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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]

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]

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]

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 paper proposes a multi-regulator control scheme for single-input systems, where the setpoint of a regulated output must be changed under the constraint that a set of minimum-phase outputs remain within prescribed bounds. The strategy is based on a max–min selector system frequently used in the aerospace field. The regulators used for the regulated and limited outputs are of the sliding mode type, where the sliding variable is defined as the difference between an output and its allowable limit. The paper establishes overall asymptotic stability, as well as invariance properties leading to limit protection. The design methodology is illustrated with a detailed simulation example on thrust control of a turbofan engine. [Copyright &y& Elsevier]

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]

Abstract: The state estimation problem for linear systems with linear state equality constraints was dealt with in Ko & Bitmead [Ko, S., & Bitmead, R. (2007). State estimation for linear systems with state equality constraints. Automatica, 43, 1363–1368]. In this correspondence, it is first shown that a necessary assumption on the covariance of the process noise is missing in the main result of the paper. It is then shown that the main result of the paper can be achieved in a convenient and more general way without any additional assumptions on the covariance of the process noise except positive definiteness. [Copyright &y& Elsevier]

Abstract: This paper extends some duality results from a standard optimization setup to a noncooperative (Nash) game framework. A Nash game (NG) with coupled constraints is considered. Solving directly such a coupled NG requires coordination among possibly all players. An alternative approach is proposed based on its relation to a special constrained optimization problem for the NG-game cost function, with respect to the second argument that admits a fixed-point solution. Specific separability properties of the NG-game cost are exploited and duality results are developed. This duality extension leads naturally to a hierarchical decomposition into a lower-level NG with no coupled constraints, and a higher-level system optimization problem. In the second part of the paper these theoretical results are applied to a coupled NG with coupled constraints as encountered in optical networks. [Copyright &y& Elsevier]

This paper is devoted to investigating the issues on extended dissipative anti-disturbance control for switched singular semi-Markovian jump systems with multiple disturbance and time-delay via disturbance observer. Different from the existing results, this paper introduces a relatively new and comprehensive system model, namely, switched semi-Markovian jump model, which is more general than Markovian jump model in describing the phenomenon of random mutation of system structure and parameters. Moreover, the uncertain transition rates in the considered switched semi-Markovian process include two cases of indeterminate bounded and thoroughly unknown, rather than the common single partially unknown case. Particularly, the designed composite controller that ensures that the closed-loop system achieves stochastic admissible is easier to calculate than the related working methods. In addition, an optimization algorithm to constrain control gain is developed in this paper, which can effectively reduce control cost in practice to some extent. Finally, for the sake of substantiating the validity of the proposed method, a numerical example is provided. [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]

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]

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 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: 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: 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: 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]

Abstract: This paper proposes a novel class of Command Governor (CG) strategies for input and state-related constrained discrete-time LTI systems subject to bounded disturbances in the absence of explicit state or output measurements. While in traditional CG schemes the set-point manipulation is undertaken on the basis of either the actual measure of the state or its suitable estimation, it is shown here that the CG design problem can be solved, with limited performance degradation and with similar properties, also in the case that such an explicit measure is not available. This approach, which will be referred to as the Feed-Forward CG (FF-CG) approach, may be a convenient alternative CG solution in all situations whereby the cost of measuring the state may be a severe limitation, e.g. in distributed or decentralized applications. In order to evaluate the method proposed here, numerical simulations on a physical example have been undertaken and comparisons with the standard state-based CG solution reported. [Copyright &y& Elsevier]

Abstract: This paper considers output feedback robust model predictive control for the quasi-linear parameter varying (quasi-LPV) system with bounded disturbance. The so-called quasi-LPV means that the varying parameters of the linear system are known at the current time, but unknown in the future. The control law is parameterized as a parameter-dependent dynamic output feedback, and the closed-loop stability is specified by the notion of quadratic boundedness. An iterative algorithm is proposed for the on-line synthesis of the control law via convex optimization. A numerical example is given to illustrate the effectiveness of the controller. [ABSTRACT FROM AUTHOR]

