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As we move to increasingly complex cyber–physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal control problems for a class of CPS with nonlinear dynamics. We exploit the property of differential flatness to simplify the Euler–Lagrange equations that arise during optimization, and this simplification eliminates the numerical instabilities that plague optimal control in general. We also present an explicit differential equation that describes the evolution of the optimal state trajectory, and we extend our results to consider both the unconstrained and constrained cases. Furthermore, we demonstrate the performance of our approach by generating the optimal trajectory for a planar manipulator with two revolute joints. We show in simulation that our approach is able to generate the constrained optimal trajectory in 4. 5 ms while respecting workspace constraints and switching between a 'left' and 'right' bend in the elbow joint. [ABSTRACT FROM AUTHOR]

This paper uses the mirror descent algorithm with periodic dynamic quantization to solve constrained distributed optimization problems with limited communication channels. Due to the imperfect network environment, obtaining accurate information is impractical, and thus a communication scheme under quantization needs to be considered. A periodic dynamic quantizer with finite quantization levels is proposed in this paper to achieve exact optimization. Moreover, a time-varying control parameter in the mirror descent algorithm is designed to control the quantization error. After a comprehensive analysis, the proposed algorithm can obtain an optimal value, and the optimal convergence rate is O (1 / T 0. 25). [ABSTRACT FROM AUTHOR]

In this work, the constrained optimization problem is studied, where the global objective function is the sum of N convex functions and a closed convex set constraint is involved. The aim of this work is to design distributed optimization algorithms with linear convergence rate over time-varying unbalanced graphs for solving the studied problem. Towards this end, the Push-DIGing based accelerated distributed constrained optimization algorithm (PDADCO) and the Push-Pull based accelerated distributed constrained optimization algorithm (PPADCO) are developed. Specially, during the algorithm developments, the method of feasible direction, which can be successfully integrated into the Push-DIGing framework and the Push-Pull framework, is newly introduced to deal with the involved closed convex set constraint. Furthermore, based on the small gain theorem, the linear convergence properties of both the PDADCO and the PPADCO are rigorously established, with the feasible regions of the step-sizes being given. Finally, a simulation example is provided to verify the effectiveness of the established theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a randomized parallel algorithm is proposed to solve the distributed optimal consensus problem of multi-agent systems. Involving both the transient response and the final consensus state, the problem is described as a constrained non-separable optimization problem. Inspired by the randomized Jacobi proximal alternating direction method of multipliers, the proposed algorithm makes it possible for only a fraction of agents to solve their private subproblems in parallel at each iteration, which greatly saves computational resources and enhances running efficiency. The convergence analysis of the algorithm gives fully distributed convergence conditions. A trade-off between the convergence speed and resource savings is then obtained, where the convergence rate is estimated to be at least O 1 t . Furthermore, the algorithm can be accelerated to enjoy a convergence rate of O 1 t 2 by adaptively adjusting the auxiliary parameters properly. Numerical simulations demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a constrained distributed optimization problem for multi-integrator agent systems with mixed neighbor interactions, where the neighbors of the agents can be classified as cooperative or noncooperative by introducing a cooperation-competition network into the modeling of the communication graph. The agent's goal is to optimize the total objective function of the cooperators. Since agents can only communicate with their neighbors, they are unable to obtain complete information about cooperators. The distributed optimization algorithm is proposed to classify cooperative subnetworks by introducing additional auxiliary variables, and the outputs of all agents exponentially converge to the optimal solution of the optimization problem under the condition of satisfying the global equality constraint of the subnetwork. The Lyapunov stability theory is used to analyze the algorithm's convergence. Simulation results show the effectiveness of the proposed algorithm in two examples of economic dispatch in smart grids and optimal area coverage in multi-sensor networks. [ABSTRACT FROM AUTHOR]

State-space models are used in a wide range of time series analysis applications. Kalman filtering and smoothing are work-horse algorithms in these settings. While classic algorithms assume Gaussian errors to simplify estimation, recent advances use a broad range of optimization formulations to allow outlier-robust estimation, as well as constraints to capture prior information. Here we develop methods on state-space models where either transition or error covariances may be singular. These models frequently arise in navigation (e.g. for 'colored noise' models or deterministic integrals) and are ubiquitous in auto-correlated time series models such as ARMA. We reformulate all state-space models (singular as well as nonsingluar) as constrained convex optimization problems, and develop an efficient algorithm for this reformulation. The convergence rate is locally linear , with constants that do not depend on the conditioning of the problem. Numerical comparisons show that the new approach outperforms competing approaches for nonsingular models, including state of the art interior point (IP) methods. IP methods converge at superlinear rates; we expect them to dominate. However, the steep rate of the proposed approach (independent of problem conditioning) combined with cheap iterations wins against IP in a run-time comparison. This suggests that the proposed approach can be a default choice for estimating state space models outside of the Gaussian context for singular and nonsingular models. To highlight the capabilities of the new framework, we focus on navigation applications that use singular process covariance models. The methods have been implemented in an open source Python code. [ABSTRACT FROM AUTHOR]

