control design for optimal power producing results. This paper formulates the AWE problem as a practical, high-level Nonlinear Model Predictive Control scheme, balancing an abstracted control augmented modeling approach with the tight computational constraints on board small fixed-wing systems for real-time, long-horizon predictive control. A power objective is developed which trades off tracking performance of a given nominal path with the expected power generation resulting from the aircraft's trajectory. An analysis of the performance gains in various wind conditions are elaborated per tuning of the power objective, and the controller is validated in simulation before deployment on a small development platform. The control system is demonstrated in practice in an exemplary tethered flight experiment.

Keywords: Energy systems, Power systems, Uncertain systems
Abstract: Real-time altitude control of airborne wind energy (AWE) systems can improve performance by allowing turbines to track favorable wind speeds across a range of operating altitudes. The current work explores the performance implications of deploying an AWE system with sensor configurations that provide different amounts of data to characterize wind speed profiles. We examine various control objectives that balance trade-offs between exploration and exploitation, and use a persistence model to generate a probabilistic wind speed forecast to inform control decisions. We assess system performance by comparing power production against baselines such as omniscient control and stationary flight. We show that with few sensors, control strategies that reward exploration are favored. We also show that with comprehensive sensing, the implications of choosing a sub-optimal control strategy decrease. This work informs and motivates the need for future research exploring online learning algorithms to characterize vertical wind speed profiles.

Keywords: Iterative learning control, Biological systems, Neural networks
Abstract: In this paper the first recorded attempt at optimizing broiler growth using iterative learning control under state-of-the-art production conditions is presented. The work is motivated by a significant predicted increase in global broiler meat, where existing optimization techniques are incompatible with state-of-the-art broiler production. The proposed method regulates broiler growth using broiler house temperature based on norm optimal iterative learning control, which is a model based control technique. To compensate for the lack of mathematical broiler growth models in scientific literature, dynamic neural network models are used, which is a data driven modeling technique. Practical results from a state-of-the-art broiler house appear promising, but not conclusive, although a maximum decrease in required feed of 2.5% was obtained.

Keywords: Iterative learning control, Flexible structures, Uncertain systems
Abstract: This paper presents an iterative learning controller for a flexible manipulator with uncertain parameters and unknown repetitive disturbance. The flexible manipulator is under-actuated with the assumption that only the rotation is controlled. Based on two sliding variables defined on the actuated and unactuated channels, the controller is designed with the compensation of the repetitive disturbance to drive the manipulator to track a time-varying trajectory. Theoretical proof and experimental studies are conducted to verify the effectiveness of the proposed controller.

Keywords: Iterative learning control, Identification for control, Mechanical systems/robotics
Abstract: Learning control methods enable significant performance improvements for systems that operate repetitively. Typical methods rely on a parametric plant model to achieve fast and robust convergence. The aim of this paper is to develop a framework for multivariable systems that enables fast and robust learning without requiring a parametric plant model. This is achieved by connecting nonparametric frequency response function identification and robust control, which enables synthesis on a frequency-by-frequency basis. A nonconservative approach is obtained by ensuring that the identified uncertainty is directly compatible with the developed synthesis framework. Application to a multivariable benchmark motion system confirms the potential of the developed framework.

Keywords: Iterative learning control, Linear systems, Mechanical systems/robotics
Abstract: The general subject area of this paper is iterative learning control based on a linear model of the dynamics using the theory of discrete repetitive processes for analysis. Linear matrix inequality based computations are develop to compute the stabilizing feedback controller in the time domain and a feedforward controller that guarantees convergence in the trial-to-trial domain. Use of the generalized Kalman-Yakubovich-Popov lemma allows a direct treatment of finite frequency range performance specifications. Since weighting filters are not used then an unnecessary increase in the controller order is avoided. To illustrate the performance of the new design, the problem of path-tracking control for wheeled mobile robot is considered. Experimental verification results using Lego EV3-based mobile robot are also given, including a comparison of trajectory tracking performance with the standard Hinf based approach.

Keywords: Biological systems, Iterative learning control
Abstract: In this paper, an approach for rapid broadband discrete nanomechanical mapping of soft samples using atomic force microscope is proposed. Nanomechanical mapping is needed to investigate, the spatial distribution of nanomechanical properties with dynamic evolution—provided that the mapping is fast enough. To enhance the mapping efficiency, we propose to significantly reduce the number of measurements by only implementing the technique at locations of interest, which further enables the broadband nanomechanical property study of soft samples undergoing dynamic processes. Firstly, an online searching learning-based optimization scheme is proposed to achieve the rapid probe engagement and withdrawal with minimum probe-sample interaction forces at each sample location. Then, a decomposition-based learning approach is used to achieve the rapid probe transition between sample locations. The proposed technique is demonstrated through multiple-location viscoelasticity measurements on a Polydimethylsiloxane (PDMS) sample in AFM experiment.

Keywords: Iterative learning control, Decentralized control, Agents-based systems
Abstract: In this paper, we present a cluster-wise decentralized model-free reinforcement learning (RL) based control design for a linear time-invariant consensus network. We assume that the fast dynamics of the network is stable and only design the control which shapes the slow dynamics. The design exploits time-scale separation properties inherent in the slow dynamics of the clusters and weak couplings between the clusters. The aggregated slow variable from each cluster is used for feedback and decentralized controllers are learned for each cluster. Using singular perturbation theory, we show the sub-optimality of the learned controller and provide closed-loop stability conditions. It shows that this decentralized learning design will produce close-to-optimal performance if the clustering is strong with weak inter-cluster couplings. This design reduces the learning time and the amount of communication links required. The effectiveness of the design is demonstrated using a numerical example.

Keywords: Autonomous robots, Stochastic optimal control
Abstract: Avoiding collisions with obstacles is of fundamental importance for the safe navigation of unmanned aerial vehicles (UAVs) and mobile robots. In this paper, we approach the avoidance problem by composing a scalable navigation strategy from multiple stochastic optimal controllers. We consider a scenario with a fixed speed Dubins vehicle, which is tasked to reach a waypoint while avoiding collisions with multiple moving obstacles. Obstacle moving directions are unknown, therefore, we use a random walk stochastic process model to anticipate that uncertainty in the design of navigation feedback control. The proposed navigation is based on a composition of minimum time stochastic optimal controllers. Each optimal controller is the solution to a minimum time problem to reach either the waypoint or a safe configuration with respect to an obstacle. The composition is based on the controller value functions and is scalable, i.e., it can deal with any number of obstacles. Our results are illustrated with a numerical simulation.

Keywords: Robotics, Cooperative control, Aerospace
Abstract: We consider multiple quadcopters with a rigid extension to transport a payload. We model the contact force between each quadcopter and the payload using a linear spring model. We develop a force and orientation control algorithm that guarantees attitude stabilization of the payload and the convergence of the contact force and the velocity of each quadcopter to desired setpoints. In particular, we develop time varying force setpoints to enforce attitude regulation. The algorithm provides desired thrust and attitude angles required for each quadcopter to cooperatively transport the payload. We analyze the stability of the system using singular perturbation theory. We demonstrate the effectiveness of the algorithms in numerical simulations.

Keywords: Robotics, Aerospace, Flight control
Abstract: In this paper, a novel foldable quadrotor (FQR) inspired by an origami mechanism is designed. The FQR can fold its arms during flight to enable aggressive turning maneuvers and operations in cluttered environments. A dynamic model of folding is built for this system with the collected data, and a feedback controller is designed to control the position and orientation of the FQR. Lyapunov stability analysis is conducted to show that the system is stable during arm folding and extension, and motion planning of the FQR is achieved based on a modified minimum-snap trajectory generation method. Simulation results are provided to demonstrate the advantage of this design over the conventional quad-rotor in obstacle avoidance during flight.

Keywords: Distributed control, Autonomous systems, Optimization
Abstract: Convergence guarantees of many resilient consensus algorithms are based on the graph theoretic properties of r- and (r,s)-robustness. These algorithms guarantee consensus of normally behaving agents in the presence of a bounded number of arbitrarily misbehaving agents if the values of the integers r and s are sufficiently high. However, determining the largest integer r for which an arbitrary digraph is r-robust is highly nontrivial. This paper introduces a novel method for calculating this value using mixed integer linear programming. The method only requires knowledge of the graph Laplacian matrix, and can be formulated with affine objective and constraints, except for the integer constraint. Integer programming methods such as branch-and-bound can allow both lower and upper bounds on r to be iteratively tightened. Simulations suggest the proposed method demonstrates greater efficiency than prior algorithms.

Keywords: Aerospace, Robotics, Predictive control for nonlinear systems
Abstract: In industrial surface inspection, unmanned multirotors are required to fly over a surface area at a given distance and reference velocity, in consideration of state and input constraints imposed by the measurement system and the multirotor itself. In this paper, the trajectory control task is investigated and split into an offline generation of a suitable path and an online model predictive trajectory optimization, paired with subordinate flatness-based state feedback linearization and stabilizing controllers. With this architecture, only one constrained quadratic programming problem needs to be solved at each time step, since nonlinearities are accounted for by using the inverse terms. Velocity is employed as primary optimization variable to achieve smooth tracking of references, time-optimality within the constraints and implicit integrating behavior. Outdoor experiments with a quadrotor show good tracking performance of both the pre-calculated path and the reference velocity even in the presence of wind disturbances.

Keywords: Aerospace, Autonomous systems, Autonomous robots
Abstract: A novel algorithm is presented in this paper for motion planning of an unmanned aerial vehicle (UAV) from a start position to a goal position in a two-dimensional environment cluttered with stationary obstacles. The algorithm, termed 'GSE', leverages a generalized shape expansion (GSE)-based sampling strategy, the main contribution of the paper, to explore the workspace efficiently. Once the shortest path is found from start position to goal position, a locally optimal trajectory is obtained within the homotopy class using sequential convex programming. Numerical simulations on the performance of the GSE algorithm and comparison of the same with that of some existing well-established algorithms are performed. The computational efficiency of the GSE algorithm is found to be significantly higher than that of the algorithms in comparison, while the trajectory costs obtained by the GSE algorithm is found to be marginally better in comparison with others.

Keywords: Game theory, Agents-based systems, Distributed control
Abstract: The design of distributed algorithms is central to the study of multiagent systems control. In this paper, we consider a class of combinatorial cost-minimization problems and propose a framework for designing distributed algorithms with a priori performance guarantees that are near-optimal. We approach this problem from a game-theoretic perspective, assigning agents cost functions such that the equilibrium efficiency (price of anarchy) is optimized. Once agents' cost functions have been specified, any algorithm capable of computing a Nash equilibrium of the system inherits a performance guarantee matching the price of anarchy. Towards this goal, we formulate the problem of computing the price of anarchy as a tractable linear program. We then present a framework for designing agents' local cost functions in order to optimize for the worst-case equilibrium efficiency. Finally, we investigate the implications of our findings when this framework is applied to systems with convex, nondecreasing costs.

Keywords: Game theory, Learning
Abstract: We consider a game in which one player (the principal) seeks to incentivize another player (the agent) to exert effort that is costly to the agent. Any effort exerted leads to an outcome that is a stochastic function of the effort. The amount of effort exerted by the agent is private information for the agent and the principal observes only the outcome; thus, the agent can misreport his effort to gain higher payment. Further, the cost function of the agent is also unknown to the principal and the agent can also misreport a higher cost function to gain higher payment for the same effort. We pose the problem as one of contract design when both adverse selection and moral hazard are present. We show that if the principal and agent interact only finitely many times, it is always possible for the agent to lie due to the asymmetric information pattern and claim a higher payment than if he were unable to lie. However, if the principal and agent interact infinitely many times, then the principal can utilize the observed outcomes to update the contract in a manner that reveals the private cost function of the agent and hence leads to the agent not being able to derive any rent. The result can also be interpreted as saying that the agent is unable to keep his information private if he interacts with the principal sufficiently often.

Keywords: Game theory, Markov processes, Modeling
Abstract: In this paper, we study system security against Advanced Persistent Threats (APTs). APTs are stealthy and persistent but APTs interact with system and introduce information flows in the system as data-flow and control-flow commands. Dynamic Information Flow Tracking (DIFT) is a promising detection mechanism against APTs which taints suspicious input sources in the system and performs online security analysis when a tainted information is used in unauthorized manner. Our objective in this paper is to model DIFT that handle data-flow and conditional branches in the program that arise from control-flow commands. We use game theoretic framework and provide the first analytical model of DIFT with data-flow and conditional-branch tracking. Our game model which is an undiscounted infinite-horizon stochastic game captures the interaction between APTs and DIFT and the notion of conditional branching. We prove that the best response of the APT is a maximal reachability probability problem and provide a polynomial-time algorithm to find the best response by solving a linear optimization problem. We formulate the best response of the defense as a linear optimization problem and show that an optimal solution to the linear program returns a deterministic optimal policy for the defense. Since finding Nash equilibrium for infinite-horizon undiscounted stochastic games is computationally difficult, we present a nonlinear programming based polynomial-time algorithm to find an epsilon- Nash equilibrium. Finally, we perform experimental analysis of our algorithm on real-world data for NetRecon attack augmented with conditional branching.

Keywords: Game theory, Networked control systems, Optimal control
Abstract: We formulate a resource-planning game between an attacker and a defender of a Network Control System (NCS). We consider the network to be operating in closed-loop with a linear quadratic regulator (LQR). We construct a general-sum, two-player, mixed strategy (MS) game, where the attacker attempts to destroy communication equipment of some nodes, and thereby render the LQR feedback gain matrix to be sparse, leading to degradation of closed-loop performance. The defender, on the other hand, aims to prevent this loss. Both players trade their control performance objectives for the cost of their actions. A Mixed Strategy Nash Equilibrium (MSNE) of the game represents the allocation of the players’ respective resources for attacking or protecting the important network nodes. Numerical results for the New England power system model demonstrate that reliable defense is feasible unless the cost of attack is much smaller than the cost of protection per generator.

Keywords: Game theory, Stability of nonlinear systems, Agents-based systems
Abstract: A new type of bifurcations is illustrated for Nash equilibrium in the noncooperative systems with a squarely bounded state space. In this type of bifurcations, a new Nash equilibrium appears with two new branches, where one of them disappears with the initial branch and the other one holds the same profile as the bifurcation parameter increases. The Nash equilibrium inside the state space is founded as a unstable Nash equilibrium in the noncooperative dynamical system. To improve the efficiency of the system, we propose a zero-sum tax/subsidy approach to stabilize the unstable Nash equilibrium without using the information of agents' personal sensitivity parameter.

Keywords: Game theory, Stochastic optimal control, Markov processes
Abstract: We consider a finite horizon repeated game with N selfish players who observe their types privately and take actions, which are publicly observed. Their actions and types jointly determine their instantaneous rewards. In each period,players jointly observe actions of each other with delay 1, and private observations of the state of the system, and get an instantaneous reward which is a function of the state and every-one’s actions. The players’ types are static and are potentially correlated among players. An appropriate notion of equilibrium for such games is Perfect Bayesian Equilibrium (PBE) which consists of a strategy and a belief profile of the players which is coupled across time and as a result, the complexity of finding such equilibria grows double-exponentially in time. We present a sequential decomposition methodology to compute structured perfect Bayesian equilibria(SPBE) of this game, introduced in [1], where equilibrium policy of a player is a function of a common and a private belief state. This methodology computes SPBE in linear time. In general, the SPBE of the game problem exhibit signaling behavior, i.e. players’ actions reveal part of their private information that is payoff relevant to other players.

Keywords: Hybrid systems, Adaptive control, Linear systems
Abstract: We propose a hybrid adaptive feed-forward control for single input single output linear plants with full relative degree. The scheme includes an adaptive law that estimates the inverse of the plant and provides a feed-forward control calculated on the basis of the desired output and its derivatives. The adaptation is performed during discrete time events, called emph{jumps}, while the feed-forward action is continuous. This combination leads to a full hybrid system.

The advantage of this framework is a conceptual separation between the adaptation dynamics, which is emph{discrete}, and the plant dynamics, which is emph{continuous}. Under an assumption of a persistence of excitation, we show through examples that the output asymptotically tracks the desired reference and that the estimate of the parameters of the inverse converges.

Keywords: Hybrid systems, Adaptive control, Power electronics
Abstract: In this work, we propose a hybrid adaptive control law for the half-bridge inverter subjected to the common problem of unknown load. This controller ensures the system robustness with respect to the output, taking into account the real nature of the signals, which means the continuous-time variables, (voltage and current signals) and the discrete-time variables, (switching signals). The adaptation is accomplished using a state observer and assuming that all states are measurable. Then, stability properties can be ensured using hybrid dynamical system theory and singular perturbation analysis. Finally, the proposed hybrid adaptive controller is validated in simulation.