Abstract: As an example of complex cooperative missions, coherent phantom track generation through controlling multiple electronic combat air vehicles is currently an area of great interest to the defense agency for the purpose of deceiving a radar network. However, it has been a challenge to design the optimal or even feasible coherent trajectories for this type of problem due to the high dimensionality and the strong coupling between the phantom and actual vehicles. This problem becomes even more difficult to solve when realistic kinematic, dynamics, and geometric constraints in a three-degree-of-freedom formation have to be considered. This paper describes how an interesting bio-inspired motion strategy can be used to design real-time trajectories for a (1) feasible constant speed coherent mission, (2) maximum-duration constant speed coherent mission, and (3) optimal trajectory mission for general cases. The proposed method will dramatically reduce the dimension of the problem and thus real-time optimal trajectory design can be achieved. Also the fact that fewer equality constraints are involved in solving the formulated nonlinear programming will make the convergence a lot easier. [ABSTRACT FROM AUTHOR]

Abstract: This paper develops an efficient offset-free output feedback predictive control approach to nonlinear processes based on their approximate fuzzy models as well as an integrating disturbance model. The estimated disturbance signals account for all the plant–model mismatch and unmodeled plant disturbances. An augmented piecewise observer, constructed by solving some linear matrix inequalities, is used to estimate the system states and the lumped disturbances. Based on the reference from an online constrained target generator, the fuzzy model predictive control law can be easily obtained by solving a convex semi-definite programming optimization problem subject to several linear matrix inequalities. The resulting closed-loop system is guaranteed to be input-to-state stable even in the presence of observer estimation error. The zero offset output tracking property of the proposed control approach is proved, and subsequently demonstrated by the simulation results on a strongly nonlinear benchmark plant. [Copyright &y& Elsevier]

Abstract: This paper introduces a mathematical framework for the study of resource allocation problems involving the deployment of heterogeneous agents to different teams. In this context, the term heterogeneous is used to describe classes of agents that differ in the basic functions they can perform (e.g., one type of agent searches for targets while another type engages those targets). The problem is addressed in terms of optimization using concepts from economic theory and the proposed algorithm was designed to ensure asymptotic stability of the optimal solution. [Copyright &y& Elsevier]

Abstract: This paper provides a design method of fixed-structure robust controllers satisfying multiple norm specifications by using a sort of randomized algorithms. First, a new tool to perform general constrained optimization is developed which does not need any gradient or derivative of the objective function. This tool is based on a particle swarm optimization (PSO), which has attracted a lot of attention recently in the evolutionary computation area due to the empirical evidence of its superiority in solving various non-convex problems. Second, it is shown how to design a fixed-structure controller satisfying given multiple specifications by using the developed optimization tool. Third, its effectiveness is evaluated through various numerical examples, because it is difficult to guarantee the performance of the proposed method theoretically due to the probabilistic nature of PSO. The simulation results demonstrate its effectiveness clearly. [Copyright &y& Elsevier]

Abstract: This paper exposes a symmetry relationship between constrained output reference tracking and constrained state estimation problems. The symmetry, which is different from the traditional duality relationship between control and estimation, is provided by means of two tables that give a complete translation of all variables of one problem into the variables of the other. An example is provided to illustrate the behaviour of the optimal solutions to the reference tracking and state estimation problems. The symmetry relationship leads to interesting interpretations of several of the resulting trajectories. [Copyright &y& Elsevier]

Abstract: Robust predictive control handles constrained systems that are subject to stochastic uncertainty but propagating the effects of uncertainty over a prediction horizon can be computationally expensive and conservative. This paper overcomes these issues through an augmented autonomous prediction formulation, and provides a method of handling probabilistic constraints and ensuring closed loop stability through the use of an extension of the concept of invariance, namely invariance with probability . [Copyright &y& Elsevier]