We introduce a novel approach to reduce the computational effort of solving convex chance constrained programs through the scenario approach. Instead of reducing the number of required scenarios, we directly minimize the computational cost of the scenario program. We exploit the problem structure by efficiently partitioning the constraint function and considering a multiple chance constrained program that gives the same probabilistic guarantees as the original single chance constrained problem. We formulate the problem of finding the optimal partition, a partition achieving the lowest computational cost, as an optimization problem with nonlinear objective and combinatorial constraints. By using submodularity of the support rank of a set of constraints, we propose a polynomial-time algorithm to find suboptimal solutions to this partitioning problem and we give approximation guarantees for special classes of cost metrics. We illustrate that the resulting computational cost savings can be arbitrarily large and demonstrate our approach on a case study from production planning. [ABSTRACT FROM AUTHOR]

There is an increasing trend to apply integrated mechatronic design approaches in precision engineering to synthesize key mechanical and controller parameters simultaneously. However, such technique is yet to be mature, due to the constraints imported by mechanical design and feedback control, as well as the existence of model uncertainties. In this work, we treat the integrated mechatronic design problem as a controller optimization problem with structural constraints. We start from the case when the composite feedback gain matrix (CFGM) has some elements either being zero or with equal or opposite relationships. First, algorithms are proposed to factorize the CFGM. Secondly, the feedback constraints are transformed from the state space to an extended parameter space. In this way, the design problem is reformulated as minimizing the ℋ 2 -norm upper bound of the closed-loop system transmittance from the exogenous disturbance to the regulated variables over the intersection of convex and non-convex domains. Eventually, cutting-plane-based numerical procedures are developed to obtain a global optimal solution, and the closed-loop robust stability is ensured with guaranteed performance. An illustrative example on a flexure-linked biaxial gantry stage is presented to reveal the practical appeal of the proposed approach. This approach is extensively applicable to a class of optimal control problems, such as controller synthesis problem with prescribed sparsity pattern, decentralized control problem with/without structural constraints, etc. [ABSTRACT FROM AUTHOR]

Abstract We propose a novel modeling and control framework for the autonomous excavator with main control valve (MCV), which distributes fluid from pumps to hydraulic actuators with the number of the pumps less than that of the actuators and whose internal hydraulic circuitry switches depending on operating conditions and internal pressures. We first derive the mathematical model of the MCV, including the switching components and supply pump flow constraint. We then design a novel velocity-field control for the bucket position/orientation, which, by relying on a constrained-optimization formulation, can adjust the velocity-field following speed reflecting the physical constraints imposed by the MCV in such a way that the bucket fully follows the desired velocity-field when the constraints are inactive or still preserves the desired direction (or automatic stopping) while slowing down when the constraints become active (e.g. flow saturation). We further show that this optimization can be reduced to simple real-time solvable formulation with its solution existence/optimality (or suboptimality) guaranteed. Simulation is also performed to verify the theory by using a detailed Simulink/Sim-Hydraulics model. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a fully asynchronous and distributed approach for tackling optimization problems in which both the objective function and the constraints may be nonconvex. In the considered network setting each node is active upon triggering of a local timer and has access only to a portion of the objective function and to a subset of the constraints. In the proposed technique, based on the method of multipliers, each node performs, when it wakes up, either a descent step on a local augmented Lagrangian or an ascent step on the local multiplier vector. Nodes realize when to switch from the descent step to the ascent one through an asynchronous distributed logic-AND, which detects when all the nodes have reached a predefined tolerance in the minimization of the augmented Lagrangian. It is shown that the resulting distributed algorithm is equivalent to a block coordinate descent for the minimization of the global augmented Lagrangian. This allows one to extend the properties of the centralized method of multipliers to the considered distributed framework. Two application examples are presented to validate the proposed approach: a distributed source localization problem and the parameter estimation of a neural network. [ABSTRACT FROM AUTHOR]