Keywords: Hybrid systems, Iterative learning control, Modeling
Abstract: Hybrid dynamical systems have steadily grown in popularity over the last few decades because they ease the task of modeling complicated nonlinear systems. However, it can be challenging to apply pre-existing control strategies to hybrid systems. This is in part because hybrid systems have been difficult to represent in closed-form, which is necessary for executing the operations required for many controllers' synthesis. The primary contribution of this work is a general closed-form state space representation of piecewise defined systems, a class of hybrid systems. The utility of this representation is demonstrated via the first-ever application of iterative learning control to a hybrid system, which is accomplished without modifying the controller design to account for the system model's hybrid nature. Secondary contributions unrelated to system's hybrid nature, however, are made to the controller itself, formalizing it for application to systems of any relative degree, and enabling the direct application of Newton's method in the controller by using automatic differentiation in the learning function derivation.

Keywords: Hybrid systems, Observers for nonlinear systems, Biological systems
Abstract: The paper deals with basin-of-attraction analysis of two observers estimating the states of a hybrid version of Goodwin's oscillator forced by a continuous exogenous signal. Under harmonic exogenous excitation, the impulsive Goodwin's oscillator exhibits bistability, which phenomenon significantly complicates observer design. The attractivity of a null solution of the hybrid state error estimation dynamics (termed as synchronous mode) has to be maximized in order to cover all possible initial state estimate deviations. A detailed analysis of the synchronous mode for a previously considered observer reveals a considerable asymmetricity in the basin of attraction relative to a jump instant and susceptibility to overjumps. As a result, for some initial conditions, the observer may converge to a stable stationary mode distinct from the synchronous one. To circumvent this, an improved hybrid observer with a more elaborate frequency modulation law in the output error feedback structure is proposed. Numerical analysis suggests that the new observer is able to approach the synchronous mode from all admissible initial estimates.

Keywords: Hybrid systems, Stability of hybrid systems, Switched systems
Abstract: This work pertains to the study of stability of limit cycles for hybrid systems with explicit logic states within a hybrid systems framework. We first focus on constructing the hybrid systems with explicit logic states and revealing basic properties of limit cycles. Application to model switched systems under dwell-time switching as such a hybrid system is provided. In addition, we establish sufficient and necessary conditions for stability of the limit cycles relying on Poincare maps. Examples illustrate the results. A discussion about the case of systems with nonunique solutions is also included.

Keywords: Hybrid systems
Abstract: As a continuation of [1] and using multiple barrier functions, this paper studies forward invariance in hybrid systems modeled by hybrid inclusions. After introducing the notion of a multiple barrier function, we propose sufficient conditions to guarantee different forward invariance properties of a closed set for hybrid systems with nonuniqueness of solutions, solutions terminating prematurely, and Zeno solutions. More precisely, we consider forward (pre-)invariance of sets, which guarantees solutions to stay in a set, and (pre-)contractivity, which further requires solutions that stay in the boundary of the set to evolve (continuously or discretely) towards its interior. Our conditions for forward invariance involve infinitesimal conditions in terms of multiple barrier functions while our conditions for precontractivity (and contractivity) involve Minkowski functionals. Examples illustrate the results.

Keywords: Adaptive control, Constrained control, Optimal control
Abstract: This paper considers the control problem with constraints on full-state and control input simultaneously. First, a novel barrier function based system transformation approach is developed to guarantee the full-state constraints. To deal with the input saturation, the hyperbolic-type penalty function is imposed on the control input. The actor-critic based reinforcement learning technique is combined with the barrier transformation to learn the optimal control policy that considers both the full-state constraints and input saturations. To illustrate the efficacy, a numeric simulation is implemented in the end.

Keywords: Optimization, Adaptive systems
Abstract: Conventional perturbation-based extremum seeking control (ESC) employs a slow time-dependent periodic signal to find an optimum of an unknown plant. To ensure stability of the overall system, the ESC parameters are selected such that there is sufficient time-scale separation between the plant and the ESC dynamics. This approach is suitable when the plant operates at a fixed time-scale. In case the plant slows down during operation, the time-scale separation can be violated. As a result, the stability and performance of the overall system can no longer be guaranteed. In this paper, we propose an ESC for periodic systems, where the external time-dependent dither signal in conventional ESC is replaced with the periodic signals present in the plant, thereby making ESC time-invariant in nature. The advantage of using a state-based dither is that it inherently contains the information about the rate of the rhythmic task under control. Thus, in addition to maintaining time-scale separation at different plant speeds, the adaptation speed of a time-invariant ESC automatically changes, without changing the ESC parameters. We illustrate the effectiveness of the proposed time-invariant ESC with a Van der Pol oscillator example and present a stability analysis using averaging and singular perturbation theory.

Keywords: Estimation, Machine learning, Intelligent systems
Abstract: The objective is to study an on-line Hidden Markov model (HMM) estimation-based Q-learning algorithm for partially observable Markov decision process (POMDP) on finite state and action sets. When the full state observation is available, Q-learning finds the optimal action-value function given the current action (Q-function). However, Q-learning can perform poorly when the full state observation is not available. In this paper, we formulate the POMDP estimation into a HMM estimation problem and propose a recursive algorithm to estimate both the POMDP parameter and Q-function concurrently. Also, we show that the POMDP estimation converges to a set of stationary points for the maximum likelihood estimate, and the Q-function estimation converges to a fixed point that satisfies the Bellman optimality equation weighted on the invariant distribution of the state belief determined by the HMM estimation process.

Keywords: Lyapunov methods, Switched systems, Adaptive control
Abstract: A novel switched systems approach is leveraged to enable a distributed multi-agent system to reach consensus under intermittent communication. A mobile information service provider (leader), that has full state feedback, switches between various (follower) agents lacking navigational sensors to provide each follower with intermittent state information. The leader uses a neural network learning approach to develop a predictor of the location of the uncertain followers. Lyapunov-based analysis methods are used to show the followers asymptotically converge to a desired goal location. A novel switched systems analysis determines the maximum dwell-time the leader can allow each follower to drift from a predicted trajectory before state correction is necessary, despite the fact that the neural network predictor only achieves asymptotic convergence. Simulation results are included to validate the results.

Keywords: Adaptive control, Optimal control, Learning
Abstract: In this paper an output-feedback model-based reinforcement learning (MBRL) method for a class of second-order nonlinear systems is developed. The control technique uses exact model knowledge and integrates a dynamic state estimator within the model-based reinforcement learning framework to achieve output-feedback MBRL. Simulation results demonstrate the efficacy of the developed method.

Keywords: Observers for nonlinear systems, Visual servo control, Adaptive control
Abstract: In this paper, a concurrent learning based observer for a perspective dynamical system (PDS) is developed. The PDS is a widely used model for estimating the depth of the feature point from a sequence of camera images. Building on the current progress of concurrent learning (CL) for parameter estimation in adaptive control, a state observer is developed for a PDS model where the inverse depth appears as a time-varying parameter in the dynamics. Using the data-recorded over a sliding time window in the near past, information about the recent depth values is used in a CL term and an observer is developed. A Lyapunov-based stability analysis is carried out to prove the uniformly ultimately bounded (UUB) stability of the observer. Comparisons in simulations are presented with the existing observers in terms of convergence, and error statistics. Comparisons reveal that CL improves the convergence and accuracy of the presented observer.

Keywords: Stability of nonlinear systems, Delay systems, Biological systems
Abstract: This paper addresses the stability problem of a biological system that describes the proliferation of sick cells in Acute Myeloid Leukemia (AML). AML therapies aim at eradicating malignant cells, reaching a biological status represented by the zero equilibrium point of the age-structured mathematical model describing pathological hematopoeisis. First, the AML stability problem is reformulated into a stability problem of a nonlinear cascaded system. Then based on a positivity property of the system, non quadratic Lyapunov candidates are constructed. Finally, necessary and stability conditions are obtained. These conditions complete and generalize previous results where the main contribution consists in providing necessary and sufficient conditions based on a general model that incorporates fast self renewal. This model is complex but more realistic from a practical pint of view. Further more, unlike previously published works, the proposed conditions do not depend on auxiliary parameters which are biologically ambiguous but depend only on the AML system which makes the results more biologically relevant for AML treatment.

Keywords: Stability of nonlinear systems, Lyapunov methods, Autonomous robots
Abstract: Steering controls for car-like robots have been studied for a long time and attracted more and more research due to the recent boom of self-driving vehicles. A novel nonlinear steering control law for a scale-model car with applicability to any size vehicle is presented in this study. The proposed control employs both the lateral and angular errors at a look-ahead distance which, along with the controller gain, is tuned dynamically as a function of velocity of the vehicle. Stability of the control law is demonstrated by Lyapunov analysis and the relationships from speed to look-ahead distance and control gain are also determined. Computation and actuator delays as well as steering saturation are modeled in the simulation for a more realistic performance index and effectiveness of the control.

Keywords: Stability of nonlinear systems, Lyapunov methods, Uncertain systems
Abstract: This paper aims to unify the construction of Lyapunov functions for interconnected systems comprising integral input-to-state stable (iISS) and input-to-state stable (ISS) subsystems. The sum-separable Lyapunov functions reported for interconnected iISS systems in the literature successfully apply to ISS and linear systems since stable linear systems are ISS, and ISS systems are iISS. However, the sum-separable Lyapunov functions remain seriously complicated and they do not agree with popular Lyapunov functions even if systems are ISS or linear. This paper resolves the complexity and disagreement by proposing a framework of chamfering the corner of the max-separable Lyapunov function which was popular for ISS systems, but could not alone accommodate iISS subsystems which are not ISS.

Keywords: Stability of nonlinear systems, Mechatronics, Control applications
Abstract: A hybrid integral controller with reset is proposed. This hybrid controller ensures improved low-frequency disturbance rejection properties under double integrator PI²D control without inducing the undesired increase of overshoot otherwise resulting from adding an extra linear integrator to a PID controller. The controller is applied to an optical lens motion system that requires PID control in one operating mode and PI²D control in the other, therewith motivating a hybrid integral control strategy. The reset element in the controller is included to improve transient performance. To guarantee closed-loop stability, a conditional (and partial) reset rule is introduced that restricts the input-output behavior of the dynamic reset element, i.e., the hybrid integrator with reset, to a bounded sector. As a result, stability can be guaranteed on the basis of a circle criterion-like argument and checked by (measured) frequency response data. Stability and performance of the hybrid integral control design with conditional (and partial) reset are investigated by application to a piezo-actuated lens system that is part of an industrial wafer scanner.

Keywords: Sampled-data control, Stability of nonlinear systems, LMIs
Abstract: This paper addresses the stability of continuous-time nonlinear rational systems subject to aperiodically sampled-data control action. By the use of differential algebraic representations and a looped-functional approach to deal with aperiodic sampling, LMI conditions that ensure the regional asymptotic stability of the origin of the closed-loop system are proposed. Optimization problems allowing to maximize an estimate of the region of attraction or to maximize the admissible sampling interval (or the sampling period in the case of periodic implementation) that guarantees the asymptotic stability in a pre-specified region around the origin are also presented. The method is illustrated by means of a numerical example.

Keywords: Stability of nonlinear systems, Robotics, Aerospace
Abstract: We study a quadrotor with a cable-suspended load, where the cable length can be controlled by applying a torque on a pulley attached to the quadrotor. A coordinate-free dynamical model of the quadrotor-pulley-load system with nine degrees-of-freedom and four degrees-of-underactuation is obtained by taking variations on manifolds. Under the assumption that the radius of the pulley is much smaller than the length of cable, the quadrotor-pulley-load system is established to be a differentially-flat system with the load position, the quadrotor yaw angle and the cable length serving as the flat outputs. A nonlinear geometric controller is developed, that enables tracking of outputs defined by either (a) quadrotor attitude, (b) load attitude, (c) load position and cable length. Specifically, the design of the controllers for load position and cable length are taken into consideration as a whole unit due to the dynamical coupling of the quadrotor-pulley-load system. Stability proofs for the control design in each case and a simulation of the proposed controller to navigate through a sequence of windows of varying sizes is presented.

Keywords: Uncertain systems, Adaptive control, Control system architecture
Abstract: Model reference adaptive control of dynamical systems with unstructured system uncertainties and unmodeled dynamics is considered in this paper. Specifically, a stability tradeoff for this class of dynamical systems is shown first. With the goal of relaxing the resulting stability tradeoff, adaptive robustifying terms are designed next. The key aspect of the proposed relaxation procedure is that the proposed terms guarantee closed-loop system stability even with respect to significant system uncertainties, subject to unmodeled dynamics satisfying a condition. An illustrative numerical example is further given to demonstrate our theoretical findings.

Keywords: Uncertain systems, Adaptive systems, Observers for Linear systems
Abstract: Adaptive schemes for unknown input and state estimation are proposed for a class of uncertain systems with bounded unknown inputs. First, using a Lyapunov approach, conditions are derived that ensure the state and unknown input estimation errors converge to zero for a constant unknown input. Next, combining a Lyapunov approach and linear matrix inequalities, conditions are given that guarantee a prescribed performance level for state and unknown input estimation for a bounded not necessarily constant unknown input.

Keywords: Uncertain systems, Estimation, Computational methods
Abstract: This paper deals with the development of a non-Gaussian filter for nonlinear systems with discrete time measurements. Specifically, for systems with no process noise, the evolution of the state probability density function is governed by the Liouville equation. In general, solving the Liouville equation is computationally challenging. To this end, we leverage the method of characteristics to propagate probabilities along the characteristics solutions of the Liouville equation. Further, a convex optimization procedure is proposed to reconstruct the state probability density function from these characteristic solutions. Numerical examples of capturing the non-Gaussian nature of the uncertainty in the duffing oscillator and the two body problem are illustrated.

Keywords: Uncertain systems, Lyapunov methods, Adaptive control
Abstract: This paper studies the path following problem of the automated guided vehicle (AGV) with both uncertain linear velocity and angular velocity. An active disturbance rejection control (ADRC) based backstepping control method is proposed to deal with the effects caused by these two uncertainties. To handle the uncertain sinusoidal term of the virtual input in the dynamics of cross-track error, the tuning law of the feedback gain is analyzed. It is proven that the proposed tuning law ensures both the compensation for the uncertainty and the elimination of the saturation of virtual input. Furthermore, the transient performance of the path following is studied by the error between the actual trajectory and the ideal trajectory. It is proven that this error during the entire time region can be tuned small enough by designing the proposed ADRC controller's parameters. Finally, the simulations results under several typical uncertain velocities demonstrate the effectiveness of the proposed ADRC method.

Keywords: Uncertain systems, Modeling, Estimation
Abstract: This paper considers affine abstractions for over-approximating uncertain affine discrete-time systems, where the system uncertainties are represented by interval matrices, by a pair of affine functions in the sense of inclusion of all possible trajectories over the entire domain. The affine abstraction problem is a robust optimization problem with nonlinear uncertainties. To make this problem practically solvable, we convert the nonlinear uncertainties into linear uncertainties by exploiting the fact that the system uncertainties are hyperrectangles and thus, we only need to consider the vertices of the hyperrectangles instead of the entire uncertainty sets. Hence, affine abstraction can be solved efficiently by computing its corresponding robust counterpart to obtain a linear programming problem. Finally, we demonstrate the effectiveness of the proposed approach for abstracting uncertain driver intention models in an intersection crossing scenario.

Keywords: Uncertain systems, Numerical algorithms
Abstract: In this paper, a novel way to compute derivative-based global sensitivity measures is presented. Conjugate Unscented Transform (CUT) is used to evaluate the multidimensional definite integrals which lead to the sensitivity measures. The method is compared with Monte Carlo estimates as well as the screening method of Morris. It is shown that using CUT provides a much more accurate estimate of sensitivity measures as compared to Monte Carlo (with far lesser computational cost) as well as the Morris method (with similar computational cost). Illustrations on three test functions are presented as evidence.

