Feasible parallel-update distributed MPC for uncertain linear systems sharing convex constraints

A distributed MPC approach for linear uncertain systems sharing convex constraints is presented. The systems, which are dynamically decoupled but share constraints on state and/or inputs, optimize once, in parallel, at each time step and exchange plans with neighbours thereafter. Coupled constraint satisfaction is guaranteed, despite the simultaneous decision making, by extra constraint tightening in each local problem. Necessary and sufficient conditions are given on the margins for coupled constraint satisfaction, and a simple on-line scheme for selecting margins is proposed that satisfies the conditions. Robust feasibility and stability of the overall system are guaranteed by use of the tube MPC concept in conjunction with the extra coupled constraint tightening.     

Continuity of dynamical systems: A system theoretic approach

This paper studies continuity of linear time-invariant dynamical systems, defined in terms of the system’s behavior. This concept is related to parameter continuity of associated system representations. For the case at hand, these will be autoregressive (AR) representations. The main result states that a family of linear time-invariant systems, with uniformly bounded dimension of the state space, converges if and only if the systems admit a convergent full rank (AR) representation.     

The contact problem for linear continuous-time dynamical systems: ageometric approach

In this paper linear time-invariant dynamical systems described by a combination of differential equalities and static inequalities in state-space formulation are investigated. Of special interest is the contact problem: the effect of the boundary of the constraint set on the behavior of the system. This effect is studied by dividing the state-space in a number of disjunct subsets. It is shown that these subsets are invariant under linear state feedback. In our framework, a specific place is reserved for modeling the laws of collision, i.e., physical modeling, which are regarded as external factors. Our main results are a system theoretical framework in which we describe what happens upon contact and a definition of the constrained state-space system in terms of its restricted behavior. The results presented here can be considered as an extension for restricted linear systems of the classic positive invariance theory for linear systems     

Bisimilar linear systems

The notion of bisimulation in theoretical computer science is one of the main complexity reduction methods for the analysis and synthesis of labeled transition systems. Bisimulations are special quotients of the state space that preserve many important properties expressible in temporal logics, and, in particular, reachability. In this paper, the framework of bisimilar transition systems is applied to various transition systems that are generated by linear control systems. Given a discrete-time or continuous-time linear system, and a finite observation map, we characterize linear quotient maps that result in quotient transition systems that are bisimilar to the original system. Interestingly, the characterizations for discrete-time systems are more restrictive than for continuous-time systems, due to the existence of an atomic time step. We show that computing the coarsest bisimulation, which results in maximum complexity reduction, corresponds to computing the maximal controlled or reachability invariant subspace inside the kernel of the observations map. These results establish strong connections between complexity reduction concepts in control theory and computer science.     

An MPC-based reference governor approach for offset-free control of constrained linear systems

This paper presents a model predictive control (MPC) based reference governor approach for control of constrained linear systems. A nominal closed-loop system is first designed to guarantee that, in the unconstrained case, asymptotic zero-error regulation for (piecewise) constant reference signals is achieved. Then, a couple of exogenous signals are added to the reference signal and to the control variable and their value is determined by formulating a MPC problem in order to guarantee that (i) when the state and control constraints are not active, the nominal closed-loop system is recovered, (ii) in transient conditions the constraints are always satisfied and the difference of the performances between the real and the nominal closed-loop systems is minimised, and (iii) when the reference signal is infeasible, the output is brought to the nearest feasible value. A simulation example is reported to witness the potentialities of the approach.     

Aggregation of a class of interconnected, linear dynamical systems

In this paper, we introduce the notion of a “meaningful” average of a collection of dynamical systems as distinct from an “ensemble” average. Such a notion is useful for the study of a variety of dynamical systems such as traffic flow, power systems, and econometric systems. We also address the associated issue of the existence and computation of such an average for a class of interconnected, linear, time invariant dynamical systems. Such an “average” dynamical system is not only attractive from a computational perspective, but also represents the average behavior of the interconnected dynamical systems. The problem of analysis and control of heirarchical, large scale control systems can be simplified by approximating the lower level dynamics of such systems with such an average dynamical system.     

Reachability of linear switched systems: Differential geometric approach

The paper investigates the structure of the reachable set of linear switched systems. The structure of the reachable set is determined using techniques from classical nonlinear systems theory, namely, the theory of orbits developed by H. Sussman and the realization theory for nonlinear systems developed by B. Jakubczyk.     