Abstract This research considers the problem of ranking the top simulated designs in the presence of stochastic constraints. The objective and constraint measures of each design must be estimated via simulation. Given a fixed simulation budget, the ranking of the top feasible designs cannot be determined with certainty. The objective of this research is to derive an efficient simulation budget allocation strategy such that the probability of correct ranking (PCR) can be maximized. To deal with this problem, we propose a lower bound on the PCR and develop an asymptotically optimal allocation rule based on the lower bound. Useful insights on characterizing the allocation rule are provided, and numerical experiments are carried out to demonstrate the efficiency of the suggested simulation procedure. [ABSTRACT FROM AUTHOR]

Abstract Explicit Model Predictive Control often has a complex solution in terms of the number of regions required to define the solution and the corresponding memory requirement to represent the solution in the online implementation. An alternative approach to constrained control is based on the use of controlled contractive sets. However, polytopic controlled contractive sets may themselves be relatively complex, leading to a complex explicit solution, and the polytopic structure can limit the size of the controlled contractive set. This paper develops a method to obtain a larger controlled contractive set by allowing higher order functions in the definition of the contractive set, and explores the use of such higher-order contractive sets in controller design leading to a low complexity explicit control formulation. [ABSTRACT FROM AUTHOR]

This article presents a novel class of control policies for networked control of Lyapunov-stable linear systems with bounded inputs. The control channel is assumed to have i.i.d. Bernoulli packet dropouts and the system is assumed to be affected by additive stochastic noise. Our proposed class of policies is affine in the past dropouts and saturated values of the past disturbances. We further consider a regularization term in a quadratic performance index to promote sparsity in control. We demonstrate how to augment the underlying optimization problem with a constant negative drift constraint to ensure mean-square boundedness of the closed-loop states, yielding a convex quadratic program to be solved periodically online. The states of the closed-loop plant under the receding horizon implementation of the proposed class of policies are mean square bounded for any positive bound on the control and any non-zero probability of successful transmission. [ABSTRACT FROM AUTHOR]

In this paper, a push-sum based distributed delayed dual averaging algorithm (PS-DDDA) is proposed to solve the distributed constrained optimization problem over the time-varying unbalanced directed graph (digraph). It considers the scenario in which each agent has delays while calculating the gradients and communicating. Both delays are assumed to be time-varying but bounded, which are more common in practice. Furthermore, we demonstrate that the cost function at the local state average converges to the optimal value and the local state average converges to the consensus with a rate of O (1 / T ) by utilizing the diminishing step size, where T is the total number of iterations. Moreover, to solve the distributed online constrained optimization problem, we propose the online version of PS-DDDA, and prove that its regret bound increases sublinearly with a rate of O (T). Finally, the effectiveness of the proposed algorithms is corroborated by solving logistic regression problems. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of system identification when frequency domain side-information is available. We mainly consider the case where the side-information is provided as the H ∞ -norm of the system being bounded by a given scalar. This framework allows considering different forms of frequency domain side-information, such as the dissipativity of the system. We propose a nonparametric identification approach for estimating the impulse response of the system under the given side-information. The estimation problem is formulated as a constrained optimization in a stable reproducing kernel Hilbert space, where suitable constraints are considered for incorporating the desired frequency domain features. The resulting optimization has an infinite-dimensional feasible set with an infinite number of constraints. We show that this problem is a well-defined convex program with a unique solution. We propose a heuristic that tightly approximates this unique solution. The proposed approach is equivalent to solving a finite-dimensional convex quadratically constrained quadratic program. The efficiency of the discussed method is verified by several numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we consider a constrained optimization problem for a large-scale multi-cluster agent system, in which a number of clusters already exist as a priori. The aim is to minimize a global objective function being the sum of multi-cluster local agents’ cost functions subject to certain global constraints. To solve this problem, a novel distributed hierarchical algorithm based on projected gradient method is proposed by using synchronous and sequential communication strategies. We firstly assign one agent as leader agent in each cluster, which can communicate with the leaders of its neighboring clusters. The agents in the same cluster conduct local optimization and communicate with their neighboring agents synchronously while the leader agents of different clusters exchange information in a sequential way. Then a scheme is proposed for each agent to iteratively estimate a solution of the optimization problem in a distributed manner. It is theoretically proved that the estimated solutions of all the agents reach consensus of the optimal solution asymptomatically when the chosen stepsizes are diminishing. Numerical examples are provided to validate the proposed method. [ABSTRACT FROM AUTHOR]