Keywords: Mechatronics, Decentralized control, Learning
Abstract: The overlay performance between different layers of semiconductor devices is a key parameter for correct functionality of such devices. With device features getting increasingly smaller, there is a need for novel and more accurate overlay metrology tools. This paper aims to increase the positioning accuracy of such a novel metrology machine below the nanometer by the application of repetitive control. At the heart of the machine is a large stroke 6-DoF hexapod motion stage, carrying a sub-nanometer accurate AFM head, whose positioning accuracy during scanning is a key performance driver. The sample under examination during scanning effectively forms an unknown repetitive disturbance on its feedback loop. For this reason a line-to-line repetitive controller in combination with decentralized feedback has been employed, in which the base harmonic is defined by one full line-scan. Experimental results on the machine with an emulated sample demonstrate a significant performance improvement, achieving nanometer accurate positioning while scanning. This shows that repetitive control in a line-to-line domain is a potential enabler for AFM-based overlay nanometrology.

Keywords: Mechatronics, Computational methods, Numerical algorithms
Abstract: This paper continues the analysis of biquad structures discretized at high sample rates, relative to the dynamic frequencies of the biquad by introducing the τ parameterization as an alternative to the venerable δ parameterization. The τ parameterization has slightly improved coefficient accuracy as the scale factor between sample frequency and biquad dynamic frequencies falls below the typical several orders of magnitude assumed in the use of the δ parameterization. The use of the τ parameterization, which is based on a Trapezoidal Rule equivalent, provides an intuitively appealing result. In the mid-range sample rates, there is a potential for significant decrease in controller latency. Furthermore, the use of a biquad based structure such as the MultiNotch or Biquad State Space allows us to seriously consider doing away with “one size fits all” discretization, applying τ or δ parameterized biquads for low frequency dynamics and traditional discrete biquads for high frequency dynamics. Finally, a restructuring of the fixed point calculations of the τ^{−1} integrator allows for improved signal fidelity while maintaining the signal growth immunity of the δ parameterization.

Keywords: Mechatronics, Simulation, Control education
Abstract: Asymptotic AFM amplitude-phase dynamics is a powerful modeling tool for the development of AFM control systems and applications. We explain the model and demonstrate simple practical examples that can be easily programmed and analyzed using simulation tools such as Control and Simulation Loop (National Instruments) or Simulink (Mathworks). We first introduce asymptotic AFM models, then formulate their mathematical properties relevant to AFM, and provide examples of simulation for Hertz and Lennard-Jones tip-sample interaction forces. Material of this paper can be used to study and practice AFM dynamics in simulation, as well as for design of AFM model-based control modes and applications.

Keywords: MEMs and Nano systems
Abstract: The sensing properties of a microelectromechanical system (MEMS)-based displacement sensor with a constant-current (CC) readout circuit are explored. The sensor comprises a pair of tilted clamped-guided silicon beams whose bulk piezoresistivity are employed for displacement sensing. To investigate the effect of driving the sensor with constant current, a readout circuit is designed and implemented. The characteristics of the sensor with the CC circuit are compared with the results obtained from a previously implemented Wheatstone half-bridge. To ensure a fair comparison, two test scenarios are considered. In the first approach, parameters of CC circuit are tuned such that the same power is delivered to the sensing beams. In the second case, these parameters are chosen so that both circuits achieve equal gains. A thorough characterization of the sensor is preformed in terms of linearity, resolution, bandwidth and noise. The results reveal that the piezoresistive sensor with the CC readout circuit provides a superior linearity compared to the Wheatstone bridge. However, using this circuit comes with challenges including a poor noise performance which are also discussed here.

Keywords: MEMs and Nano systems, Robust control
Abstract: In this article, a robust feedback control scheme is presented for dual-stage nanopositioning platforms. Dual-stage nanopositioners consist typically of a long-range, low-speed actuator connected in series with a low-range, high-speed actuator. A sliding mode control structure is designed to dedicate sliding actions to the short-range actuator, effectively utilizing the secondary actuator for disturbance rejection. A multi-input, single-output high-gain observer is incorporated for robust state estimation. A hybrid serial-parallel-kinematic positioner is selected to demonstrate robustness of the control design through the mitigation of cross-talk and hysteresis nonlinearities. Simulation results show significant performance improvement on robust control of a standard long-range actuator, reducing the tracking error of a desired 100 Hz triangle trajectory by almost 90%. When disturbances are bounded by the long-range actuator control system to less than the range of the short-range actuator, root-mean-square and maximum error can be reduced to less than 1% of the magnitude of the desired trajectory.

Keywords: Mechatronics
Abstract: In [1], we introduced an algorithm to identify rate-independent hysteresis nonlinearities of a class of smart material-based actuators, which is modeled as a Hammerstein system, that is, a cascade of a Prandtl-Ishlinskii (PI) hysteresis nonlinearity with a linear dynamic system. In this paper, we extend the results in [1] to Hammerstein systems with rate-dependent hysteresis nonlinearities. We consider a rate-dependent PI model, which has been used to model rate-dependent hysteresis nonlinearities in smart micro-positioning actuators such as piezoceramic actuators and magnetostrictive actuators. The rate-dependent hysteresis nonlinearity, the linear dynamic system, and the intermediate signal between them are assumed to be unknown. Least squares is used with a finite impulse response (FIR) model structure to identify the linear part of the Hammerstein system. Then, the output of the Hammerstein system is used along with the identified model of the linear plant to reconstruct the unknown intermediate signal. A nonparametric model of the rate-dependent hysteresis loop is obtained by plotting the reconstructed intermediate signal versus the input signal.

Keywords: Kalman filtering, Autonomous robots, Robust control
Abstract: We present a velocity controller for persistent monitoring applications that minimizes the maximum eigenvalue of the Kalman filter covariance for any initial sensing position and any initial covariance. A set of points of interest in the environment can be measured along a closed static path by an autonomous, mobile robotic sensing platform. We model the environmental phenomenon at the points of interest as a Wiener process that is estimated by a Kalman filter. We propose a Greedy Knockdown Algorithm to determine the optimal number of observations for each point of interest per cycle and formulate the problem as a linear program with a set of robustness constraints. In simulation, the proposed controller is compared to constant velocity and existing first-order velocity controllers in the literature. The proposed method outperforms existing methods across test cases with a range of different parameters: number of points of interest, noise level of the observation model, and maximum velocity.

Keywords: Kalman filtering, Estimation, Automotive systems
Abstract: Trailers of commercial vehicle combinations are sparsely equipped with intelligent electronic components compared to trucks. Therefore, in many cases necessary information for the development of intelligent systems for the trailer is not provided. Reasons for that may be missing sensors due to unprofitable costs or because the information is truck related and not passed to the trailer. Online model-based methods can be used to estimate the missing information. In this paper, an Extended Kalman Filter based on a nonlinear single track lateral dynamics model of a truck-semitrailer combination is designed. For the simultaneous estimation of the articulation angle and the truck’s steering angle, representing an input to the system, the Extended Kalman Filter is enhanced towards an unknown input estimation approach. The measured signals for the algorithm are solely trailer related yaw rate and longitudinal speed. The method is applied to and validated on a real vehicle.

Keywords: Kalman filtering, Estimation, Nonlinear systems identification
Abstract: The accurate and rapid acquisition of locomotive longitudinal velocity is of great significance for adhesion control. However, the longitudinal velocity of the locomotive can’t be directly measured. Therefore, a new kind of distributed locomotive velocity estimation method based on the cubature Kalman filter(CKF) is studied in this paper. In order to avoid large errors in the estimation of wheel slip, a comprehensive locomotive velocity estimation module is designed. Based on a six-axle locomotive dynamics model and a wheel-rail model, the cubature Kalman filter algorithm is used to obtain the velocity of each bogie. Then combined with the wheel slip signal of the idle-recognition module, the locomotive running velocity is estimated by the locomotive velocity comprehensive estimation module. Compared with the simulation results of EKF algorithm, the results show that the method is more robust and the estimation accuracy is higher.

Keywords: Kalman filtering, Estimation, Observers for nonlinear systems
Abstract: The extended Kalman filter has been used to estimate a harmonic signal from noisy measurements. Most algorithms are based on the Cartesian model, which is a discretization in time of the continuous state space model associated with the differential equation that is satisfied by a sinusoidal signal with constant amplitude and frequency. In order to handle the more realistic case where both amplitude and frequency are changing, this basic model is modified by including ad hoc extensions. This paper starts by deriving a differential equation that explicitly includes time varying amplitude and frequency, and it is shown that this can be reduced to a Bessel's equation of order 1/2 that has a closed form solution. This is used to derive an explicit expression for a discrete-time model, which forms the basis of an extended Kalman filter. Simulation results show that this algorithm outperforms other approaches, particularly for harmonic signals where the frequency is changing rapidly.

Keywords: Kalman filtering, Fuzzy systems, Spacecraft control
Abstract: Over the past two decades, advances in spacecraft technologies have prompted the development of autonomous onboard navigation systems. This paper presents the design of a novel Fuzzy Adaptive Extended Kalman Filter (FAEKF) suitable for estimating the relative position and velocity between two spacecraft flying in formation. A fuzzy adaptation architecture is embedded within a standard Extended Kalman Filter (EKF), thereby allowing the filter to adapt internal noise characteristics that would otherwise remain constant after the initial filter design. Inaccurate tuning of the process and measurement noise covariance matrices within an EKF are commonly a limiting factor in the estimation performance, especially in situations where the behaviour of the noise processes are poorly defined or subject to change. In this context, the proposed approach provides a method to update the process and measurement noise covariances online based on a covariance-matching analysis of the filter residuals. A demonstration of the technique is given through numerical simulations of a spacecraft formation in low-Earth orbit, which are used to compare state estimates from the FAEKF with those from measurement-only and non-adaptive EKF solutions.

Keywords: Control applications, Kalman filtering
Abstract: We study a measurement framework motivated by considering macroscopic (i.e. large, active, and with finite temperature) measurement of microscopic (i.e. small and lossless) but classical dynamics. This unavoidably leads to ``measurement back action'' on the microscopic dynamics that nevertheless still allows for optimal filtering to minimize estimation error, but with tradeoffs between errors due to estimation and errors due to the back action. We focus on a simple case in which the deterministic effects of the measurement process are completely canceled by active control, and the remaining (coupled) stochastic back action and measurement noise is optimally filtered to minimize estimation error. This leads to a particularly interesting tradeoffs and limits on estimation and back action, analogous in many respects with the Heisenberg uncertainty principle but in an entirely classical framework.

Keywords: Distributed parameter systems, Observers for nonlinear systems, Adaptive systems
Abstract: We design an adaptive model-based observer for state and parameter estimation in 2x2 semi-linear hyperbolic systems with uncertain parameters where we assume that one of the two distributed states is available through distributed sensing. The uncertainties appear in the equation for the unmeasured distributed state and may be non-linear in the unmeasured state, although linearly parameterized. The adaptive law is designed using a Lyapunov approach and expressed in terms of known signals by utilizing the specific model structure which gives rise to a general solution strategy valid for a large class of non-linear source terms.

Keywords: Distributed parameter systems, Estimation, Sensor networks
Abstract: We propose an algorithm based on general simplicial decomposition for optimal node activation in large-scale sensor networks. The resulting measurements are to be used to estimate unknown parameters of a spatiotemporal process described by a partial differential equation. We address the sensor subset selection problem with a minimax optimality criterion defined on the Fisher information matrix associated with the estimated parameters. Such nondifferentiable metrics of estimation accuracy inevitably appear, e.g., when the design objective is to simultaneously maximize the efficiencies of several alternative differentiable criteria (e.g., D- and A-optimality) or when solving robust design problems. In this setting, continuous relaxations of the sensor subset selection problem quickly become computationally intractable for extraordinarily large numbers of sensors. We show how generalized simplicial decomposition, which is a recent extension of the classical simplicial decomposition to nondifferentiable optimization, can be employed to drastically reduce the dimensionality of the design problem. Computationally, the resulting algorithm alternates between solving a linear programming subproblem which has an explicit solution and a convex programming subproblem whose dimensionality is typically moderate. A simple separability characterization of optimal solutions is provided. The use of the proposed approach is illustrated with a numerical example.

Keywords: Distributed parameter systems, Estimation
Abstract: This paper proposes a domain decomposition scheme as a means for low order modeling of estimators for systems governed by partial differential equations. This entails the decomposition of the state estimator defined over the entire spatial domain into two separate estimators defined over two non-overlapping subdomains and coupled through the transmission conditions at their boundary. Each estimator is a copy of the original process defined over its subdomain and having an output injection term which is weighted by a filter kernel. Each of the filter kernels is related to the filter kernel of the estimator of the process defined over the entire spatial domain. The sensor providing process information is in the interior of the inner subdomain. Using a hybrid version of the domain decomposition method wherein the kernel of the outer domain is nullified, a significant computational savings can be obtained and is viewed as an alternate for low order approximation of estimators for PDEs. This decoupling facilitates a multi-grid implementation whereby the inner subdomain uses a refined grid as a means of increasing spatial resolution and the outer subdomain where the value of information is minimal, uses a coarse grid. The well-posedness of the proposed hybrid domain decomposition estimator is established and numerical studies of an advection-diffusion PDE over a rectangular domain are presented to provide an appreciation of the domain decomposition methods as a means of low order modeling of estimators for PDEs.

Keywords: Distributed parameter systems, Networked control systems, Process Control
Abstract: This work addresses the problem of control actuator and communication scheduling in spatially-distributed processes with discrete and delayed sensor-controller communication over a resource-constrained network. We focus on systems modeled by uncertain highly-dissipative Partial Differential Equations (PDEs) with low-order dominant dynamics. A finite-dimensional model-based controller with an embedded propagation unit that compensates for the communication delay is initially designed and the feasible ranges of control actuator locations and sensor-controller communication rates are explicitly characterized in terms of the communication delay. This characterization is used to formulate and solve a receding-horizon model-based optimization problem, subject to delay-dependent stability constraints, which yields the optimal control actuator and sensor-controller communication schedules that optimize the closed-loop performance and network resource utilization simultaneously. The developed methodology is illustrated through an application to a simulated diffusion-reaction process.

Keywords: Distributed parameter systems, Delay systems
Abstract: We consider the stabilization problem of a 1-D 2 x 2 unstable diffusion-reaction partial differential equation system with distinct input delays. The input delays are represented with a system of first-order hyperbolic PDEs, which then convert the parabolic system into a 2 + 2 x 2 mixed-type system of hyperbolic-parabolic type. We establish two integral transformations over the two types of systems, which will admit a target system with triangular trace terms. Exponential stability is shown in the H₁ x H₁ norm. The transformations also admit a corresponding companion mixed-type gain kernel PDE system to be solved. We employ method of characteristics and Galerkin methods to show existence of solutions to the gain kernel PDE, which guarantee the invertibility of the transformation and thus confirm the exponential stability results to hold.

Keywords: Distributed parameter systems, Observers for Linear systems, Linear parameter-varying systems
Abstract: In this work, we consider the problem of prescribed-time stabilization of a reaction-diffusion equation by means of time-varying feedback control. Our approach is the backstepping method, where a new target equation whose state converges to zero in a prescribed time and with a desired trajectory is utilized. By characterizing the growth-in-time of the solution of the resulting backstepping kernel equations, we establish fixed-time stabilization of the plant with a feedback controller that converges to zero within the prescribed time. Next, we present a state observer whose error converges to zero in a prescribed-time, accompanied by an output feedback result for which the separation principle is verified.

Keywords: Electrical machine control, Feedback linearization, Automotive systems
Abstract: In this paper, we regulate the speed of a surface mount Permanent Magnet Synchronous Motor (PMSM) with only using current sensors. We use a back-Electromotive Force (back-EMF) based sensorless speed control technique. We reduce the α-β model of the PMSM using singular perturbation theory, which reveals two algebraic expressions for the estimation of the back-EMF signals. We use these expressions to drive a Quadrature Phase Locked Loop (Q-PLL) that estimates rotor position and speed and also estimates the disturbance. The rotor position estimate is used for Park transformation while the speed and disturbance estimates are used in a feedback linearization law to regulate the speed. Our development of the controller only assumes knowledge of the nominal parameters of the PMSM. In addition, we assume the external load to be time-varying and bounded but otherwise unknown. Finally, results from simulation and experiment are shown to confirm robustness, and high performance of the output feedback system.

Keywords: Electrical machine control, Lyapunov methods, Observers for nonlinear systems
Abstract: Control of synchronous AC motors requires accurate knowledge of the orientation of the rotor magnetic field. While this could most directly be obtained via measurement of the rotor mechanical angle, the sensors required for this approach introduce cost and reliability issues to the system. Phase-locked loops (PLLs) are commonly utilized for in conjunction with measured or observed back EMF signals to achieve a sensorless implementation. The stability of such systems, especially in the presence of unknown back EMFs, is difficult to prove. An observer design is proposed in this work which seeks to observe the rotor electrical angle without the need for intermediate observation of the back EMFs or a PLL. This holistic design is motivated by a Lyapunov stability analysis which proves boundedness of all observer signals and convergence of the observed rotor electrical angle. This analysis is further validated by experimental results.