Discerning controllers for switching linear systems: Existence and genericity

This paper presents recent developments in the study of non-autonomous switching linear systems. For such systems, we address the issue of how to systematically design linear controllers allowing the active process mode to be observable from closed-loop data. The results are stated formally by introducing the notion of discerning controllers. Both existence and genericity problems are discussed. It is finally shown how a given family of discerning controllers can be implemented as a single hybrid system which preserves the discerning capability of the original controllers. Examples are discussed to substantiate the analysis.     

Stochastic model predictive control for constrained discrete-time Markovian switching systems

In this paper we study constrained stochastic optimal control problems for Markovian switching systems, an extension of Markovian jump linear systems (MJLS), where the subsystems are allowed to be nonlinear. We develop appropriate notions of invariance and stability for such systems and provide terminal conditions for stochastic model predictive control (SMPC) that guarantee mean-square stability and robust constraint fulfillment of the Markovian switching system in closed-loop with the SMPC law under very weak assumptions. In the special but important case of constrained MJLS we present an algorithm for computing explicitly the SMPC control law off-line, that combines dynamic programming with parametric piecewise quadratic optimization.     

Distributed model predictive control of linear systems with persistent disturbances

This article presents a new form of robust distributed model predictive control (MPC) for multiple dynamically decoupled subsystems, in which distributed control agents exchange plans to achieve satisfaction of coupling constraints. The new method offers greater flexibility in communications than existing robust methods, and relaxes restrictions on the order in which distributed computations are performed. The local controllers use the concept of tube MPC – in which an optimisation designs a tube for the system to follow rather than a trajectory – to achieve robust feasibility and stability despite the presence of persistent, bounded disturbances. A methodical exploration of the trades between performance and communication is provided by numerical simulations of an example scenario. It is shown that at low levels of inter-agent communication, distributed MPC can obtain a lower closed-loop cost than that obtained by a centralised implementation. A further example shows that the flexibility in communications means the new algorithm has a relatively low susceptibility to the adverse effects of delays in computation and communication.     

Constrained control for uncertain discrete-time linear systems

In this paper the problem of stabilizing uncertain linear discrete-time systems under state and control linear constraints is studied. Many formulations of this problem have been given in the literature. Here we consider the case of finding a linear state feedback control law making a given polytope in the state space positively invariant while the control remains bounded within prefixed values under the effect of all the uncertainty sequences belonging to a given polytope in the perturbations space. A necessary and sufficient condition for the existence of a solution of this problem is first given. This condition leads to a set of linear constraints which can be solved using linear programming tecniques by defining an appropriate objective function. A worked example shows the effectiveness of the proposed algorithm. © 1998 John Wiley & Sons, Ltd.     

Discretisation of sparse linear systems: An optimisation approach

This paper addresses the discretisation problem for sparse linear systems. Classical methods usually destroy sparsity patterns of continuous-time systems. We develop an optimisation procedure that yields the best approximation to the discrete-time dynamical matrix with a prescribed sparsity pattern and subject to stability and other constraints. By formulating this problem in an adequate manner, tools from convex optimisation can be then applied. Error bounds for the approximation are provided for special classes of matrices. Numerical examples are included.     

Regularizability of complex switched server queueing networks modelled as hybrid dynamical systems

The paper considers the problem of the qualitative analysis of complex switched server queueing networks. Such networks can be used to model various flexible manufacturing, communications, and computer systems. We introduce the concept of regularizability for such systems and obtain a necessary and sufficient condition for a switched server queueing network to be regularizable.     

On the controllability of switching linear systems

This note presents a necessary and sufficient condition for small time controllability of a linear switching system (that is, a collection of linear time-invariant control systems, where a trajectory is any concatenation of trajectories of the individual systems). This result extends the controllability condition recently obtained for unconstrained linear switching systems to the case of control which is constrained in a cone.     

指挥控制参考模型

指挥控制参考模型（Ｃｏｍｍａｎｄ ａｎｄ Ｃｏｎｔｒｏｌ Ｒｉｆｉｒｉｎｃｅ Ｍｏｄｉｌ,简记为Ｃ＾２ＲＭ）试图为Ｃ＾２系统的概念、术语、定义和原理等基本问题进行统一的描述,提供了一个标准的、面向对象的开放系统体系结构和开放系统互边框架,以用于Ｃ＾２系统及其下辖资源的建模和仿真,并为异构和分布的Ｃ＾２系统资源间皎互提供标准的Ｃ＾２协议和接口,以推动Ｃ＾２系统技术和应用的发展。本文阐述了Ｃ＾２ＲＭ的     