The optimization-based stabilization of manifolds for nonlinear dynamical systems with constraints is investigated. Manifolds in the state or output space are considered for which the original system description can be transformed into a so-called transverse normal form. With this formulation, the motion of the system transverse and tangential to the manifold can be separately described. The transverse normal form is combined with a tailored model predictive control scheme to achieve the objectives of stabilizing the manifold, rendering it invariant, and imposing a desired motion on the manifold under due consideration of constraints. Furthermore, the stabilization of the manifold is prioritized over the movement on the manifold. Convergence of the model predictive control scheme is proven. The applicability of the proposed concept is demonstrated by an illustrative simulation example. [ABSTRACT FROM AUTHOR]

We address the optimal dynamic formation problem in mobile leader–follower networks where an optimal formation is generated to maximize a given objective function while continuously preserving connectivity. We show that in a convex mission space, the connectivity constraints can be satisfied by any feasible solution to a mixed integer nonlinear optimization problem. For the class of optimal formation problems where the objective is to maximize coverage, we show that the optimal formation is a tree which can be efficiently constructed without solving a MINLP. In a mission space constrained by obstacles, we separate the formation process into intervals with no obstacles detected and intervals where one or more obstacles are detected. In the latter case, we propose a minimum-effort reconfiguration approach for the formation which still optimizes the objective function while avoiding the obstacles and ensuring connectivity. We include simulation results illustrating this dynamic formation process. [ABSTRACT FROM AUTHOR]

By time discretization of a second-order primal–dual dynamical system with damping α / t where an inertial construction in the sense of Nesterov is needed only for the primal variable, we propose a fast primal–dual algorithm for a linear equality constrained convex optimization problem. Under a suitable scaling condition, we show that the proposed algorithm enjoys a fast convergence rate for the objective residual and the feasibility violation, and the decay rate can reach O (1 / k α − 1) at the most. We also study convergence properties of the corresponding primal–dual dynamical system to better understand the acceleration scheme. Finally, we report numerical experiments to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called pseudo-gradient to guide the updates of the decision variables, which can be applied in the fields where the gradient information is unknown, not available or non-existent. A surplus-based method is adopted to remove the doubly stochastic requirement on the weighting matrix, which enables the implementation of the algorithm in graphs having no associated doubly stochastic weighting matrix. For the convergence results, the proposed algorithm is able to obtain the exact convergence to the optimal value with any positive, non-summable and non-increasing step-sizes. Furthermore, when the step-size is also square-summable, the proposed algorithm is guaranteed to achieve the exact convergence to an optimal solution. In addition to the standard convergence analysis, the convergence rate of the proposed algorithm is also investigated. Finally, the effectiveness of the proposed algorithm is verified through numerical simulations. [ABSTRACT FROM AUTHOR]

This communique presents simple simulation-based algorithms for obtaining an approximately optimal policy in a given finite set in large finite constrained Markov decision processes. The algorithms are adapted from playing strategies for “sleeping experts and bandits” problem and their computational complexities are independent of state and action space sizes if the given policy set is relatively small. We establish convergence of their expected performances to the value of an optimal policy and convergence rates, and also almost-sure convergence to an optimal policy with an exponential rate for the algorithm adapted within the context of sleeping experts. [ABSTRACT FROM AUTHOR]

Most extremum-seeking control (ESC) approaches focus solely on the problem of finding the extremum of some unknown, steady-state input–output map, providing parameter settings that lead to optimal steady-state system performance. However, many industrial applications also have to deal with constraints on operating conditions due to, e.g., actuator limitations, limitations on tunable system parameters, or constraints on measurable variables. In particular, constraints on measurable variables are typically unknown in terms of their relationship with the tunable system parameters. In addition, the constraints on system inputs as a result of the constraints on measurable variables may conflict with the otherwise optimal operational condition, and hence should be taken into account in the data-based optimization approach. In this work, we propose a sampled-data extremum-seeking framework for the constrained optimization of a class of nonlinear dynamical systems with measurable constrained variables. In this framework, barrier function methods are employed, exploiting both the objective function and constraint functions which are available through output measurement only. We show, under the assumption that the parametric initialization yield operating conditions that do not violate the constraints, that (1) the resulting closed-loop dynamics is stable, (2) constraint satisfaction of the inputs is guaranteed for all iterations of the optimization process, and (3) constrained optimization is achieved. We illustrate the working principle of the proposed framework by means of an industrial case study of the constrained optimization of extreme ultraviolet light generation in a laser-produced plasma source within a state-of-the-art lithography system. [ABSTRACT FROM AUTHOR]