Keywords: Energy systems, Optimization, Power systems
Abstract: Standard economic dispatch problems that consider line losses are linear approximations of a non-convex economic dispatch problem formulated by fixing voltage magnitudes and assuming the decoupling of real and reactive power. This paper formulates and analyzes the general non-convex economic dispatch problem, incorporating and generalizing the Fictitious Nodal Demand (FND) model, resulting in a slack bus independent formulation that provides insight into standard formulations by pointing out commonly used but unnecessary assumptions and by deriving proper choices of ``tuning parameters.'' The proper choice of loss allocation is derived to assign half of the losses of each transmission line to adjacent buses, justifying approaches in the literature. Line constraints are proposed in the form of voltage angle difference limits and are proven equivalent to various other line limits including current magnitude limits and mid-line power flow limits. The formulated general economic dispatch problem with marginal losses consistently models flows and loss approximation, results in approximately correct outcomes and is proven to be reference bus independent. Various approximations of this problem are compared using realistically large transmission network test cases.

Keywords: Energy systems, Power electronics, Power systems
Abstract: Stability certification of microgrids can be challenging due to the lack of information on exact values of system parameters. Moreover, full-scale direct stability analysis for every system configuration can be economically and technically unjustified. There exist a demand for simple conditions imposed on system components that guarantee the whole system stability under arbitrary interconnections. Most of existing methods are relying on the so-called passivity property which can be difficult to realize by all the system components simultaneously. In the present manuscript we develop an approach for certifying the system stability by separately considering its properties in different regions of frequency domain. We illustrate our method on the case of droop-controlled inverters and show that while these inverters can never be made passive, reasonable stability certificates can be formulated by careful consideration of their input admittance for different frequency regions. We discuss the generalization of the method for different types of microgrid components.

Keywords: Game theory, Optimization, Stochastic systems
Abstract: We present a two stage auction mechanism that renewable generators (or aggregators) could use to allocate renewable energy among load serving entities (LSEs). The auction is conducted day-ahead. LSEs submit bids specifying their valuation per unit, as well as their real-time fulfillment costs in case of shortfall in generation. We present an allocation rule and a de-allocation rule that maximizes expected social welfare. Since the LSEs are strategic and may not report their private valuations and costs truthfully, we design a two-part payment, one made in Stage 1, before renewable energy generation level W is realized, and another determined later to be paid as compensation to those LSEs that have to be “de-allocated” in case of a shortfall. We propose a two-stage Stochastic VCG mechanism which we prove is incentive compatible in expectation (expected payoff maximizing bidders will bid truthfully), individually rational in expectation (expected payoff of all participants is non-negative) and is also efficient. To the best of our knowledge, this is the first such two-stage mechanism for selling random goods.

Keywords: Indirect adaptive control, Aerospace, Energy systems
Abstract: This paper presents an online learning scheme based on reinforcement learning and adaptive dynamic programming for the power management of hybrid electric systems. Current methods for power management are conservative and unable to fully account for variations in the system due to changes in the health and operational conditions. These conservative schemes result in less efficient use of available power sources, increasing the overall system costs and heightening the risk of failure due to the variations. The proposed scheme is able to compensate for modeling uncertainties and the gradual system variations by adapting its performance function using the observed system measurements as reinforcement signals. The reinforcement signals are nonlinear and consequently neural networks are employed in the implementation of the scheme. Simulation results for the power management of an autonomous hybrid system show improved system performance using the proposed scheme as compared with a conventional offline dynamic programming approach.

Keywords: Autonomous robots, Mechanical systems/robotics, Robotics
Abstract: Path planning for mobile robots involves finding feasible trajectories through a workspace from an initial state to a final, desired state while avoiding workspace obstacles. Due to the variety of mobile robots and the environments in which they can operate, various path-planning methods have been developed. However, the majority of these planning methods have been designed for rigid systems. When applied to flexible systems, these methods typically produce unwanted vibration, which contributes to trajectory-tracking error. Therefore, trajectory tracking for flexible, mobile systems typically involves sequentially planning a path using algorithms designed for rigid systems, then applying vibration control methods to track the trajectory. This paper proposes a modified Rapidly-exploring Random Tree (RRT) algorithm that plans feasible paths that limit the vibration amplitude induced in flexible systems. The algorithm incrementally generates trajectories that minimize deflection cost and path length. Simulations were performed to compare standard RRT to the proposed algorithm. The proposed algorithm generated shorter trajectories with less deflection than those of standard RRT as well as generated trees which utilized a greater amount of the workspace.

Keywords: Autonomous robots, Multivehicle systems, Optimization algorithms
Abstract: In this paper we study a multi-robot path planning problem for persistent monitoring of an environment. We represent the areas to be monitored as the vertices of a weighted graph. For each vertex, there is a constraint on the maximum time spent by the robots between visits to that vertex, called the latency, and the objective is to find the minimum number of robots that can satisfy these latency constraints. The decision version of this problem is known to be PSPACE-complete. We present a O(log p) approximation algorithm for the problem where p is the ratio of the maximum and the minimum latency constraints. We also present an orienteering based heuristic to solve the problem and show through simulations that in most of the cases the heuristic algorithm gives better solutions than the approximation algorithm. We evaluate our algorithms on large problem instances in a patrolling scenario and in a persistent scene reconstruction application. We also compare the algorithms with an existing solver on benchmark instances.

Keywords: Autonomous robots, Neural networks, Control applications
Abstract: Pedestrian flows in densely-populated areas may cause crowd accidents, and effective pedestrian flow regulation is highly desirable for flow optimization. In this paper, we investigate the problem of regulating two merging pedestrian flows by introducing a mobile robot moving within the flow. The pedestrian flows are regulated through dynamic human-robot interaction during their collective motion. We propose a method based on adaptive dynamic programming (ADP) to learn the optimal motion control of the robot in real time and the pedestrian outflow through the bottleneck area is maximized. Extensive simulations are performed using social force models of pedestrian motion. Simulation results show that the pedestrian outflow is significantly improved with our proposed ADP control.

Keywords: Autonomous robots, Neural networks, Pattern recognition and classification
Abstract: Next generation Unmanned Aerial Vehicles (UAVs) must reliably avoid moving obstacles. Existing dynamic collision avoidance methods are effective where obstacle trajectories are linear or known, but such restrictions are not accurate to many real-world UAV applications. We propose an efficient method of predicting an obstacle's motion based only on recent observations, via online training of an LSTM neural network. Given such predictions, we define a Nonlinear Probabilistic Velocity Obstacle (NPVO), which can be used select a velocity that is collision free with a given probability. We take a step towards formal verification of our approach, using statistical model checking to approximate the probability that our system will mispredict an obstacle's motion. Given such a probability, we prove upper bounds on the probability of collision in multi-agent and reciprocal collision avoidance scenarios. Furthermore, we demonstrate in simulation that our method avoids collisions where state-of-the-art methods fail.

Keywords: Autonomous robots, Predictive control for nonlinear systems, Optimal control
Abstract: This paper investigates the problem of energy-optimal control for autonomous underwater vehicles (AUVs). To improve the endurance of AUVs, we propose a novel energy-optimal control scheme based on the economic model predictive control (MPC) framework. We first formulate a cost function that computes the energy spent for vehicle operation over a finite-time prediction horizon. Then, to account for the energy consumption beyond the prediction horizon, a terminal cost that approximates the energy to reach the goal (energy-to-go) is incorporated into the MPC cost function. To characterize the energy-to-go, a thorough analysis has been conducted on the globally optimized vehicle trajectory computed using the direct collocation (DC) method for our test-bed AUV, DROP-Sphere. Based on the two operation modes observed from our analysis, the energy-to-go is decomposed into two components: (i) dynamic and (ii) static costs. This breakdown facilitates the estimation of the energy-to-go, improving the AUV energy efficiency. Simulation is conducted using a six-degrees-of-freedom dynamic model identified from DROP-Sphere. The proposed method for AUV control results in a near-optimal energy consumption with considerably less computation time compared to the DC method and substantial energy saving compared to a line-of-sight based MPC method.

Keywords: Autonomous robots, Robotics, Feedback linearization
Abstract: This article studies the dynamics and control of a novel underactuated system : a ball and plate system suspended by a team of quadrotors via cables. The plate is sought to be horizontally stabilized at a certain height, with the ball stabilized at the center of mass of the plate. The freely moving ball adds 2 degrees of underactuation to the system. The design proceeds through a decoupling of the quadrotors and the plate dynamics. Through a partial feedback linearization approach, the attitude of the plate and the translational height of the plate is initially controlled, while maintaining a bounded velocity along the y and x directions. These inputs are then synthesized through the quadrotors with a backstepping and timescale separation argument based on Tikhonov’s theorem

Keywords: Traffic control, Agents-based systems, Autonomous systems
Abstract: In this paper we consider connected and autonomous vehicles (CAV) in a traffic network as moving waves defined by their frequency and phase. This outlook allows us to develop a multi-layer decentralized control strategy that achieves the following desirable behaviors: (1) safe spacing between vehicles traveling down the same road, (2) coordinated safe crossing at intersections of conflicting flows, (3) smooth velocity profiles when traversing adjacent intersections. The approach consist of using the Kuramoto equation to synchronize the phase and frequency of agents in the network. The output of this layer serves as the reference trajectory for a back-stepping controller that interfaces the first-order dynamics of the phase-domain layer and the second order dynamics of the vehicle. We show the performance of the strategy for a single intersection and a small urban grid network. The literature has focused on solving the intersection coordination problem in both a centralized and decentralized manner. Some authors have even used the Kuramoto equation to achieve synchronization of traffic lights. Our proposed strategy falls in the rubric of a decentralized approach, but unlike previous work, it defines the vehicles as the oscillating agents, and leverages their inter-connectivity to achieve network-wide synchronization. In this way, it combines the benefits of coordinating the crossing of vehicles at individual intersections and synchronizing flow from adjacent junctions.

Keywords: Traffic control, Control applications, Observers for nonlinear systems
Abstract: As an alternative to installing traffic sensors on all highway segments, traffic density estimation routines can be utilized to estimate traffic state on sensor-less segments. To that end, we first derive a generalized traffic flow model for stretched highways with arbitrary number and location of ramp flows. The flow model is based on the Lighthill-Whitham-Richards (LWR) model and Greenshield's fundamental diagram. This derived model is written as a nonlinear state-space system, making it amenable to control-theoretic formulations for nonlinear dynamic networks. We then show that the nonlinearities present in the derived models are locally Lipschitz continuous by providing analytical Lipschitz constants that depend on the network parameters and topology. The analytical derivation is then used to perform traffic density estimation given a limited number of traffic sensors using a vintage Lipschitz-based state estimator. This estimator design graciously scales to thousands of highway segments. Numerical tests are given providing early confidence in the potential of the proposed methods.

Keywords: Traffic control, Decentralized control, Optimal control
Abstract: Urban intersections, merging roadways, roundabouts, and speed reduction zones along with the driver responses to various disturbances are the primary sources of bottlenecks in corridors that contribute to traffic congestion. The implementation of connected and automated technologies can enable a novel computational framework for real-time control aimed at optimizing energy consumption and travel time. In this paper, we propose a decentralized energy-efficient optimal control framework for two adjacent intersections. We derive a closed-form analytical solution that includes interior boundary conditions and evaluate the effectiveness of the solution through simulation. Fuel consumption and travel time are significantly reduced compared to the baseline scenario designed with conventional fixed time signalized intersections.

Keywords: Transportation networks, Optimization, Traffic control
Abstract: This paper investigates the use of Infrastructure-To-Vehicle (I2V) communication to generate routing suggestions for drivers in transportation systems, with the goal of optimizing a measure of overall network congestion. We define link-wise levels of trust to tolerate the non-cooperative behavior of part of the driver population, and we propose a real-time optimization mechanism that adapts to the instantaneous network conditions and to sudden changes in the levels of trust. Our framework allows us to quantify the improvement in travel time in relation to the degree at which drivers follow the routing suggestions. We then study the resilience of the system, measured as the smallest change in routing choices that results in roads reaching their maximum capacity. Interestingly, our findings suggest that fluctuations in the extent to which drivers follow the provided routing suggestions can cause failures of certain links. These results imply that the benefits of using Infrastructure-To-Vehicle communication come at the cost of new fragilities, that should be appropriately addressed in order to guarantee the reliable operation of the infrastructure.

Keywords: Transportation networks, Traffic control
Abstract: In a traffic network, vehicles normally select their routes selfishly. Consequently, traffic networks normally operate at an equilibrium characterized by Wardrop conditions. However, it is well known that equilibria are inefficient in general. In addition to the intrinsic inefficiency of equilibria, the authors recently showed that, in mixed–autonomy networks in which autonomous vehicles maintain a shorter headway than human–driven cars, increasing the fraction of autonomous vehicles in the network may increase the inefficiency of equilibria. In this work, we study the possibility of obviating the inefficiency of equilibria in mixed–autonomy traffic networks via pricing mechanisms. In particular, we study assigning prices to network links such that the overall or social delay of the resulting equilibria is minimum. First, we study the possibility of inducing such optimal equilibria by imposing a set of undifferentiated prices, i.e. a set of prices that treat both human–driven and autonomous vehicles similarly at each link. We provide an example which demonstrates that undifferentiated pricing is not sufficient for achieving minimum social delay. Then, we study differentiated pricing where the price of traversing each link may depend on whether vehicles are human-driven or autonomous. Under differentiated pricing, we prove that link prices obtained from the marginal cost taxation of links will induce equilibria with minimum social delay if the degree of road capacity asymmetry (i.e. the ratio between the road capacity when all vehicles are human–driven and the road capacity when all vehicles are autonomous) is homogeneous among network links.

Keywords: Traffic control, Transportation networks, Game theory
Abstract: In this paper, we present a discussion on smart parking systems in urban traffic networks.

Reduced vehicle speed when drivers search for parking lots contributes to increased traffic jams in recent urban traffic networks.

We aim to shorten the searching time for parking lots, which is one of the causes of traffic jams, by allocating available parking lots to drivers.

Furthermore, we design a dynamic parking fee system and redistribute parking lots to equalize the profits earned by managers of multiple parking lots in traffic-congested areas.

We then finally confirm the effectiveness of the proposed algorithm through numerical simulations.

Keywords: Cooperative control, Autonomous robots, Agents-based systems
Abstract: Formation control has attracted considerable attention for its wide applications, e.g, military reconnaissance, environment exploration. However, the formation suffers additional security vulnerabilities due to its distributed fashion, networked communication and openness to outside environments. Existing works focus on detection and countermeasures for some classic attacks, e.g., Denial of Service (DoS), replay and deception attacks. Nevertheless, those attacks are generally from cyberspace and the methods are based on an assumption that the attacker has some knowledge or access to the formation system, like the system dynamics is known or internal nodes are compromised. It remains an open issue given how to design a feasible attack or under what conditions an attack can be implemented. In this paper, we aim to design a feasible and intelligent attack scheme against the obstacle-avoidance of formation control. We describe it as “intelligent” for the following: i) Without any prior information of the system dynamics, the attacker can learn the detection area and goal position of an agent by trial and observation; ii) The obstacle-avoidance mechanism is regressed using support vector regress (SVR) method; iii) The strategy exhibits attack efficiency. Furthermore, a sufficient condition is obtained to guarantee the success of the intelligent attack. Simulations illustrate the effectiveness of the proposed attack scheme.

Keywords: Cooperative control, Autonomous robots, Control applications
Abstract: This paper proposes a novel moving obstacle avoidance algorithm for multi-agent systems. The method has robustness in maintaining formation shape. Even if link failure occurs among agents when avoiding obstacles, the communication topology of the system can be recovered based on the conditions we obtain. The main idea includes two parts, i) a flexible function of relative velocities and positions between agents and obstacles is designed to avoid moving/stationary obstacles, and ii) based on initial adjacent matrix and graph connection characteristic, a topology recover mechanism is proposed to guarantee formation shape and no extra links are involved. The proposed algorithm has the following advantages: i) It is able to recover formation shape, even if some links among agents are broken while avoiding moving obstacles; ii) In the process of rebuilding communication links, the proposed algorithm can protect communication topology from being altered maliciously. Furthermore, we obtain conditions of the topology recovery for both directed and undirected graph. Some simulations are conducted to demonstrate the efficiency of the proposed algorithm.