Stealthy output injection attacks on control systems with bounded variables

As more and more critical infrastructures such as transportation, power systems and water are being embedded with sensing and control and linked to the Internet, the resulting security vulnerability can be exploited to inflict systematic damage to the connected physical systems. The class of false-data injection attacks is of particular interest as it only requires the ability to compromise the measurements. We construct such attacks, that are stealthy to set-membership-based anomaly detectors over widely used constrained control systems with bounded disturbances. The design of robust controllers and detectors based on the ability to withstand disturbance lets the attacker masquerade itself as disturbance and necessitates the development of a disturbance set-estimator as a soft-constrained optimisation problem. We then formulate another constrained optimisation problem that maximises the state estimation error by manipulating measurements and results in a computable performance loss and derive its explicit solution as the attack vector. These methods are used to demonstrate the vulnerability of a test system, with attacker having limited knowledge of the control system.     

Distributed iterative command governor schemes for interconnected linear systems

A novel distributed command governor (CG) supervision strategy relying on iterative optimization procedure is presented for multi‐agent interconnected linear systems subject to pointwise‐in‐time set‐membership coordination constraints. Unlike non‐iterative distributed CG schemes, here all agents undertake several optimization iterations and data exchange before arriving to the optimal solution. As a result, these methods are able to achieve Pareto‐optimal solutions not only in steady‐state conditions as the ones based on non‐iterative optimization procedures but also during transients and are not hampered by the presence of undesirable Nash‐equilibria or deadlock situations. The main properties of the method are fully investigated and in particular its optimality, stability, and feasibility properties rigorously proved. A final example is presented where the proposed distributed solution is contrasted with existing centralized and distributed non‐iterative CG solutions. Copyright © 2017 John Wiley & Sons, Ltd.     

Stabilizing adaptive controller for uncertain dynamical systems: An LMI approach

Adaptive stabilization of a class of linear systems with matched and unmatched uncertainties is considered in this paper. The proposed controller indeed stabilizes the uncertain system for any positive values of its non-adaptive gain that may be tuned to enhance dynamic response of system. The performance of uncertain system along with the Algebraic Riccati Equation that arises from the adaptive stabilizing controller is now formulated as a multi-objective Linear Matrix Inequality optimization problem. The decay rate and a factor governing the ultimate bound of the system states are considered to characterize the closed loop system performance. Finally, the effectiveness of the proposed controller is illustrated via stabilizing a mass-spring system. Recommended by Editorial Board member Gang Tao under the direction of Editor Young Il Lee. The authors would like to thank the reviewers for their valuable comments and suggestions that have improved the quality of this paper. Sandip Ghosh received the B.E. in Electrical Engineering from Bengal Engineering College (D.U.), Howrah, and Master in Control System Engineering from Jadavpur University, Kolkata, India, in 1999 and 2003 respectively. Presently he is pursuing the Ph.D. degree at Indian Institute of Technology, Kharagpur, India. His research interests include adaptive control, robust control and control of time-delay systems. Sarit K. Das is a Professor of Electrical Engineering Department, Indian Institute of Technology, Kharagpur, India. He received the Ph.D. degree in 1985 from the same department. His research interests include design of periodic controller, decoupling of multivariable systems, modeling and robust control of complex systems. Goshaidas Ray is a Professor of Electrical Engineering Department, Indian Institute of Technology, Kharagpur, India. He received the Ph.D. degree in 1982 from Indian Institute of Technology Delhi, India. His research interests include modeling, estimation, model-based control, intelligent control, robotic systems and distributed control systems.     

A dissipative dynamical systems approach to stability analysis of time delay systems

In this paper the concepts of dissipativity and the exponential dissipativity are used to provide sufficient conditions for guaranteeing asymptotic stability of a time delay dynamical system. Specifically, representing a time delay dynamical system as a negative feedback interconnection of a finite‐dimensional linear dynamical system and an infinite‐dimensional time delay operator, we show that the time delay operator is dissipative with respect to a quadratic supply rate and with a storage functional involving an integral term identical to the integral term appearing in standard Lyapunov–Krasovskii functionals. Finally, using stability of feedback interconnection results for dissipative systems, we develop sufficient conditions for asymptotic stability of time delay dynamical systems. The overall approach provides a dissipativity theoretic interpretation of Lyapunov–Krasovskii functionals for asymptotically stable dynamical systems with arbitrary time delay. Copyright © 2004 John Wiley & Sons, Ltd.