This item explains a technical problem in the justification of Theorem 10 in Kenanian et al. (2019). The theorem refers to a result in chance-constrained convex programming, but the hypotheses for applying this result are not satisfied since the optimization problem involved in Theorem 10 is nonconvex. However, under an additional mild assumption on the system, the conclusions of Theorem 10 hold, as shown in this item. [ABSTRACT FROM AUTHOR]

This communique first presents a novel multi-policy improvement method which generates a feasible policy at least as good as any policy in a given set of feasible policies in finite constrained Markov decision processes (CMDPs). A random search algorithm for finding an optimal feasible policy for a given CMDP is derived by properly adapting the improvement method. The algorithm alleviates the major drawback of solving unconstrained MDPs at iterations in the existing value-iteration and policy-iteration type exact algorithms. We establish that the sequence of feasible policies generated by the algorithm converges to an optimal feasible policy with probability one and has a probabilistic exponential convergence rate. [ABSTRACT FROM AUTHOR]

In this note we discuss a novel graph partitioning problem, namely continuous graph partitioning, and we discuss its application to the design of surveillance trajectories for camera networks. In continuous graph partitioning, each edge is partitioned in a continuous fashion between its endpoint vertices, and the objective is to minimize the largest load among the vertices. We show that the continuous graph partitioning problem is convex and non-differentiable, and we characterize a solution amenable to distributed computation. The continuous graph partitioning problem naturally arises in the context of camera networks, where intruders appear at arbitrary locations and times, and the objective is to design camera trajectories for quickest detection of intruders. Finally, we propose a surveillance strategy for networks of PTZ cameras and we characterize its performance. [ABSTRACT FROM AUTHOR]

To further understand the underlying mechanism of various reinforcement learning (RL) algorithms and also to better use the optimization theory to make further progress in RL, many researchers begin to revisit the linear–quadratic regulator (LQR) problem, whose setting is simple and yet captures the characteristics of RL. Inspired by this, this work is concerned with the model-free design of stochastic LQR controller for linear systems subject to Gaussian noises, from the perspective of primal–dual optimization. We first reformulate the stochastic LQR problem as a constrained non-convex optimization problem, which is shown to have strong duality. Then, to solve this non-convex optimization problem, we propose a model-based primal–dual (MB-PD) algorithm based on the properties of the resulting Karush–Kuhn–Tucker (KKT) conditions. We also give a model-free implementation for the MB-PD algorithm by solving a transformed dual feasibility condition. More importantly, we establish the connection between the proposed MB-PD algorithm and classical policy iteration algorithm, which provides a novel primal–dual optimization perspective to understand the common RL algorithms. Finally, we provide a high-dimensional case study to show the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This communique presents an algorithm called "value set iteration" (VSI) for solving infinite horizon discounted Markov decision processes with finite state and action spaces as a simple generalization of value iteration (VI) and as a counterpart to Chang's policy set iteration. A sequence of value functions is generated by VSI based on manipulating a set of value functions at each iteration and it converges to the optimal value function. VSI preserves convergence properties of VI while converging no slower than VI and in particular, if the set used in VSI contains the value functions of independently generated sample-policies from a given distribution and a properly defined policy switching policy, a probabilistic exponential convergence rate of VSI can be established. Because the set used in VSI can contain the value functions of any policies generated by other existing algorithms, VSI is also a general framework of combining multiple solution methods. [ABSTRACT FROM AUTHOR]

Abstract: This communique provides an exact iterative search algorithm for the NP-hard problem of obtaining an optimal feasible stationary Markovian pure policy that achieves the maximum value averaged over an initial state distribution in finite constrained Markov decision processes. It is based on a novel characterization of the entire feasible policy space and takes the spirit of policy iteration (PI) in that a sequence of monotonically improving feasible policies is generated and converges to an optimal policy in iterations of the size of the policy space at the worst case. Unlike PI, an unconstrained MDP needs to be solved at iterations involved with feasible policies and the current best policy improves all feasible policies included in the union of the policy spaces associated with the unconstrained MDPs. [Copyright &y& Elsevier]

Abstract: This paper concerns the stabilization of discrete-time two-input two-output (TITO) linear time-invariant (LTI) systems over communication channels. We consider parallel additive white noise (AWN) channels, in which each individual channel is independently constrained in the signal-to-noise ratio (SNR). Necessary and sufficient conditions for stabilizability are obtained on the SNRs of the channels for both state and output feedback architectures. Our main results are derived assuming that the channel is located between the controller and the plant. We also consider stabilizability when the channel is between the plant and the controller, showing that there exists a duality between the results for both architectures. [Copyright &y& Elsevier]

Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of matrix variables and the number of constraints increases. To improve scalability, SDPs can be approximated with lower and upper bounds through the use of structured subsets (e.g., diagonally-dominant and scaled-diagonally dominant matrices). Meanwhile, any underlying sparsity or symmetry structure may be leveraged to form an equivalent SDP with smaller positive semidefinite constraints. In this paper, we present a notion of decomposed structured subsets to approximate an SDP with structured subsets after an equivalent conversion. The lower/upper bounds found by approximation after conversion become tighter than the bounds obtained by approximating the original SDP directly. We apply decomposed structured subsets to semidefinite and sum-of-squares optimization problems with examples of H ∞ norm estimation and constrained polynomial optimization. An existing basis pursuit method is adapted into this framework to iteratively refine bounds. [ABSTRACT FROM AUTHOR]

This paper introduces distributed adaptive algorithms for optimal step size selection in a distributed constrained optimization problem that involves stochastic target variations and noisy observations. The limit behavior of the step size sequences reflects fundamental impact that must be balanced between tracking the target changes and attenuating observation noises. Algorithms for simultaneously estimating target variation, tracking the global optimal solution, and finding the optimal step size are derived, which are shown to achieve convergence on all the sequences simultaneously to their respective optimal values. [ABSTRACT FROM AUTHOR]

In this paper we deal with decision-coupled problems involving multiple agents over a network. Each agent has its own local objective function and local constraints, and all agents aim at finding the value of a common decision vector that minimizes the sum of all agents' cost functions and satisfies all local constraints. To this purpose, we introduce a Proximal-Tracking distributed optimization algorithm that integrates dynamic average consensus within the proximal minimization method. Convergence to an optimal consensus solution is guaranteed for any value of a constant penalty parameter, under a convexity assumption only, without requiring differentiability, Lipschitz continuity, or smoothness of the local objective functions. Numerical simulations show the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Abstract: In this work, by proposing a Barrier Composite Energy Function (BCEF) method with a novel Barrier Lyapunov Function (BLF), we present a new iterative learning control (ILC) scheme for a class of single-input single-output (SISO) high order nonlinear systems to deal with output-constrained problems under alignment condition with both parametric and nonparametric system uncertainties. Nonparametric uncertainties such as norm-bounded nonlinear uncertainties satisfying local Lipschitz condition can be effectively handled. Backstepping design with the newly proposed BLF is incorporated in analysis to ensure output constraint not violated. Through rigorous analysis, we show that under this new ILC scheme, uniform convergence of state tracking error is guaranteed. In the end, an illustrative example is presented to demonstrate the efficacy of the proposed ILC scheme. [Copyright &y& Elsevier]

Abstract: The goal of multi-parametric quadratic programming (mpQP) is to compute analytic solutions to parameter-dependent constrained optimization problems, e.g., in the context of explicit linear MPC. We propose an improved combinatorial mpQP algorithm that is based on implicit enumeration of all possible optimal active sets and a simple saturation matrix pruning criterion which uses geometric properties of the constraint polyhedron for excluding infeasible candidate active sets. In addition, techniques are presented that allow to reduce the complexity of the discussed algorithm in the presence of symmetric problem constraints. Performance improvements are discussed for two example problems from the area of explicit linear MPC. [Copyright &y& Elsevier]

Abstract: We consider the problem of maximizing the algebraic connectivity of the communication graph in a network of mobile robots by moving them into appropriate positions. We define the Laplacian of the graph as dependent on the pairwise distance between the robots and we approximate the problem as a sequence of Semi-Definite Programs (SDP). We propose a distributed solution consisting of local SDPs which use information only from nearby neighboring robots. We show that the resulting distributed optimization framework leads to feasible subproblems and through its repeated execution, the algebraic connectivity increases monotonically. Moreover, we describe how to adjust the communication load of the robots based on locally computable measures. Numerical simulations show the performance of the algorithm with respect to the centralized solution. [Copyright &y& Elsevier]

Abstract: The constrained stabilization of linear uncertain systems is investigated via the set-theoretic framework of control Lyapunov R-functions. A novel composition rule allows the design of a composite control Lyapunov function with external level set that exactly shapes the maximal controlled invariant set and inner sublevel sets arbitrarily close to any choice of smooth ones, generalizing both polyhedral and truncated ellipsoidal control Lyapunov functions. The feasibility test of the proposed smooth control Lyapunov functions can be cast into matrix inequalities conditions. The constrained linear quadratic control is addressed as an application. [Copyright &y& Elsevier]