Keywords: Cooperative control, Autonomous systems, Aerospace
Abstract: A pursuit-evasion scenario with two pursuers and one evader is considered. The evader aims at reaching a goal line which is protected by the pursuers. When reaching this goal is not possible, the evader strives to position itself as close as possible with respect to the goal line at the time of capture. The pursuers try to capture the evader as far as possible from the goal line. The problem is posed as a zero-sum differential game where the two pursuers cooperate against the evader. It represents an extension of Isaacs' game of guarding a target except now there are two cooperating defenders. State feedback strategies are derived in this paper and the Value function is obtained. It is also shown that the Value function is continuous, continuously differentiable, and it satisfies the Hamilton-Jacobi-Isaacs equation.

Keywords: Cooperative control, Autonomous robots, Sensor networks
Abstract: This paper studies a k-order coverage control problem where a network of agents must deploy themselves over a desired area. The objective is to deploy all the agents in a decentralized manner such that the coverage performance of the network is maximized. Unlike many prior works that consider multi-agent deployment, we explicitly consider applications where more than one agent may be required to service an event that occurs in the domain. The proposed method ensures that the agents move to an optimal configuration while simultaneously relaxing the requirement of constant communication among the agents. In order to achieve the stated goals, a self-triggered coordination method is developed that both determines how agents should move without having to continuously acquire information from other agents, as well as when to acquire new information. Simulation results illustrate that the self-triggered algorithm reduces the amount of communication necessary to accomplish the deployment task while not having to sacrifice performance in meeting the goal.

Keywords: Cooperative control, Control applications
Abstract: The distributed cooperative control problem for high-speed train is investigated in this paper. Cars in a high-speed train are modeled as a group of ordered particles connected by flexible couplers. Each car is viewed as an intelligent agent that communicates with its neighbors, making the train a multi-agent system. The information transmission topology among these agents is represented by a connected undirected graph. Distributed cooperative control laws are constructed that achieve displacement and speed consensus among cars at a desired profile, while guaranteeing the coupler displacements to be within a safety range and converge to the nominal value. Simulation results are presented to illustrate the theoretical conclusions we have reached.

Keywords: Network analysis and control, Adaptive systems, Distributed control
Abstract: We consider the problem of designing distributed algorithms that enable a group of agents (followers) to track a reference trajectory generated by a leader agent. Such algorithms are an integral part of a variety of distributed estimation and control techniques like the attitude control problem for spacecraft formation flying. Existing methods assume that the leader’s reference dynamics are fully known to one or more follower agents, and they typically require significant amounts of inter-agent communication. In this paper, we propose a novel distributed adaptive observer in which no follower agent knows the leader’s reference dynamics. In addition, our method does not require as much inter-agent communication as existing methods. We use appropriate Lyapunov functions to prove convergence, and we present numerical examples to demonstrate the efficacy of our approach.

Keywords: Network analysis and control, Agents-based systems, Linear systems
Abstract: We study the problem of maximizing opinion diversity in a social network that includes opinion leaders with binary opposing opinions. The members of the network who are not leaders form their opinions using the French-DeGroot model of opinion dynamics. To quantify the diversity of such a system, we adapt two diversity measures from ecology to our setting, the Simpson Diversity Index and the Shannon Index. Using these two measures, we formalize the problem of how to place a single leader with opinion 1, given a network with a leader with opinion 0, so as to maximize the opinion diversity. We give analytical solutions to these problems for paths, cycles, and trees, and we highlight our results through a numerical example.

Keywords: Network analysis and control, Agents-based systems, Stability of nonlinear systems
Abstract: This paper proposes a distributed continuous-time epidemic model, called networked SIWS (Susceptible-Infected-Water-Susceptible) model, for an SIS type waterborne disease spreading over a network of multiple groups of individuals sharing a water source. A sufficient condition is obtained for the healthy state, at which all individuals are not infected and the water is not contaminated, to be globally asymptotically stable. The effects of the shared water source on the disease spreading are analyzed through the comparison of the basic reproduction number with the networked SIS model without water and demonstrated via simulations.

Keywords: Network analysis and control, Control of networks, Agents-based systems
Abstract: Distributed decision-making processes with two types of manipulative actors, which enact feedback controls to alter the process dynamics, are modeled and analyzed. The main contribution of the work is to evaluate the interplay among the manipulative actors in deciding: 1) the asymptotic decisions reached by the agents and 2) network's transient dynamics. In particular, the dependence of the asymptotic opinions on the network's topology and the manipulative actors' control schemes is characterized. Then, the impacts of the actors' control schemes on the intrinsic settling dynamics of the network, as well on each other actors' transfer functions, is determined. Finally, an example is presented to illustrate the results. The key finding is that asymptotics and transients both show a sophisticated spatial dependence on the relative locations of manipulated agents within the network.

Keywords: Control applications
Abstract: In this paper, a stochastic dynamic control strategy is presented to prevent the spread of an infection over a homogeneous network. The infectious process is persistent, i.e., it continues to contaminate the network once it is established. It is assumed that there is a finite set of network management options available such as degrees of nodes and promotional plans to minimize the number of infected nodes while taking the implementation cost into account. The network is modeled by an exchangeable controlled Markov chain, whose transition probability matrices depend on three parameters: the selected network management option, the state of the infectious process, and the empirical distribution of infected nodes (with not necessarily a linear dependence). Borrowing some techniques from mean-field team theory the optimal strategy is obtained for any finite number of nodes using dynamic programming decomposition and the convolution of some binomial probability mass functions. For infinite-population networks, the optimal solution is described by a Bellman equation. It is shown that the infinite-population strategy is a meaningful sub-optimal solution for finite-population networks if a certain condition holds. The theoretical results are verified by an example of rumor control in social networks.

Keywords: Network analysis and control, Control of networks, Cooperative control
Abstract: In this paper we consider single input influenced consensus for networked systems featuring agents acting on independent time scales. We are able to show that some key characteristics from mono-scale networks are retained by our formulation, which allows us to investigate the performance limitations for scaled networks under the influence of constant and time-varying input signals. In contrast to results for mono-scale networks, the performance of the scaled network to an influencing signal is dependent on the selected influence node; we use this feature to offer insights into how to best interact with scaled networked systems.

Keywords: Optimization algorithms, Aerospace, Learning
Abstract: Effective path planning of unmanned aerial vehicles (UAVs) operating under avoidance zones is one of the critical capabilities to guarantee mission success. To obtain an optimized solution within reasonable computational time, an iterative learning optimization method (ILOM) is proposed to solve the UAV path planning problem with guaranteed computational performance in terms of convergence and objective value. First, the UAV path planning problem is formulated as a quadratically constrained quadratic programming (QCQP) problem. Next, a method combining matrix decomposition and iterative optimization is developed to solve QCQPs. However, computational performance is influenced by the algorithmic parameters involved in the iterative optimization method. Considering the implicit relationship between the algorithmic parameters and computational performance, convolutional neural network is applied to optimally select parameters in the iterative method instead of determining them from experience. Finally, the proposed ILOM is implemented in simulation examples to validate improved computational efficiency.

Keywords: Optimization algorithms, Agents-based systems, Game theory
Abstract: In this paper, distributed algorithms are designed to search the Nash equilibrium (NE) for an N-player game in continuous-time. The agents are not assumed to have direct access of other agents' states, and instead, they estimate other agents' states by communicating with their neighbours. Advanced consensus algorithms are implemented for such purposes, and consequently the game is decentralised into N subsystems interacting over a communication network. It is proved that, for any communication network with a connected graph, a fixed-time consensus is achieved, independent of the initial conditions, based on which an NE can be obtained asymptotically by the gradient descent term for the fixed-time consensus-based algorithm. Then, the results are extended to a fixed-time NE seeking with modifications of the gradient terms, where both the consensus and the optimisation can be obtained in fixed time, and the upper bound of the settling time is established by the Lyapunov theory. A simulation example is presented to verify the effectiveness of the theoretical development, where some comparisons with other works are studied to demonstrate the advantages of the proposed algorithms.

Keywords: Optimization algorithms, Cooperative control, Multivehicle systems
Abstract: We frame the collision avoidance problem of multi-agent autonomous vehicle systems into an online convex optimization problem of minimizing certain aggregate cost over the time horizon. We then propose a distributed real-time collision avoidance algorithm based on the online gradient algorithm for solving the resulting online convex optimization problem. We characterize the performance of the algorithm with respect to a static offline optimization, and show that, by choosing proper stepsizes, the upper bound on the performance gap scales sublinearly in time. The numerical experiment shows that the proposed algorithm can achieve better collision avoidance performance than the existing Optimal Reciprocal Collision Avoidance (ORCA) algorithm, due to less aggressive velocity updates that can better prevent the collision in the long run.

Keywords: Optimization algorithms, Network analysis and control, Large-scale systems
Abstract: This paper presents an efficient asynchronous distributed algorithm for the problem of balancing a nonnegative matrix using a network of processors, each of which has access to a portion of the global matrix. The goal of the algorithm is for the processors to collaborate through local information exchange so that each processor can determine its local weighting coefficients that balance the matrix. Our algorithm is of Gauss-Seidel type with strict relaxation and converges geometrically under mild assumptions on the communication model between neighboring processors. The analysis of our algorithm is based on a novel reformulation of matrix balancing as a network consensus problem, from which an upper bound on the convergence rate can be derived. Finally, we demonstrate the applicability of the algorithm to a problem of optimally allocating curing resources for suppressing epidemic spread in a directed weighted network, where the spreading dynamic is captured by a susceptible-infected-susceptible model.

Keywords: Optimization algorithms, Numerical algorithms, Agents-based systems
Abstract: In this article, we consider the problem of planning an optimal route for an unmanned vehicle, tasked with persistently monitoring a set of targets. The targets are grouped into m subsets, referred to as clusters. To monitor a cluster, the vehicle must collect data from any one target in the cluster, by making a physical visit to the target. The vehicle has a finite fuel capacity, which is specified in terms of the number of visits it can make, at the end of which it must be refueled/recharged at a depot (which is one of the targets). Given k allowed visits for the vehicle, the problem of interest is to plan a closed walk (route) of k visits that can be repeated continuously, such that the maximum time between successive visits to the clusters is minimized (the minimum value is mathcal R^*(k)). Here, we prove that for k geq m^2-m, mathcal R^*(k) takes only two values, mathcal R^*(m) when k is an integral multiple of m, and mathcal R^*(m+1) otherwise, leading to significant computational savings. We corroborate this result by performing numerical simulations on a Dubins vehicle.

Keywords: Optimization algorithms, Numerical algorithms, Large-scale systems
Abstract: We consider a resource allocation problem over an undirected network of agents, where edges of the network define communication links. The goal is to minimize the sum of agent-specific convex objective functions, while the agents' decisions are coupled via a convex conic constraint. We derive two methods by applying the alternating direction method of multipliers (ADMM) for decentralized consensus optimization to the dual of our resource allocation problem. Both methods are fully parallelizable and decentralized in the sense that each agent exchanges information only with its neighbors in the network and requires only its own data for updating its decision. We prove convergence of the proposed methods and demonstrate their effectiveness with a numerical example.

Keywords: Process Control, Computer-aided control design, Uncertain systems
Abstract: Achieving a new set point and maintaining it with a desired precision is a common control problem. In case the reference is not fixed, or a priori unknown disturbances are present, the problem is often referred to as offset-free control. We consider the problem of finding suitable controller parameters to obtain an offset-free control up to a certain degree. We tackle the problem in two steps: first, we find controller parameters to steer the controlled system in the neighborhood of the desired reference; second, we identify controller parameters such that the system is robustly con- trolled invariant with respect to the desired neighborhood of the reference value. For each subproblem we determine the set of parameters that guarantee the desired behavior despite bounded uncertainties. We employ a set-based feasibility formulation which is able to handle nonlinear systems with set constraints. The approach is illustrated with an example.

Keywords: Process Control, Feedback linearization
Abstract: The interior of a fuel cell is a complex chemical reaction process. How to design an algorithm to achieve energy optimization is a challenging problem. Due to the nonlinearity of the system, it is usually difficult to obtain the real-time global optimal control strategy directly. In this paper, a near-optimal controller is proposed for a polymer electrolyte membrane fuel cell (PEMFC) air supply system. The control goal is to maximize net output power of the PEMFC system by tracking a desired optimal oxygen excessive ratio. The tracking problem is formulated as a receding-horizon optimal control problem and a predictive timescale approximation technique is adopted to solve the optimal control law and effectively reduces the computational complexity especially with nonlinear systems like PEMFC. The simulation of dynamic excess oxygen ratio adjustment and various comparison with other control methods show the rapidity, high accuracy and fine capacity of resisting disturbance of the proposed method.

Keywords: Process Control, PID control
Abstract: In this paper we propose a new ratio control architecture that exploits the use of inversion-based feedforward actions to achieve a fast set-point step response while keeping the required ratio between two process variables. The recently developed ratio tracking station is then achieved to increase the robustness of the system. A user design parameter allows the selection of the trade-off between the settling time of the step response and the performance in keeping the desired ratio. Simulation results demonstrate the effectiveness of the method.

Keywords: Process Control, Robust control, Optimal control
Abstract: We propose the a novel data-driven robust model predictive control (RMPC) approach for irrigation system operations, where uncertainty in evapotranspiration and precipitation forecast is explicitly taken into account. A data-driven uncertainty set is constructed to describe the distribution of evapotranspiration forecast error. Meanwhile, the distribution of precipitation forecast error data is analyzed in detail, which is shown to directly rely on forecast values and manifest a time-varying characteristics. To address this issue, we design a tailored data-driven conditional uncertainty set to disentangle the dependence of distribution of forecast error on forecast values. The generalized affine decision rule is employed to yield a tractable approximation to the optimal control problem. Case studies based on real weather data show that, by effectively utilizing information within historical uncertainty data, the proposed data-driven RMPC approach can help better maintaining the soil moisture above the safety level with less water consumptions than traditional control strategies.

Keywords: Pulp and Paper Control, Control applications, Computational methods
Abstract: In addition to the Kappa number, which indicates the residual lignin content in the wood pulp, microscopic properties of wood chips such as porosity are also very important as it determines the paper quality as well as the rate of delignification. However, there are very few models that are able to describe the evolution of porosity of wood chips in delignification processes like pulp digester. Motivated by this consideration, in this work, a multiscale model for a batch-type digester is developed. Specifically, the Purdue model is used to describe the interactions among the free liquor, entrapped liquor and solid phases, and a hybrid kinetic Monte Carlo model is employed to show the evolution of wood chip porosity. Then, a model-based control system is developed to regulate the porosity and Kappa number to desired values.

Keywords: Energy systems, Estimation, Model Validation
Abstract: In wind farms, wake interaction leads to losses in power capture and accelerated structural degradation when compared to freestanding turbines. One method to reduce wake losses is by misaligning the rotor with the incoming flow using its yaw actuator, thereby laterally deflecting the wake away from downstream turbines. However, this demands an accurate and computationally tractable model of the wind farm dynamics. This problem calls for a closed-loop solution. This tutorial paper fills the scientific gap by demonstrating the full closed-loop controller synthesis cycle using a steady-state surrogate model. Furthermore, a novel, computationally efficient and modular communication interface is presented that enables researchers to straight-forwardly test their control algorithms in large-eddy simulations. High-fidelity simulations of a 9-turbine farm show a power production increase of up to 11% using the proposed closed-loop controller compared to traditional, greedy wind farm operation.

Keywords: Agents-based systems, Autonomous systems, Energy systems
Abstract: In an autonomous wind farm, turbines will use information from nearby turbines to achieve wind farm level objectives such as optimizing the overall performance of a wind farm, ensuring resiliency when other sensors fail, and adapting to changing local conditions. In this paper, the wind farm can be modeled as a network within which turbines (nodes) share information across designated communication channels, with a focus on turbines at the outside of the wind farm capturing local effects and sharing that information with downstream turbines. Understanding of varied inflow conditions can be especially important in complex terrain. This information can be used to monitor turbines, self-organize turbines into groups, and predict the power performance of a wind farm. In particular, this paper describes an autonomous wind farm that incorporates information from local sensors in real-time to predict wind speed and wind direction at each turbine over a short-term horizon. Results indicate that the estimate of wind direction can be used to improve the knowledge of the wind speed and direction over the persistence method on a 10-15 minute time horizon. These short-term forecasts can also be used to facilitate advanced control methods such as feed-forward control within a wind farm.