Abstract: Despite the well-known conservatism of sector-based results for systems consisting of an interconnection of a linear-time-invariant (LTI) system and a static, sector-bounded nonlinearity, they are widely used in control system analysis and synthesis. This paper shows how, when the sector-bounded nonlinearity is a dead-zone, standard sector based results can be modified to allow the synthesis of a nonlinear controller which can deliver improved performance over standard results. The appealing feature of the method is that, as the main part of the design proceeds using standard sector results, the computation associated with the improved controller is essentially the same as with the standard controller. [Copyright &y& Elsevier]

Abstract: This paper introduces a notion of possible controllability for a class of uncertain linear systems with structured uncertainty described by averaged integral quadratic constraints. This notion relates to the question of when a state is controllable for some possible value of the uncertainty. The notion of possible controllability is motivated by a desire to extend the theory of minimal realization for linear time invariant systems to the case of uncertain systems with structured uncertainty. [Copyright &y& Elsevier]

Abstract: In this paper, the use of Set Membership (SM) methodologies is investigated in the approximation of Model Predictive Control (MPC) laws for linear systems. Such approximated MPC laws are derived from a finite number of exact control moves computed off-line. Properties, in terms of guaranteed approximation error, closed-loop stability and performance, are derived assuming only the continuity of the exact predictive control law. These results are achieved by means of two main contributions. At first, it will be shown that if the approximating function enjoys two key properties (i.e. fulfillment of input constraints and explicit evaluation of a bound on the approximation error, which converges to zero as increases), then it is possible to guarantee the boundedness of the controlled state trajectories inside a compact set, their convergency to an arbitrary small neighborhood of the origin, and satisfaction of state constraints. Moreover, the guaranteed performance degradation, in terms of maximum state trajectory distance, can be explicitly computed and reduced to an arbitrary small value, by increasing . Then, two SM approximations are investigated, both enjoying the above key properties. The first one minimizes the guaranteed approximation error, but its on-line computational time increases with . The second one has higher approximation error, but lower on-line computational time which is constant with when the off-line computed moves are suitably chosen. The presented approximation techniques can be systematically employed to obtain an efficient MPC implementation for “fast” processes. The effectiveness of the proposed techniques is tested on two numerical examples. [Copyright &y& Elsevier]

In this paper, a class of optimization problems is investigated, where the objective function is the sum of N convex functions viewed as local functions and the constraints are N nonidentical closed convex sets. Additionally, it is aimed to solve the considered optimization problem in a distributed manner and thus a sequence of time-varying unbalanced directed graphs is introduced first to depict the information connection topologies. Then, the novel push-sum based constrained optimization algorithm (PSCOA) is developed, where the new gradient descent-like method is applied to settle the involved closed convex set constraints. Furthermore, the rigorous convergence analysis is shown under some standard and common assumptions and it is proved that the developed distributed discrete-time algorithm owns a convergence rate of O ( ln t t ) in general case. Specially, the convergence rate of O ( 1 t ) can be further obtained under the assumption that at least one objective function is strongly convex. Finally, simulation results are given to demonstrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present an analysis and synthesis approach for guaranteeing that the phase of a single-input, single-output closed-loop transfer function is contained in the interval for a given at all frequencies. Specifically, we first derive a sufficient condition involving a frequency domain inequality for guaranteeing a given phase constraint. Next, we use the Kalman–Yakubovich–Popov theorem to derive an equivalent time domain condition. In the case where , we show that frequency and time domain sufficient conditions specialize to the positivity theorem. Furthermore, using linear matrix inequalities, we develop a controller synthesis approach for guaranteeing a phase constraint on the closed-loop transfer function. Finally, we extend this synthesis approach to address mixed gain and phase constraints on the closed-loop transfer function. [Copyright &y& Elsevier]