Abstract: In this paper a three-dimensional non-holonomic integrator (NI) with drift terms is considered. For this type of plant, the question how to obtain desired piecewise constant output functions with minimum norm control inputs is explored. It is shown that this can be achieved by a nonlinear controller that provides simultaneous modulation of both the amplitude and the frequency of the harmonic input vector. The internal states are implicitly forced to follow natural periodic orbits satisfying the non-holonomic constraints of the plant. Global asymptotic stability and high dynamics in the output response are achieved. The problem of singularity at zero initial state is solved by a time optimal control scheme for the internal states. By combining the nonlinear controller and the time-optimal controller using an appropriate switching strategy, a powerful control concept can be established. The torque control of an induction machine is considered as an illustrative example for the application of the control scheme. Experimental results of the closed loop feedback control system are presented. [Copyright &y& Elsevier]

Abstract: In this paper we consider a linear system structured into physically coupled subsystems and propose an innovative distributed control scheme capable of guaranteeing asymptotic stability and satisfaction of constraints on system inputs and states. Our method hinges on the availability of a decentralized stabilizing regulator for the unconstrained system and provides a two-layer controller for each subsystem. Upper controllers receive planned state trajectories from neighboring subsystems and exploit the notion of tubes (Langson, Chryssochoos, Raković, & Mayne, 2004) for achieving robustness of stability with respect to coupling. Lower controllers generate planned trajectories using Model Predictive Control (MPC) independently of the other subsystems. The proposed control scheme is arguably easier to design and apply than existing distributed controllers with similar features. A comparison of the proposed approach with existing centralized and distributed MPC regulators is conducted using an illustrative example. [Copyright &y& Elsevier]

Abstract: For industrial nonlinear batch processes that can be practically divided into a series of piecewise affine operating regions, a two-dimensional (2D) closed-loop iterative learning control (ILC) method is proposed for robust tracking of the set-point profile against cycle-to-cycle process uncertainties and load disturbances. Both state feedback and output feedback are considered for the control design, together with the process input and output constraints for implementation. Based on a 2D system description for the batch operation, a few synthetic performance and robust control objectives are proposed for developing the 2D ILC schemes, in combination with the 2D Lyapunov–Krasovskii functions that can guarantee monotonic state energy (or output error) decrease in both the time (during a cycle) and batch (from cycle to cycle) directions. Both the polyhedral and norm-bounded descriptions of process uncertainties are considered to derive the corresponding linear matrix inequality (LMI) conditions for the closed-loop ILC system robust stability. An important merit of these LMI conditions is that there are adjustable convergence indices prescribed for both the time and batch directions, and an adjustable robust control performance level for the closed-loop system. By specifying/optimizing these adjustable parameters to solve these LMI conditions, the 2D ILC controller can be explicitly derived for implementation. The application to a highly nonlinear continuous stirred tank reactor (CSTR) is shown to illustrate the effectiveness and merits of the proposed ILC method. [Copyright &y& Elsevier]

Abstract: To synthesize the optimal control strategies of nonlinear systems on infinite horizon while subject to mixed equality and inequality constraints has been a challenge to control engineers. This paper regards it as a problem of finite-time optimization in infinite-horizon control then devises a reinforcement learning agent, termed as the Adaptive Optimal Control (AOC) agent, to carry out the finite-time optimization procedures. Adaptive optimal control is in the sense of activating the finite-time optimization procedure whenever needed to improve the control strategy or adapt to a real-world environment. The Nonlinear Quadratic Regulator (NQR) is shown a typical example that the AOC agent can find out. The optimality conditions and adaptation rules for the AOC agent are deduced from Pontryagin’s minimum principle. The requirements for convergence and stability of the AOC system are shown. [Copyright &y& Elsevier]

Abstract: This paper introduces the concept and characterization of Disturbance-Dwell-Time invariance (DDT-invariance) and Constraint Admissible DDT-invariance (CADDT-invariance) for constrained systems with additive disturbance under dwell-time switching. Using the characterization, necessary and sufficient conditions for DDT-invariance and algorithms for the computation of the minimal and maximal constraint admissible convex DDT-invariant sets are provided. Numerical examples of such sets for several systems are also provided. [Copyright &y& Elsevier]