Keywords: Energy systems, Large-scale systems, Modeling
Abstract: Controlling the air flow within wind power plants has the potential to improve plant performance and is an active area of research in the wind energy control community. In order to develop, test, and tune wind power plant controllers efficiently, an accurate engineering model of the turbine wake dynamics is required. Two elements of flow control are wake steering via yaw and tilt of a turbine. When a turbine is yawed or tilted away from the incoming wind field, the wake shape is changed. This is largely due to shed vortices that produce a curled wake. In this work, the well-known wake engineering model FLOw Redirection and Induction in Steady State (FLORIS) wake engineering model is enhanced to include these curled wake effects due to tilt. Since decay of these vortices has not been previously captured in an engineering model, the authors describe how vortices with decay have been added to FLORIS and how the updated model has been used to study the effects due to tilt in the wake. Results are demonstrated and compared to high-fidelity large-eddy simulations. Potential wind power plant performance gains due to flow control using tilt are investigated across different wind conditions and sites. Preliminary results show power gains by using tilt to implement flow control in a variety of wind distributions and tilt values.

Keywords: Modeling, Reduced order modeling, Uncertain systems
Abstract: We present a novel method to derive a surrogate model for wind farm control. The procedure is based on a stochastic approach using generalized polynomial chaos (PC) and high-fidelity simulations. The turbine control law and the incoming wind conditions, such as speed and directions, are treated as uncertain variables. Wind farm power production is then viewed as the random process depending on these uncertain variables. Thus, polynomial chaos expansion can be used to obtain a response function that provides the wind farm power production as a function of the turbine control parameters and the wind speed and direction. The response function is obtained by using a finite set of deterministic realizations, which consist in high-fidelity simulations for certain values of wind speed, direction and control parameters, interpolated by polynomials. In PC, the interpolating polynomial basis and the set of realizations are selected according to the probability density function of the uncertain parameters. This allows using a limited number of realizations to obtain an accurate response function and provides uncertainty bounds on the model. Thus, a mapping of the optimal control settings is obtained for any wind speed and direction to be employed for real-time wind farm operations. In this work, the procedure is validated against field measurements in a real wind farm in north Texas. The surrogate model is obtained by performing 64 simulations with our in house code interpolated by 7th-order Legendre polynomials. The energy production computed with the surrogate model is accurate within 2% of the measured SCADA data. Once the response function has been obtained, an optimization problem is solved to find the control parameters maximizing the farm power production.

Keywords: Iterative learning control, Linear systems, Predictive control for linear systems
Abstract: A data-based policy for iterative control task is presented. The proposed strategy is model-free and can be applied whenever safe input and state trajectories of a system performing an iterative task are available. These trajectories, together with a user-defined cost function, are exploited to construct a piecewise affine approximation to the value function. Approximated value functions are then used to evaluate the control policy by solving a linear program. We show that for linear system subject to convex cost and constraints, the proposed strategy guarantees closed-loop constraint satisfaction and performance bounds on the closed-loop trajectory. We evaluate the proposed strategy in simulations and experiments, the latter carried out on the Berkeley Autonomous Race Car (BARC) platform. We show that the proposed strategy is able to reduce the computation time by one order of magnitude while achieving the same performance as our model-based control algorithm.

Keywords: Iterative learning control, Linear systems, Stability of linear systems
Abstract: Repetitive processes arise in the modeling of physical systems and have a 2D systems structure as there are two directions of information propagation, one of which is spatial and the other is time over a finite duration. Recently, a stability theory for nonlinear repetitive processes has been developed. This paper uses nonlinear stability theory to develop a parameterized control law for linear dynamics. Applied to iterative learning control law design, this law allows for gain scheduling tuning to achieve better performance. The new design is illustrated by application to an example where the model representing the dynamics has been obtained by frequency response test data obtained from a physical example.

Keywords: Iterative learning control, Networked control systems, Optimal control
Abstract: In this paper we present an online wide-area oscillation damping control (WAC) design for uncertain models of power systems using ideas from reinforcement learning. We assume that the exact small-signal model of the power system at the onset of a contingency is not known to the operator and use the nominal model and online measurements of the generator states and control inputs to rapidly converge to a state-feedback controller that minimizes a given quadratic energy cost. However, unlike conventional linear quadratic regulators (LQR), we intend our controller to be sparse, so its implementation reduces the communication costs. We, therefore, employ the gradient support pursuit (GraSP) optimization algorithm to impose sparsity constraints on the control gain matrix during learning. The sparse controller is then implemented using distributed communication. The proposed method is validated using the IEEE 39-bus power system model with 1149 unknown parameters.

Keywords: Iterative learning control, Neural networks, Learning
Abstract: The purpose of this work is to develop an effective approach to design the high-order iterative learning control scheme based on neural networks. The idea adopted here is to propose the high-order learning controller which is able to combine the control information from the previous trials and in this way to improve its convergence speed. Sufficient conditions for convergence of the developed ILC scheme are derived and constructively incorporated into training process of neural controller. The efficiency of the proposed approach is illustrated on the example of a pneumatic servomechanism.

Keywords: Iterative learning control
Abstract: This paper considers the high performance consensus tracking problem of networked dynamical systems working in a repetitive manner that find applications in a wide range of areas. To achieve the high performance requirement, recent design uses iterative learning control (ILC) to avoid the use of accurate model information in traditional control methods. However, existing learning based methods either use simple forms of ILC design or explicitly utilise the model inverse, limiting their performance in practice. To address this limitation, this paper proposes an optimisation based ILC design using the well-known norm optimal ILC (NOILC) framework by designing a novel performance index. The resulting algorithm achieves monotonic convergence of the tracking error norm to zero, and can be applied to both heterogeneous and nonminimum phase systems. Using the alternating direction method of multipliers (ADMM), a distributed implementation of the algorithm is developed. Convergence properties of the algorithm are analysed in detail and numerical examples are presented to demonstrate the effectiveness of the proposed design.

Keywords: Iterative learning control
Abstract: This paper discusses the robustness of a plant-inversion based Switched Iterative Learning Control (SILC) scheme for a special class of multivariable systems where measurement access is limited to only one output channel at any time. Previous work has shown that it is impossible for such systems to achieve asymptotic stability, or equivalently zero error convergence, with standard Iterative Learning Control (ILC); however, zero error convergence is possible when using SILC with an appropriate learning matrix. In this case convergence conditions in both the iteration and switch domains are satisfied. The most intuitive and convenient approach to construct such a learning matrix is to directly invert the plant dynamics. Although this approach perfectly decouples the nominal plant dynamics and, thus, automatically satisfies the convergence conditions, its effectiveness when the system is contaminated with uncertainty is not examined. This work investigates the degree of robustness of this plant-inversion based approach to a multiplicative uncertainty. The result demonstrates to what extent to which the robustness of the proposed approach is achieved.

Keywords: Flight control, Aerospace, Automotive control
Abstract: To achieve a high performance level during ground operations, the lateral dynamics of an aircraft must be controlled using all available actuators (rudder, nose wheel steering system and brakes), which gives rise to a challenging allocation problem. This provides an excellent benchmark to compare various kinds of control allocation techniques. In this paper, an exhaustive literature review is first presented. The most relevant allocation methods are then applied to an on-ground aircraft model, which has been previously validated against a high-fidelity Airbus simulator. An extensive evaluation is finally performed based on a set of performance indicators such as the number of iterations, the convergence time, the error and the actuators consumption.

Keywords: Flight control, Aerospace, Control applications
Abstract: This paper presents a control algorithm for the autonomous landing of a fixed-wing aircraft. In the proposed approach, the classical PID control technique is augmented with a state-dependent coefficient (SDC) nonlinear model inversion. The SDC-based nonlinear model inversion eliminates the need for a linearization of the aircraft dynamics. The control law provides accurate autonomous landing in adverse atmospheric conditions such as crosswind and turbulence. The effectiveness is demonstrated for autonomous descent, flare, touch down, as well as crab and de-crab maneuvers for the Cessna 172 aircraft simulation model.

Keywords: Flight control, Optimal control, Control applications
Abstract: This paper presents a computational optimal con- trol problem formulation for solving optimal gain programs for pure proportional navigation (PPN). The influence of 3 degree-of-freedom (DOF) missile flight dynamics is considered explicitly. The development provides an approach for exploring the optimality of conventional fixed-gain missile guidance laws (that consider missile kinematics only) and for extending the performance of conventional PPN. Algebraic constraint equations are utilized to sidestep computational challenges associated with the engagement equations. Furthermore, the navigation gain may be box-constrained to ensure that the solution retains sufficient control authority against an uncertain engagement. The results show that a fixed navigation gain is not acceleration optimal when 3-DOF missile flight dynamics are considered and that implementing an optimal gain program can be utilized to improve impact angles and/or acceleration margins as compared to fixed-gain PPN.

Keywords: Flight control, Predictive control for nonlinear systems, Feedback linearization
Abstract: We propose an NMPC scheme for stabilizing the translational thrust-propelled dynamics. The novelty lies in the design of a nonlinear feedback linearization controller and of its associated terminal region. We show, in a constructive manner, that the region, given as an ellipsoidal set, is made invariant by the aforementioned controller under restrictive input constraints and thus ensures recursive feasibility and asymptotic stability for the closed-loop scheme. Simulation results and comparisons validate the proposed approach.

Keywords: Constrained control, Flight control, Control applications
Abstract: This paper proposes a composite anti-windup design approach, featuring both dynamic and static components. The extra static component is specially structured to limit classical integrator wind-up, and is useful in nonlinear systems which operate far from their design operating point. An approach for stability analysis and design of the combined scheme is also provided. The work was motivated by the need to stabilise quadcopters subject to large disturbances, and excerpts from an extensive simulation campaign are reported. The simulations indicate that the combination of dynamic and static terms provide stability for significantly larger disturbances than either static or dynamic anti-windup alone.

Keywords: Aerospace, Robust adaptive control, Constrained control
Abstract: This paper analyzes the dynamics of tilt-rotor quadcopters with H-configuration and synthesizes a control system for these vehicles. Our analysis is the first to show a nonlinear effect in the vehicle's rotational dynamics due to the fact that not all propellers of a tilt-rotor are aligned to one of the vehicle's principal axes. The proposed control system relies on an original robust model reference adaptive control law to guarantee user-defined constraints on both the trajectory tracking error and the adaptive gains at all time despite parametric, matched, and unmatched uncertainties due to unknown external disturbances and dangling payloads.

Keywords: Stochastic optimal control, Autonomous systems, Stochastic systems
Abstract: Real-time controllers must satisfy strict safety requirements. Recently, Control Barrier Functions (CBFs) have been proposed that guarantee safety by ensuring that a suitably-defined barrier function remains bounded for all time. The CBF method, however, has only been developed for deterministic systems and systems with worst-case disturbances and uncertainties. In this paper, we develop a CBF framework for safety of stochastic systems. We consider complete information systems, in which the controller has access to the exact system state, as well as incomplete information systems where the state must be reconstructed from noisy measurements. In the complete information case, we formulate a notion of barrier functions that leads to sufficient conditions for safety with probability 1. In the incomplete information case, we formulate barrier functions that take an estimate from an extended Kalman filter as input, and derive bounds on the probability of safety as a function of the asymptotic error in the filter. We show that, in both cases, the sufficient conditions for safety can be mapped to linear constraints on the control input at each time, enabling the development of tractable optimization-based controllers that guarantee safety, performance, and stability. Our approach is evaluated via simulation study on an adaptive cruise control case study.

Keywords: Stochastic optimal control, Optimal control, Stochastic systems
Abstract: This paper presents a design method for a sub-optimal feedback controller to minimize the expectation of a cost function for uncertain nonlinear systems. The uncertainty is described by time-invariant stochastic parameters, which cause difficulties in solving the optimal control problem. The conventional notion of the principle of optimality cannot be applied to solve this problem. Furthermore, the optimal input and the expected cost cannot be described explicitly because of the nonlinearity of the system. These difficulties are overcome by combining a parametric approximation with a gradient-based optimization method. This approach enables us to obtain the gradient of an approximated cost function in an explicit form. A Monte Carlo (MC) approximation is employed to calculate the expectation of the derived gradient with respect to the stochastic parameters. This expected gradient is used to optimize the parameter of the controller.

Keywords: Stochastic optimal control, Optimization, Computer-aided control design
Abstract: This paper considers the problem of stochastic optimal control of a Gaussian-perturbed linear system subject to soft polytopic state constraints, hard polytopic input constraints, and a convex cost function. We propose two conservative approaches using risk allocation that can be implemented via existing solvers, and characterize the approximations. Unlike existing approaches, we do not decouple the risk allocation from the optimal controller synthesis. We first show that risk allocation in conjunction with optimal controller synthesis introduces reverse convex constraints into the optimization problem. Next, we use piecewise-affine approximations of the nonlinear terms in the optimization problem to propose a mixed-integer convex program. Our piecewise-affine approximation produces a solver-friendly convex program when the safety probability threshold is larger than 0.5. Using two stochastic motion planning problems, we demonstrate that the proposed approach outperforms existing approaches like iterative risk allocation and particle control approaches in computation time, without compromising on the solution quality.

Keywords: Stochastic optimal control, Robust control
Abstract: Control systems are increasingly targeted by malicious adversaries, who may inject spurious sensor measurements in order to bias the controller behavior and cause suboptimal performance or safety violations. This paper investigates the problem of tracking a reference trajectory while satisfying safety and reachability constraints in the presence of such false data injection attacks. We consider a linear, time-invariant system with additive Gaussian noise in which a subset of sensors can be compromised by an attacker, while the remaining sensors are regarded as secure. We propose a control policy in which two estimates of the system state are maintained, one based on all sensors and one based on only the secure sensors. The optimal control action based on the secure sensors alone is then computed at each time step, and the chosen control action is constrained to lie within a given distance of this value. We show that this policy can be implemented by solving a quadratically-constrained quadratic program at each time step. We develop a barrier function approach to choosing the parameters of our scheme in order to provide provable guarantees on safety and reachability, and derive bounds on the probability that our control policies deviate from the optimal policy when no attacker is present. Our framework is validated through numerical study.

Keywords: Stochastic optimal control, Stochastic systems, Numerical algorithms
Abstract: A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of reachability analysis and risk measures to devise a risk-sensitive reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set as a set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk (CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set and provide arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton- Jacobi reachability analysis) to risk-neutral (which is the case for stochastic reachability analysis).

Keywords: Stochastic optimal control, Uncertain systems, Stochastic systems
Abstract: Uncertainty propagation is an important step inthe derivation of optimal control strategies for dynamic systemsin the presence of state and parameter uncertainty. Manystochastic control formulations seek to optimize an expectedvalue of a score or cost function, or otherwise enforce aprobabilistic constraint through the use of an expected value.The time-varying state density needed for this expected valuecomputation may be quantified through Monte Carlo methodsor explicit approaches such as the Frobenius-Perron operator.This paper explores an alternative approach to the computationof the expected value by leveraging the adjoint relationshipbetween the Frobenius-Perron operator and the Koopmanoperator. This relationship states that the expected value of aforward-propagated density with a score function is equivalentto the expected value of the initial density with the score func-tion mapped back to the initial state space. By computing theexpected value through use of the Koopman operator, severalcomputational issues arising when using the Frobenius-Perronoperator can be mitigated, while maintaining the benefits of anexplicit method over Monte Carlo. A general stochastic optimalcontrol problem is formulated wherein the expected value iscomputed between the initial state density and a score functionusing the Koopman operator. The computational benefits ofcomputing the expected value through use of the Koopmanoperator are discussed, particularly with respect to numericalissues encountered using explicit forward propagation of thestate probability density. A series of numerical examples high-light these computational advantages and illustrate the benefitof using this adjoint approach in solution to a range of optimalcontrol problems in the presence of uncertainty.

Keywords: Biological systems, Quantized systems
Abstract: Layered control architectures in biology and neuroscience can be used to mitigate speed-accuracy tradeoffs, with low-layer quantized controllers carrying out time-sensitive tasks at reduced precision. Here, we describe and optimize the worst-case approximation loss for a quantized controller: the maximum control and state costs paid in the quantized case that would not be paid in the full-precision case. We show that the optimal design of a quantizer depends on the dynamics and the state and control costs, leading notably to cases in which systematically biased estimates of state are optimal for control. We further show that high-layer input can direct a low-layer controller to flexibly execute quantized control across context-related cost functions, with component-level mechanisms that are plausibly implementable in biological settings.