Abstract: In this paper, we develop a computational method for a class of optimal control problems where the objective and constraint functionals depend on two or more discrete time points. These time points can be either fixed or variable. Using the control parametrization technique and a time scaling transformation, this type of optimal control problem is approximated by a sequence of approximate optimal parameter selection problems. Each of these approximate problems can be viewed as a finite dimensional optimization problem. New gradient formulae for the cost and constraint functions are derived. With these gradient formulae, standard gradient-based optimization methods can be applied to solve each approximate optimal parameter selection problem. For illustration, two numerical examples are solved. [Copyright &y& Elsevier]

Abstract: Periodic smoothing splines appear for example as generators of closed, planar curves, and in this paper they are constructed using a controlled two point boundary value problem in order to generate the desired spline function. The procedure is based on minimum norm problems in Hilbert spaces and a suitable Hilbert space is defined together with a corresponding linear affine variety that captures the constraints. The optimization is then reduced to the computationally stable problem of finding the point in the constraint variety closest to the data points. [Copyright &y& Elsevier]

This paper presents a sufficient condition and its certification algorithm for solving box-constrained linear model predictive control (MPC) problems within a certain number of iterations equal to the number of constrained prediction points. For implementing a model predictive controller in industrial applications, it is crucial to guarantee a concrete upper bound on the computational load so that the processor specifications can be determined. To address this matter, we transform the constrained quadratic optimization of MPC into an equivalent linear complementarity problem (LCP). Then, we show that if a modified n-step vector exists for a given problem, the corresponding LCP is feasible and solvable within a predetermined number of iterations, each comprising fundamental arithmetic operations. The existence of a modified n-step vector is independent of the current states and box constraint bounds. Thus, the total computational load required to solve an MPC problem can be explicitly determined. In addition, an explicit certification algorithm for checking the existence of a modified n-step vector is proposed. Utilizing this algorithm, the existence range of a modified n-step vector is investigated for various problem configurations. Numerical tests show that the computational speed of the proposed method is competitive with those of commonly available algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a new class of robust zero-order algorithms for the solution of real-time optimization problems with acceleration. In particular, we propose a family of extremum seeking (ES) dynamics that can be universally modeled as singularly perturbed hybrid dynamical systems with restarting mechanisms. From this family of dynamics, we synthesize four fast algorithms for the solution of convex, strongly convex, constrained, and unconstrained optimization problems. In each case, we establish robust semi-global practical asymptotic or exponential stability results, and we also show how to obtain well-posed discretized algorithms that retain the main properties of the original dynamics. Given that existing averaging theorems for singularly perturbed hybrid systems are not directly applicable to our setting, we derive an extended averaging theorem that relaxes some of the assumptions made in the literature, allowing us to make a clear link between the K L bounds that characterize the rates of convergence of the hybrid dynamics and their average dynamics. We also show that our results are applicable to non-hybrid algorithms, thus providing a general framework for accelerated ES dynamics based on averaging theory. We present different numerical examples to illustrate our results. [ABSTRACT FROM AUTHOR]

We consider a linear system affected by an additive stochastic disturbance and address the design of a finite horizon control policy that is optimal according to some cost criterion and accounts also for probabilistic constraints on both the input and state variables. The resulting policy can be implemented over a receding horizon according to the model predictive control strategy. Such a possibility, however, is hampered by the fact that a feasibility issue may arise when recomputing the policy. Infeasibility indeed can occur if the disturbance has unbounded support and the state is required to remain in a bounded set. In this paper, we propose a solution to this issue that is based on the introduction of a constraint relaxation that becomes effective only when the original problem turns out to be unfeasible. This is obtained via a cascade of two probabilistically-constrained optimization problems where, in the first one, performance is neglected and the policy is designed to fully recover feasibility or – if this is not possible – to determine the minimum level of relaxation which is needed to recover feasibility; in the second step, such a minimum relaxation level is imposed while optimally (re-)tuning the control policy parameters. Both problems are solved through a computationally tractable scenario-based scheme using a finite number of disturbance realizations and providing an approximate solution that satisfies with high confidence the original probabilistic constraints of the cascade. [ABSTRACT FROM AUTHOR]