Abstract: The main difficulty in stability analysis of reset control systems comes from their state-dependent reset mechanism. It becomes more challenging when output matrix suffers from uncertainties which make the reset time instants uncertain. In this paper, existing quadratic stability results for uncertainty-free reset systems are extended to the case with uncertainty in the output matrix. By constructing special parameter-dependent full rank annihilators of the output matrix, it is proved that the dissipativeness of reset action is equivalent to the feasibility of an LMI plus some structural constraints on the Lyapunov matrix. For the time-varying uncertainty case, necessary and sufficient conditions for quadratic stability are obtained. For the constant uncertainty case, a sufficient condition for affine quadratic stability is also obtained. All the results are given in terms of LMIs which can be efficiently verified. [Copyright &y& Elsevier]

Abstract: We analyze the stability of a constrained piecewise continuous hybrid system that is controlled by a receding horizon controller across an unreliable communication channel. We assume the presence of a buffer at the actuator to store the control input sequence received from the controller to compensate for any possible packet dropouts in future transmissions. Input-to-state stability is considered under the assumption that the number of consecutive packet dropouts is bounded using tightened state constraints in the optimization problem solved by the controller. [Copyright &y& Elsevier]

Abstract: In this work, we study a discrete-time consensus protocol for a group of agents which communicate over a class of stochastically switching networks inspired by fish schooling. The network model incorporates the phenomenon of numerosity, that plays a prominent role in the collective behavior of animal groups, by defining the individuals’ perception of numbers. The agents comprise leaders, which share a common state, and followers, which update their states based on information exchange among neighboring agents. We establish a closed form expression for the asymptotic convergence factor of the protocol, that measures the decay rate of disagreement among the followers’ and the leaders’ states. Handleable forms of this expression are derived for the physically relevant cases of large networks whose agents are composed of primarily leaders or followers. Numerical simulations are conducted to validate analytical results and illustrate the consensus dynamics as a function of the number of leaders in the group, the agents’ persuasibility, and the agents’ numerosity. We find that the maximum speed of convergence for a given population can be enhanced by increasing the proportion of leaders in the group or the agents’ numerosity. On the other hand, we find that increasing the numerosity has also a negative effect as it reduces the range of agents’ persuasibility for which consensus is possible. Finally, we compare the main features of this leader–follower consensus protocol with its leaderless counterpart to elucidate the benefits and drawbacks of leadership in numerosity-constrained random networks. [Copyright &y& Elsevier]

Abstract: This paper presents a continuous-time version of recent results on unconstrained nonlinear model predictive control (MPC) schemes. Based on a controllability assumption and a corresponding infinite-dimensional optimization problem, performance estimates and stability conditions are derived in terms of the prediction horizon and the sampling time of the MPC controller. Moreover, improved estimates for small sampling times are discussed and a comparison to the application of the discrete-time results in a sampled-data context is provided. [Copyright &y& Elsevier]

Abstract: The robust model predictive control for constrained linear discrete time systems is solved through the development of a homothetic tube model predictive control synthesis method. The method employs several novel features including a more general parameterization of the state and control tubes based on homothety and invariance, a more flexible form of the terminal constraint set and a relaxation of the controlled dynamics of the sets that define the state and control tubes. Under natural assumptions, the proposed method is computationally efficient and it induces strong system theoretic properties. [Copyright &y& Elsevier]

Abstract: Nonlinear constrained optimal trajectory planning is a challenging and fundamental area of research. This paper proposes bio-inspired fast-time approaches for this type of problems based on the inspiration drawn from the natural phenomenon known as the motion camouflage. Two algorithms are proposed: the virtual motion camouflage (VMC) subspace method and the sequential VMC method. As a hybrid approach, the sequential VMC method works through a two-step structure in each iteration. First, the VMC subspace method will solve for an optimal solution over a selected subspace. Second, an algorithm consisting of a linear programming and a line search will vary the subspace so that the next VMC subspace result will be guaranteed not to be worse than that of the current step. The dimension and time complexities of the algorithms will be analyzed, and the optimality of the solution via the sequential VMC approach will be studied. Through the VMC approaches, the state and control variables in the kinematics or dynamics models of vehicles in the selected subspace can be represented by a single degree-of-freedom vector, called the path control parameter vector. The reduction in dimension and no involvement of equality constraints will in practice make the convergence faster and easier, and a much smaller computational cost is expected. Two simulation examples, the Breakwell problem and a minimum time robot obstacle avoidance problem with different numbers of obstacles, are used to demonstrate the capabilities of the algorithms. [Copyright &y& Elsevier]