Keywords: Mechatronics, Observers for Linear systems, Quantized systems
Abstract: Disturbance observer-based motion control, one of effective schemes for force control and uncertainty compensation has been widely used in industrial systems such as manipulators and servo systems. Despite its effectiveness reported in the literature, security measures applicable to industrial equipment and motion control systems have not yet been established in comparison to those to information equipment. A lack of cybersecurity measures may result in critical incidents in the future. This study proposes a method to enhance the cybersecurity of an integral-type servo controller with a full-order state observer, or disturbance observer, for an industrial motion control system based on controller encryption. Feasibility of the controller encryption method was confirmed through position servo control experiments with a feed drive testbed. Influences on computational latency for real-time control were examined by varying the size of the key used for encryption. Performance degradation of the proposed encrypted control systems was millimeter order, and thus the controller encryption method can be applied as a security measure in motion control systems.

Keywords: Iterative learning control, Learning, Mechatronics
Abstract: Equidistant sampling in control system may lead to quantization errors for certain measurement equipment, e.g., encoders. The aim of this paper is to develop an Iterative Learning Control (ILC) framework that eliminates quantization by exploiting time stamping. The developed ILC framework employs the non-equidistant time stamps in a linear time-varying (LTV) approach. Since the data at the time-stamps does not suffer from quantization, unparalleled performance can be achieved, while the intersample behaviour is bounded by definition. A simulation example confirms superiority of the ILC framework which employs time stamping.

Keywords: Estimation, Quantized systems, Identification
Abstract: The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a novel linear programming approach, which is effective to tackle this problem. In particular, we prove theoretical guarantees of robustness, and we present numerical results that show improved performance with respect to the state-of-the-art methods.

Keywords: Hybrid systems, Modeling
Abstract: In this paper, we define solutions for hybrid systems with pre-specified hybrid inputs. Unlike previous work where solutions and inputs are assumed to be defined on the same domain a priori, we consider the case where intervals of flow and jump times of the input are not necessarily synchronized with those of the state trajectory. The proposed approach relies on reparametrizing the jumps of the input in order to write it on a common domain. The solutions then consist of a pair made of the state trajectory and the reparametrized input. Our definition generalizes the notions of solutions of continuous and discrete systems with inputs. We provide an algorithm that automatically performs the construction of solutions for a given hybrid input. Examples illustrate the notions and algorithm.

Keywords: Hybrid systems, Formal verification/synthesis, Lyapunov methods
Abstract: In this paper, we consider the problem of symbolic models design for the class of incrementally stable singularly perturbed hybrid affine systems. Contrarily to the existing results in the literature where only switching are taken into account, here we consider a more general class of hybrid systems including switches, impulsions and dynamics evolving in different timescales. Firstly, a discussion about incremental stability of the considered class of systems is given. Secondly, a new method for designing symbolic models for incrementally stable singularly perturbed hybrid affine systems is proposed. Inspired from singularly perturbed techniques based on decoupling the slow dynamics from the fast ones, the obtained symbolic abstraction is designed by discretizing only a part of the state space representing the slow dynamics. An e-approximate bisimulation relation between the original singularly perturbed hybrid affine system and the symbolic model obtained by discretizing the slow dynamics is provided. Indeed, since the discrete abstraction is designed for a system of lower dimension, the number of its transitions is drastically reduced. Finally, an example is proposed in order to illustrate the efficiency of the proposed results.

Keywords: Adaptive control, Decentralized control, Uncertain systems
Abstract: We present a decentralized adaptive harmonic control, which is effective for rejection of sinusoidal disturbances of known frequencies that act on a completely unknown asymptotically-stable linear time-invariant system. The decentralized control architecture consists of multi-input multi-output subsystems, where each local controller does not have access to any information regarding the system or the nonlocal measurements. We analyze stability and performance properties of the closed-loop for multi-input multi-output subsystems. We show that the decentralized control rejects sinusoidal disturbances asymptotically. We also demonstrate the effectiveness of the controller through numerical simulations.

Keywords: Adaptive control, Direct adaptive control, Delay systems
Abstract: In this paper the output adaptive tracking problem for the class of multi input multi output (MIMO) linear time-invariant plants with known parameters, unmeasurable state and known multiple input delay is considered. The reference signals for each output are represented by multi-sinusoidal functions generated by autonomous linear dynamical system of known order but with unknown parameters. The amplitudes, phase shifts and frequencies of harmonics of these functions are unknown. Two different solutions of the problem are proposed and based on modified augmented error scheme that removes the delays from adaptation loop. The first solution uses standard gradient adaptation algorithm providing convergence properties of the closed-loop system and has relatively slow transients, while the second one uses adaptation algorithm with the regressor recording (and hence “memory” of regressor) and dramatically improved parametric convergence. The algorithms can be applied for arbitrary input delays without loss of stability. The designed adaptive control law ensures boundness of all signals in the closed-loop system and drives tracking error to zero. Besides, the controls are free from requirement of identification of the reference model parameters.

Keywords: Output regulation, Switched systems, Adaptive control
Abstract: We consider the problem of rejection of a sinu- soidal disturbance of unknown frequency, phase and magnitude acting on an uncertain internally stable SISO linear system. We present a solution that extends our previous work on adaptive feedforward control of uncertain systems by disposing of the need to know the frequency of the harmonic disturbance. The proposed methodology reposes upon a switching-based combination of an adaptive feedforward control algorithm and a deadbeat frequency estimator. The method accounts for the presence of bounded sensor noise as well as imprecise frequency estimation; it is shown that the regulation error is bounded by a function of the norm of the noise that depends on the choice of the controller and the estimator gains.

Keywords: Adaptive control, Uncertain systems, Linear systems
Abstract: This paper focuses on designing an adaptive controller for unknown minimum-phase LTI systems with known relative degree and system order. The controller objective is to reject the unknown, unmatched sinusoidal disturbances and make the output track a given trajectory with the output feedback. The controller design procedure is composed of three steps: disturbance parametrization, K-filter technique and adaptive backstepping. Firstly, the K-filter approach is employed to redefine the system states. Then, parametrization technique is used for the representation of the disturbance information in the output signal. In this way, the problem is converted to an adaptive control problem. After that, an adaptive output feedback controller is designed using a backstepping approach. It is proven that the equilibrium at the origin is globally stable and the output signal tracks the reference signal asymptotically. Finally, the performance of the controller is validated with a numerical simulation.

Keywords: Output regulation, Adaptive control, Uncertain systems
Abstract: This paper proposes an extremum-seeking regulator design based on a Lie bracket averaging technique for nonlinear systems in the presence of unknown disturbance dynamics. The approach adopts a post-processing output regulation method for the regulation of nonlinear systems to the unknown minimum of a measured objective function. The stability analysis demonstrates that one can achieve practical output regulation of the unknown optimum equilibrium. A simulation study demonstrates the ability of the proposed technique to solve general output regulation problems in the absence of exact knowledge of the process dynamics, disturbance dynamics and a corresponding internal model.

Keywords: Robust adaptive control, Output regulation, Robust control
Abstract: In this paper we consider controller design for robust output tracking and disturbance rejection for linear distributed parameter systems. In output regulation the frequencies of the reference and disturbance signals are typically assumed to be known in advance. In this paper we propose a new control design for robust output regulation for signals with unknown frequencies. Our controller is based on a time-dependent internal model where the frequencies are updated based on an adaptive estimator. We use the main results to design a controller for output tracking of an electromagnetic system which models magnetic drug delivery.

Keywords: Stability of nonlinear systems, Robotics, Mechanical systems/robotics
Abstract: A quadrotor with a point-mass payload suspended with an offset from the center-of-mass of the quadrotor to the suspension point is studied in this paper. This system consists of eight degrees of freedom and four degrees of underactuation. A coordinate-free dynamic model is obtained by taking variations on manifolds. We also establish that under a mild assumption that the angular acceleration of quadrotor is small, the offset quadrotor-load system is a differentially-flat system with the load position and the quadrotor yaw serving as the flat outputs. A nonlinear geometric control design based on this assumption is developed. With this controller, the following states (a) quadrotor attitude, (b) load attitude, and (c) load position can be tracked. Stability proofs for the controller design, as well as simulation of the proposed controller are presented. A comparison of a geometric controller developed for a zero offset quadrotor-load model is also presented to motivate the need as well as demonstrate the advantages of our proposed geometric controller for the offset quadrotor-load model.

Keywords: Stability of nonlinear systems, Stochastic systems, Switched systems
Abstract: In this paper, stability analysis of deterministic and stochastic nonlinear discrete-time dynamical systems is considered. It is shown that some difficulties, such as independency or identical distribution of random variable sequence, that may arise in using Lyapunov's and LaSalle's approaches for stability analysis of discrete-time stochastic systems may be overcome by means of fixed point theory. Furthermore, suitable definitions of stability are provided. Ultimately, numerical examples are given in order to show the results.

Keywords: Stability of nonlinear systems, Switched systems, Biologically-inspired methods
Abstract: Motivated by the problem of developing a system that can switch between low-level control vector fields, we study the feedback interconnection of a decision mechanism based on the pitchfork bifurcation with a plant whose dynamics are given by the linear combination of two control vector fields; the state of the pitchfork system then determines the linear combination coefficients for the plant. We show how the plant state can be fed back to the pitchfork by using the Lyapunov functions of the control vector fields as an unfolding parameter in the pitchfork, and derive conditions under which the closed-loop system exhibits a Hopf bifurcation leading to stable limit cycles.

Keywords: Stability of nonlinear systems, Switched systems, Mechatronics
Abstract: In this paper, the use of quasi-linear tools for the closed-loop design and analysis of Hybrid Integrator-Gain Systems (HIGS) is considered. A nonlinear motion control design procedure is proposed in which quasi-linear loop-shaping methods, based on describing functions, are combined with rigorous conditions for closed-loop stability. The latter are established by means of multiple piecewise quadratic Lyapunov functions. Admissible functions are found by solving a set of numerically tractable linear matrix inequalities (LMIs). The potential of the robust design method is illustrated by simulation results of a two-mass-spring-damper system.

Keywords: Stability of nonlinear systems
Abstract: In this paper, we develop partial dissipativity theory for nonlinear dynamical systems using basic input-output and state properties. Specifically, partial dissipativity is characterized using both an input-output as well as a state dissipation inequality involving a partial storage function that is nonnegative definite with respect to part of the system state. The results are then used to derive Kalman-Yakubovich-Popov conditions for characterizing necessary and sufficient conditions for partial dissipativity of nonlinear dynamical systems using continuously differentiable partial storage functions that are nonnegative definite with respect to part of the systems state. In addition, feedback interconnection partial stability results for nonlinear dynamical systems are developed thereby providing a generalization of the small gain and positivity theorems for guaranteeing partial stability of feedback systems.

Keywords: Mechanical systems/robotics, Aerospace, Stability of nonlinear systems
Abstract: A singularity-free nonlinear hierarchical control framework is proposed in this paper for control of a quad rotorcraft unmanned aerial vehicle (UAV). A saturation con- trol scheme with hyperbolic tangent function is designed for the position loop controller to ensure non-singular command attitude extraction and the effect of nonlinear coupling between the position and attitude subsystem is subsequently analyzed. The problem of sign-ambiguity commonly appears in reference attitude is overcome using arc tangent function by considering the signs of both the arguments. To obviate the problem of singularity during attitude tracking, a non-singular attitude loop controller using barrier Lyapunov function (BLF) with corresponding initial condition constraint is proposed. A rigorous stability analysis proves that the overall closed-loop system is asymptotically stable (AS) and all the signals are bounded in the cascaded control structure. The singularity-free hierarchical control development and its stability analysis exploits the full state space Euler-Lagrange under-actuated dynamics in terms of generalized coordinates with generalized force and torque collocated with generalized velocities. Simulation results show the performance of the proposed controller.

Keywords: Uncertain systems, Robust control, Lyapunov methods
Abstract: The recently developed notion of "prescribed-time" stabilization considers regulation of the state to the origin in a prescribed time interval (specified by the control designer) irrespective of the initial state. While prior results on prescribed-time stabilization considered systems in a normal form structure (chain of integrators with uncertainties matched with the control input), we address here a general strict-feedback-like system structure with uncertain nonlinear functions throughout the system dynamics and develop a prescribed-time stabilizing controller based on our dynamic high gain scaling technique along with a novel temporal transformation and scaling dynamics with temporal forcing terms.

Keywords: Uncertain systems, Robust control, LMIs
Abstract: This paper extends the dissipativity-based framework for robustness analysis using integral quadratic constraints (IQCs) to the class of uncertain distributed systems. We consider linear time-varying subsystems interconnected over finite arbitrary directed graphs, where each subsystem is affected by an uncertainty operator described using an IQC, and the interconnections between the subsystems are represented using spatial states. The effectiveness of the proposed framework is demonstrated using an illustrative example.

Keywords: Uncertain systems, Robust adaptive control, Lyapunov methods
Abstract: In this study, we consider the stabilization of a class of cascaded nonlinear systems in strict feedback form with unknown dynamics and known relative order. The stabilization of the unknown system is achieved by a cascaded feedback design procedure that uses a backstepping-like approach. The unknown system functions are estimated using a phasor estimation approach using a single sinusoidal perturbation. The stability analysis shows the semi-global practical stability of the closed loop system and the practical convergence of the entire system to the origin. A simulation example demonstrates the effectiveness of the proposed technique.

Keywords: Uncertain systems, Stability of linear systems, Computational methods
Abstract: In this paper, new mu-based algorithms are proposed in the field of probabilistic robustness analysis. The objective is to compute tight bounds on the probability for a parametrically uncertain and possibly high order system to meet some stability and performance criteria. In this approach, uncertain parameters are treated as random variables with given probability distributions. Internal stability is treated first and Hinf performance in the scalar case is considered next. The main contribution is to provide tight bounds on the probability measure in the latter case. The proposed algorithms are based on branch-and-bound techniques and tested on several benchmarks from the literature, demonstrating their efficiency and the potential of the probabilistic setting in reducing the conservatism of μ-analysis. They have been integrated in the SMART Robustness Analysis Library of the SMAC Toolbox developed by ONERA (http://w3.onera.fr/smac).

Keywords: Uncertain systems, Stochastic systems
Abstract: We analyze the observability of a dynamical sys- tem when each sensor is subject to random failure. In particular, we model the fact that each sensor may fail independently of the other and this failure is assumed to be a Bernoulli random variable with known parameter. We leverage results from random matrix theory to obtain probabilistic bounds on three metrics of observability, viz. the (negative of) maximum eigenvalue, the minimum eigenvalue and the (negative of) trace of the inverse of the observability Gramian. The goal is to perform sensor selection to maximize the expected value of the metric, which we show becomes equivalent to optimizing the metric evaluated over the expected value of the Gramian, with a known probability. A greedy algorithm is then used to perform the selection for which we characterize the factor of sub-optimality relative to the optimal corresponding to each metric. For a specific class of systems, the analytic bounds are reasonable for the extreme eigenvalues, but can be very conservative for the trace of the inverse Gramian.

Keywords: Algebraic/geometric methods, Lyapunov methods, Uncertain systems
Abstract: As modern engineering systems grow in complexity, attitudes toward a modular design approach become increasingly more favorable. A key challenge to a modular design approach is the certification of robust stability under uncertainties in the rest of the network. In this paper, we consider the problem of identifying the parametric region, which guarantees stability of the connected module in the robust sense under uncertainties. We derive the conditions under which the robust stability of the connected module is guaranteed for some values of the design parameters, and present a sum-of-squares (SOS) optimization-based algorithm to identify such a parametric region for polynomial systems. Using the example of an inverter-based microgrid, we show how this parametric region changes with variations in the level of uncertainties in the network.

Keywords: Mechanical systems/robotics, Constrained control, Robust control
Abstract: Simultaneous Localization and Mapping (SLAM)system equipped quadrotors are preferable candidates for autonomous building inspections and surveillance tasks, because of their mobility and capability of working in both indoor and outdoor environments. However, the lack of robustness still remains as one of the challenging problems of SLAM implementations. Sudden camera moving, motion blur, occlusion all might cause a pose lost and map corruption. This problem becomes significant when the SLAM system is mounted on a quadrotor, since the high agility of the quadrotor might lead to a wide camera motion. Therefore, a control strategy that can constrain the quadrotor motion angles is proposed in this paper. A bounded design is embedded into the existing uncertainty and disturbance estimator (UDE) control framework, which can regulate the motion angles, e.g., roll and pitch angles of the quadrotor, always within predefined appropriate ranges. The proposed control strategy eliminates the sudden camera motion and provides a suitable platform for SLAM. Finally, experimental studies are provided for validation.