This paper presents a novel transformation-proximal bundle algorithm for multistage adaptive robust optimization problems. By partitioning recourse decisions into state and control decisions, the proposed algorithm applies affine control policy only to state decisions and allows control decisions to be fully adaptive, thus transforming the original problem into an equivalent two-stage Adaptive Robust Optimization (ARO) problem. Importantly, this multi-to-two transformation is general enough to be employed with any two-stage ARO solution algorithms, thus opening a new avenue for a variety of multistage ARO algorithms. The proximal bundle method is developed for the resulting two-stage problem along with convergence analysis. In an inventory control application, the affine disturbance-feedback control policy suffers from a severe suboptimality with an average gap of 34.88%, while the proposed algorithm generates an average gap of merely 1.68%. [ABSTRACT FROM AUTHOR]

This paper presents a filtering adaptive tracking control architecture for multivariable nonlinear systems subject to constraints by employing an online optimization method. A piecewise constant adaptive law updates the adaptive parameters which represent the uncertainty estimates by solving the error dynamics between the state predictor and the real system with the neglection of unknowns. A filtering control law is designed to compensate the nonlinear uncertainties and deliver a good tracking performance with guaranteed robustness. In the control scheme, the nonlinear uncertainty compensation component is always active whereas the tracking component is subject to a switching logic. The controller will remain in the tracking mode as long as there exists feasible solution, otherwise this component will be replaced by a new part updated periodically by numerically solving a constrained optimization problem online. The uniform performance bounds are derived for the system states and control inputs as compared to the corresponding signals of a bounded closed-loop reference system, which assumes partial cancellation of uncertainties within the bandwidth of the control signal. Compared to the model predictive control (MPC) method and unconstrained controller, the proposed approach is capable of solving the tracking control problems of multivariable nonlinear systems subject to both constraints and uncertainties. [ABSTRACT FROM AUTHOR]

In this paper, we study chance constrained trajectory optimization of linear systems with general ellipsoidal and polytopic state-input constraints where the constraints must be met with some prescribed confidence level. We use the sampling techniques, specifically scenario approach, due to their generality and tractability compared to the analytical methods. To address the main drawback of scenario approach, which may require large number of samples, we introduce an approximate convex hull-based method to significantly reduce the number of samples. Based on the allowable computational complexity, the prominent samples are selected in a proper mapping and the rest are truncated. The truncation error is later compensated for by adjusting (buffering) the constraint set, so that the satisfaction of constraints with the desired confidence level is still guaranteed. Simulation results confirm the theoretical predictions with solid performance of the proposed method after discarding about 99% of samples from the scenario approach, which remarkably speeds up the online computations. [ABSTRACT FROM AUTHOR]

Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a class of novel distributedapprox − Newton algorithms that approximate the standard Newton optimization method. We first develop the notion of an optimal edge weighting for the communication graph over which agents implement the second-order algorithm, and propose a convex approximation for the nonconvex weight design problem. We next build on the optimal weight design to develop a discrete distributed approx-Newton algorithm which converges linearly to the optimal solution for economic dispatch problems with unknown cost functions and relaxed local box constraints. For the full box-constrained problem, we develop a continuous distributed approx-Newton algorithm which is inspired by first-order saddle-point methods and rigorously prove its convergence to the primal and dual optimizers. A main property of each of these distributed algorithms is that they only require agents to exchange constant-size communication messages, which lends itself to scalable implementations. Simulations demonstrate that the distributedapprox − Newton algorithms with our weight design have superior convergence properties compared to existing weighting strategies for first-order saddle-point and gradient descent methods. [ABSTRACT FROM AUTHOR]