Keywords: Modeling, Reduced order modeling, Mechanical systems/robotics
Abstract: The transfer matrix method (TMM) is a powerful modeling approach with unique strengths for modeling flexible structures under feedback control. The TMM can model distributed parameter systems without special discretization, ensuring that the models are protected against model spillover. Feedback and actuator dynamics can be directly included in the structural model, leading to accurate models of actuator/structure interaction. The TMM can produce closed-form symbolic expressions for the infinite-dimensional closed-loop transfer functions of distributed parameter systems under feedback control. These infinite-dimensional transfer functions can be used directly for compensator design via Bode plots. However, if modern state-space control design tools are to be applied to a flexible structure model with the TMM, the TMM model must first be discretized.

The infinite-dimensional nature of TMM models and the fact that they involve transcendental expressions in the Laplace variable s make it difficult to apply most of the model reduction procedures in the literature. This paper presents a technique for discretizing TMM models that is an improvement upon one discretization technique from the literature that is specific to the TMM.

Keywords: Mechanical systems/robotics, Filtering, Optimization algorithms
Abstract: In this paper, an approach is proposed to achieve simultaneous imaging and broadband nanomechanical mapping of heterogeneous soft materials in air using atomic force microscope (AFM). Simultaneous imaging and mechanical mapping (SIMM) is developed to, for example, correlate morphological and mechanical evolutions of the samples together. Current methods to SIMM, however, are limited to frequency region(s) that is(are) much higher than that of interests for most soft polymers and biological samples. Such a limitation has been addressed in the recently-developed simultaneous imaging and broadband nanomechanical mapping (SIBNM) technique for materials of relatively small mechanical spatial variations. We propose, in this work, to extend the SIBNM technique to heterogeneous materials. Firstly, a gradient-based adaptive Kalman filter algorithm is proposed to decouple and split the deflection signal into the response to topography variations and the indentation-caused response, respectively. Then, a compressed-sensing-based mechanical property recovery method is introduced to adaptively tune the gain of adaptive Kalman filter. Experiment results show that both topography imaging and qualitative broadband mechanical mapping of heterogeneous soft samples can be reliably quantified by using the proposed technique.

Keywords: Mechanical systems/robotics, Optimization
Abstract: An efficient suboptimal semi-active control for mitigating structural vibration is studied. The control relies on a practical state-feedback switching law and, as demonstrated in the previous research, it guarantees the asymptotic stability. The focus of this work is to provide the qualitative and quantitative analysis on the control's optimality in the sense of an energy-related performance index. Firstly, a method for optimal selection of the passive strategy that underlies a design of the control's switching law is proposed. Next, the conditions asserting the performance of the semi-active control are formulated and proven. Finally, the controller's performance is validated by numerical experiments involving a 2DOF semi-active structure, where the suboptimal control is compared to the optimal open-loop solution and a heuristic strategy.

Keywords: Mechanical systems/robotics
Abstract: One of the challenges for redundant robotic manipulators is generating a trajectory that goes from an initial configuration to a task configuration. Often, the resolution of kinematic redundancy in trajectory generation problems is accomplished by adding a constraint, or by subjecting the motion to a cost function and searching for an optimal solution. This paper investigates the remote center of motion (RCM) constraint, which specifies an insertion point that a link can rotate about and translate into, but not deviate from. Using the RCM constraint, this paper theoretically and experimentally demonstrates how to create trajectories that enable a KUKA LBR iiwa 7 R800 robotic serial-link manipulator to insert several links into a single-entrance enclosure. Both a Jacobian-based and an optimization-based trajectory generation method are explored by physical demonstration. The maximum positional RCM errors were 1.2 mm and 0.9 mm respectively. The small positional error suggests that both methods are capable of generating trajectories for redundant manipulators that accomplish a task requiring both RCM constraint adherence and multiple link insertions.

Keywords: Sensor fusion, Estimation, Mechanical systems/robotics
Abstract: This paper presents a method to calibrate the extrinsic parameters of LIDARs mounted on a Bucket Wheel Reclaimer (BWR). BWR’s are widely used for stacking and reclaiming bulk materials in stockyards. Current BWR systems are either manually operated, remotely operated or semi-automated using the real-time point cloud data generated by one or more LIDARs. Accurate calibration is of crucial importance as the accuracy of the Earth frame point cloud data depends on it. Automated calibration is also a pre-requisite for fully autonomous BWR control. Calibration of BWR systems are more difficult than many other LIDAR systems because of their limited pose variation capabilities and the environmental constraints of stockyards. This paper analyzes the problem, presents observability conditions, presents a method to estimate the calibration parameters and discusses the challenges involved with BWR systems. The results demonstrate subdecimeter accuracy.

Keywords: Kalman filtering, Model Validation, Estimation
Abstract: Estimation of state of charge (SOC) is imperative in the battery management system that ensures safe and reliable operations. Lithium iron phosphate cells are preferred for high power applications because of their electrochemical and thermal stability. On the other hand, these cells are characterized by voltage plateau and path dependence, which impede the accurate estimation of SOC. In this work, a new method is proposed to estimate the SOC using a physics-based reduced order model (ROM), where the two-phase transition of cathode is modeled and validated. In addition, an extended Kalman filter (EKF) is used to minimize the estimation errors of the SOC caused by the inaccuracy of the ROM or the initial errors. The insensitivity of voltage at the plateau is further compensated by combining Coulomb counting. This method is then validated against experimental data obtained with different C-rates at both single and multiple cycles. The effect of EKF on SOC estimation is also analyzed. The results show that the absolute SOC error is kept less than 3% for all the tested conditions.

Keywords: Kalman filtering, Sensor fusion, Estimation
Abstract: This paper considers sliding window filtering in an invariant framework for estimation of attitude and rate gyro bias in a matrix Lie group formulation. The multiplicative extended Kalman filter (MEKF) and invariant extended Kalman filter (IEKF), variants of the extended Kalman filter well suited to estimation on matrix Lie groups, are discussed. The sliding window formulation of both the MEKF and IEKF is presented, leading to the sliding window filter (SWF), the invariant SWF (ISWF), and the imperfect ISWF for systems that are not group affine. Simulation results for an attitude and heading reference system with bias are presented, comparing the ISWF to the traditional SWF, MEKF, and IEKF.

Keywords: Kalman filtering
Abstract: This paper presents an application of the continuous-discrete Kalman filter to the dynamics of a section of the convection pass of a once-through power boiler. The approach uses a high fidelity model of the plant's thermal and fluid mechanics in Flownex to generate simulated plant measurement data. A simpler, lumped parameter model is developed in Matlab (independent from this simulation) around which the state estimator is built. Based on measurements available at the system boundary, the estimator allows insight into the internal states of the physical system from which the presence of fouling can be detected. Furthermore, correct modelling of state- and measurement-noise, critical to the set-up of a Kalman filter, is shown.

Keywords: Smart grid, Power systems, Kalman filtering
Abstract: A passive, inverter-centric method for islanding detection using multiple-model filtering (MMF) is presented in the presence of multiple photovoltaic inverters (PVIs). Islanding is the situation that parts of power distribution circuits are disconnected from the grid by switches for protection from the effects of faults while the disconnected circuits are still being energized by active sources, including solar PVIs. The purpose of the MMF-based islanding detection is to timely inform a behind-the-meter grid-connected PVI whether to trip itself offline or to stay grid-connected with minimum communications. Detection filters are built based on all anticipated circuit models corresponding to switch states observable by the PVI, and a weighted local measurement residuals is used to obtain model probabilities. An autocovariance least-squares method is adopted to estimate the process and measurement noise covariance matrices of each filter design model. Two scenarios are detailed for a modified Roy Billinton Test System (RBTS): i) multiple PVIs are located along the same radial circuit (feeder), and ii) multiple PVIs are located at different feeders. The minimum communication requirements among the PVIs are determined for successful islanding detection.

Keywords: Sensor fusion, Robotics, Kalman filtering
Abstract: Water pipe leakage is a common and significant problem around the world. In recent years, an increasing amount of effort has been put into developing effective leak detection solutions for water pipes. Among them, the pressure gradient based method developed at the Massachusetts Institute of Technology excels for its sensitivity in low pressure, small diameter pipes. It can also work in both plastic and metallic pipes. However, in order for leaks detected to be fixed, one must also know the locations of the leaks. In addition, sensing the robot's location via GPS or remote sensors requires greater power and relies on certain ground properties. Thus this paper sets out to localize the robot using only the on board sensors which are an IMU, gyro, and the leak sensors. Through pipe joint measurement and the extended Kalman filter simulations show the tracking error is about 0.5% of the total distance of the robotic inspection. With a minimal number of additional leak sensors added, a complementary method was developed to function in more heavily tuberculated pipes.

Keywords: Uncertain systems, Distributed parameter systems, Linear systems
Abstract: Recently, a new type of evolution equations for measures, called Measure Differential Equations (briefly MDE), was introduced, based on the concept of Probability Vector Field. The latter is a map associating to a probability measure on a manifold a probability measure on the tangent bundle, whose projection on the base is the original measure. Such approach allows the modeling of finite-speed diffusion, thus provides a new approach to uncertainty for differential equations. After showing some explicit examples of modeling uncertainty with finite-speed diffusion, the theory of MDEs is extended to the time-varying case. This allows the application to control systems, including basic results on disturbance rejection.

Keywords: Flexible structures, Modeling, Biological systems
Abstract: In this work a one dimensional micro air vehicle model with flexible wings incorporating spatial hysteresis internal damping is analyzed. The control initial value problem is shown to be well-posed and the first order system operator of the linearized system is shown to generate a strongly continuous contraction semigroup. The importance of a theoretical foundation is generally understated in science and this work provides any numerical results from this model with a rigorous foundation. The theoretical analysis of control design for the model in this work provided motivation for and makes use of a recently published inequality that is easy to understand yet was quite non-trivial to prove.

Keywords: Distributed parameter systems, Delay systems, Stability of linear systems
Abstract: We propose a controller design for a system composed of two sets of linear heterodirectional hyperbolic PDEs, with actuation at one boundary, and coupled at the other boundary by ODEs in a PDE-ODE-PDE configuration. The design approach employs a backstepping transformation, however, the under-actuation limits the choice of target system. To deal with this limitation, we propose to use stability results from delay systems to find a stable target system. Furthermore, we propose to use a high-pass filter of the proximal reflection, in place of cancellation, to obtain controllers that are robust to small delays.

Keywords: Distributed parameter systems, Control of metal processing, Optimal control
Abstract: An optimal control approach for minimizing metallurgical length deviation during casting speed increase under constraints on the secondary cooling flow rates for continuous steel casting process is proposed. The process is described as a single-phase Stefan problem. The temperature and the shell growth are controlled by the steel surface heat flux generated by the cooling sprays. A cost function reflecting the error in tracking of a reference shell thickness is chosen, and the control objective is formulated as the minimization of this cost function under the spray rate constraints. Finding the control law satisfying this objective is formulated as a two-step procedure. First, an analytical setting for the cost function minimization is established through deriving the corresponding direct, adjoint, and sensitivity systems. Then, a computational procedure for solving this analytical setting, which finds the actual control law, is given. A numerical example presents the application of the method proposed. The results are then extended to a 2D model, with the corresponding numerical example provided.

Keywords: Distributed parameter systems, Linear systems, Fluid flow systems
Abstract: We utilize control-theoretic tools to study the receptivity of pre-transitional boundary layers to persistent stochastic excitation sources. White-in-time stochastic excitation is used to model the effect of free-stream turbulence on the linearized Navier-Stokes dynamics. We discuss similarities and differences resulting from local and global approaches in terms of steady-state energy amplification of velocity fluctuations and the underlying flow structures. While parallel flow analysis predicts a flow response that is dominated by the principal eigenmode of the covariance matrix, we show that global analysis yields subordinate eigenmodes that have nearly equal energetic contributions to that of the principal mode. We investigate this observation and provide a possible explanation for the disparity between the results of local and global receptivity analysis in spatially evolving flows.

Keywords: Distributed parameter systems
Abstract: This work considers disaster management from a system theoretic framework. Assuming that disasters result in spatiotemporally varying fields, such as hazardous plumes that are harmful to humans and equipment, it proposes a three-step approach to disaster management: (i) detection of the presence of a disaster, (ii), reconstruction of the effects of the disaster and (iii) adaptive evacuation in terms of active path planning using information on the effects of the disaster. The second step is considered here and an integrated design for the reconstruction of the state of the spatiotemporally varying field, as described by advection-diffusion PDE, with a mobile sensor is proposed. The mobile sensor has tolerance limits on the measurements, beyond of which ceases to operate. A modification to the sensor guidance is proposed and which initially moves the sensor using a gradient ascent policy. The guidance policy switches to a gradient descent policy whenever the measurements are within a percentage of the tolerance limit ensuring the life prolongation of the sensor. Simulation studies for a 2D advection-diffusion PDE are included to demonstrate the effects of modified guidance on life extension of a sensor.

Keywords: Stochastic optimal control, Game theory, Stochastic systems
Abstract: In this paper, we study the design of a stochastic predictive controller based on discrete-time mean-field-type games (MFTG-SPC) involving an arbitrary number of decision makers. We consider a dynamical system described by a stochastic difference equation that includes mean-field terms, e.g., the expected value for both the system state and control inputs. In addition, the cost function incorporates the mean and variance of both system state and control inputs. We provide a semi-explicit solution for the optimization problem that is behind the predictive controller. Finally, we present some simulations over a microgrid application consisting of the energy storage problem.

Keywords: Smart grid, Energy systems, Decentralized control
Abstract: In this paper, we propose a decentralized model predictive control (MPC) method as the energy management strategy for a large-scale electrical power network with distributed generation and storage units. The main idea of the method is to periodically repartition the electrical power network into a group of self-sufficient interconnected microgrids. In this regard, a distributed graph-based partitioning algorithm is proposed. Having a group of self-sufficient microgrids allows the decomposition of the centralized dynamic economic dispatch problem into local economic dispatch problems for the microgrids. In the overall scheme, each microgrid must cooperate with its neighbors to perform repartitioning periodically and solve a decentralized MPC-based optimization problem at each time instant. In comparison to the approaches based on distributed optimization, the proposed scheme requires less intensive communication since the microgrids do not need to communicate at each time instant, at the cost of suboptimality of the solutions. The performance of the proposed scheme is shown by means of numerical simulations with a well-known benchmark case.

Keywords: Manufacturing systems, Energy systems, Optimal control
Abstract: In this paper, a control scheme for both reducing the electric power consumption and minimizing power peaks during the operation of machine tools without effecting its throughput is proposed. The controller is designed to only manage peripheral devices without modifying the machining processes and the cycle time of the machine tool. Based on a test bench to emulate the energy consumption of a machine tool, a real data set is used to obtain models of electric power consumption by using data-driven model techniques such as subspace identification. Then, an optimization-based controller is designed considering both power consumption models and operating constraints of peripheral devices. The proposed controller is tested for both nominal and disturbed cases, i.e., with and without disturbances/uncertainties, achieving reductions up to 15% in the power peaks with respect to other control systems usually implemented for such systems. From this approach, both energy cost and economical penalties by overloads could be reduced and the energy efficiency of these machines can be improved.

Keywords: Distributed control, Predictive control for linear systems, Network analysis and control
Abstract: In this paper, a method typically used in economics is applied to distributed decision-making problems solved by model predictive control. The main purpose is to analyze the changes in certain aggregate indicators under study, which are decomposed among a number of factors. In particular, the logarithmic mean divisia index (LMDI) method is used to study how controllers contribute to the performance and how disturbances are generated. Finally, a flow network, which is a system structure that appears in many real problems such as power grids, is used as an academic case study to illustrate the proposed method.

Keywords: Smart grid, Control applications, Networked control systems
Abstract: We consider enhancing cyber security in voltage regulation of distribution systems in the presence of malicious attacks. Due to the increase in distributed generation, the regulation of voltage has become more complicated, requiring more sensor data to be used for control. Recently, we have developed an attack detection algorithm to find data falsification attacks on voltage measurements transmitted by sectionizing switches in the feeders to a centralized controller. In this paper, the security level of the system is further improved by introducing a controller that is capable of operating the regulation in the presence of attacks by utilizing the detection results. In particular, it identifies abnormal behavior in the sensor data and ignores measurements taking extreme values among those received. Through detailed simulation studies on a small scale distribution system, we show the effectiveness of the proposed control and analyze the relation between the number of attacks and the detectability of the attacks.