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.     

Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations

Given a parameterized (by sampling period T) family of approximate discrete-time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all T sufficiently small, we present conditions which guarantee that the same family of controllers semi-globally practically stabilizes the exact discrete-time model of the plant for sufficiently small sampling periods. When the family of controllers is locally bounded, uniformly in the sampling period, the inter-sample behavior can also be uniformly bounded so that the (time-varying) sampled-data model of the plant is uniformly semi-globally practically stabilized. The result justifies controller design for sampled-data nonlinear systems based on the approximate discrete-time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied. Our analysis is applicable to a wide range of time-discretization schemes and general plant models.     

Input-to-state stable finite horizon MPC for neutrally stable linear discrete-time systems with input constraints

MPC or model predictive control is representative of control methods which are able to handle inequality constraints. Closed-loop stability can therefore be ensured only locally in the presence of constraints of this type. However, if the system is neutrally stable, and if the constraints are imposed only on the input, global asymptotic stability can be obtained; until recently, use of infinite horizons was thought to be inevitable in this case. A globally stabilizing finite-horizon MPC has lately been suggested for neutrally stable continuous-time systems using a non-quadratic terminal cost which consists of cubic as well as quadratic functions of the state. The idea originates from the so-called small gain control, where the global stability is proven using a non-quadratic Lyapunov function. The newly developed finite-horizon MPC employs the same form of Lyapunov function as the terminal cost, thereby leading to global asymptotic stability. A discrete-time version of this finite-horizon MPC is presented here. Furthermore, it is proved that the closed-loop system resulting from the proposed MPC is ISS (Input-to-State Stable), provided that the external disturbance is sufficiently small. The proposed MPC algorithm is also coded using an SQP (Sequential Quadratic Programming) algorithm, and simulation results are given to show the effectiveness of the method.     

On globally stable adaptive control providing l 1 tracking performance for linear discrete-time systems

Existing adaptive control algorithms at best guarantee that the tracking error is a l ₂ sequence. This paper presents globally stable adaptive control algorithms for linear discrete-time systems providing l ₁ tracking performance. Two algorithms with different degree of complexity are proposed, one for the case of known control directions, and a separate algorithm for the case of unknown control directions. It is demonstrated that in both cases the tracking error is l ₁ sequence, while the input and output signals are uniformly bounded.     

Sufficient condition for asymptotic stability of discrete interval systems

A counter-example is given to a recent result on the stability analysis of interval matrices by Jiang (1988). A sufficient condition is then presented for the asymptotic stability of the discrete-time interval system X(k + 1) = A _I X(k), by testing the norms of extreme matrices of the interval matrix A _I such that they are all less than one.     

A component-based simulation environment for statistical process control systems analysis

This paper describes a simulation environment, called Prosim, which permits a user to define components, subsystems, and their interconnections to analyse a statistical process control (SPC) system. The components and systems are defined and analysed interactively. A library of standard SPC objects containing models for the Xbar, range, exponential weighted moving average, p-chart and other SPC techniques have been created which help define the control application. The PC-based tool is tested on theoretical, and real data, and is useful for the design and trouble shooting of a manufacturing system. It is also an effective teaching and research tool.     

Robust stabilisation control for discrete-time networked control systems

We consider the analysis and synthesis of discrete-time networked control systems (NCSs), where the plant has additive uncertainty and the controller is updated with the sensor information at stochastic time intervals. It is shown that the problem is linked to H_∞-control of linear discrete-time stochastic systems and a new small gain theorem is established. Based on this result, sufficient conditions are given for ensuring mean square stability of the NCS, and the genetic algorithm is utilised to design the controller of the NCS based on a linear matrix inequality technique. An illustrative example is given to demonstrate the effectiveness of our proposed method.     

A second-order maximum principle for discrete-time bilinear control systems with applications to discrete-time linear switched systems

A powerful approach for analyzing the stability of continuous-time switched systems is based on using optimal control theory to characterize the “most unstable” switching law. This reduces the problem of determining stability under arbitrary switching to analyzing stability for the specific “most unstable” switching law. For discrete-time switched systems, the variational approach received considerably less attention. This approach is based on using a first-order necessary optimality condition in the form of a maximum principle (MP), and typically this is not enough to completely characterize the “most unstable” switching law. In this paper, we provide a simple and self-contained derivation of a second-order necessary optimality condition for discrete-time bilinear control systems. This provides new information that cannot be derived using the first-order MP. We demonstrate several applications of this second-order MP to the stability analysis of discrete-time linear switched systems.     

Near-optimal tracking control for discrete-time systems with delayed input

This paper considers the near-optimal tracking control problem for discrete-time systems with delayed input. Using a variable transformation, the system with delayed input is transformed into a non-delayed system, and the quadratic performance index of the optimal tracking control is transformed into a relevant format. The optimal tracking control law is constructed by the solution of a Riccati matrix equation and a Stein matrix equation. A reduced-order observer is constructed to solve the physically realizable problem of the feedforward compensator and a near-optimal tracking control is obtained. Simulation results demonstrate the effectiveness of the optimal tracking control law.     

Finite-time control for discrete-time switched systems with time delay

The problem of finite-time state feedback control is considered in this paper for a class of discrete-time switched systems with time delay. Firstly, the concepts of finite-time stability and finitetime boundedness are extended to discrete-time switched systems with time delay, respectively. Then, by resorting to the average dwell time approach and Lyapunov-Krasovskii functional technology, some new delay-dependent criteria guaranteeing finite-time boundedness and stability are developed. The state feedback controller is also obtained by virtue of a cone complement linearization (CCL) method. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed results.     

Robust decentralized model reference adaptive control of discrete-time interconnected systems

A robust decentralized model reference adaptive controller is proposed for a class of large-scale systems composed of several interconnected subsystems and described by state space equations. We have formulated a local adaptive controller for each subsystem using only local information such that the state of this subsystem tracks the corresponding state of a reference model. The content of the paper is limited to interconnected subsystems which are described by linear, deterministic, single-input single-output and discrete-time models with unknown and/or slowly time-varying parameters. Sufficient conditions, formulated by utilizing Lyapunov theory, are given for the overall system to be stabilizable by decentralized state feedback adaptive control laws. The results are illustrated by a numerical example.     

Passivity analysis and control for discrete-time two-dimensional switched systems in Roesser model

This paper investigates the passivity issues of discrete-time two-dimensional switched systems in Roesser model under a state-dependent switching law. Conditions for passivity of discrete-time two-dimensional switched systems are obtained without the requirement of passivity of subsystems. When the system states are completely available, state feedback controllers and switching laws are designed. In the case of partial state measurements, dynamic output feedback controllers and switching laws depending only on the state of the output feedback controllers are constructed to guarantee passivity of the closed-loop switched system. Finally, numerical examples are provided to illustrate the efficiency of the results.     

Decentralized control for two time-scale discrete-time systems

Output feedback design of discrete-time decentralized systems with slow and fast modes is considered. Conditions for the complete separation of slow and fast subsystems are given. The slow and fast subsystem outputs, which are obtained by applying the slow and fast subcontrollers to the corresponding subsystems, will be shown to approximate those of the original system. Also, the composite control, when being applied to the original system, will place the eigenvalues sufficiently close to the desired locations.     

Minimax control for discrete-time time-varying stochastic systems

This paper gives a self-contained presentation of minimax control for discrete-time time-varying stochastic systems under finite- and infinite-horizon expected total cost performance criteria. Suitable conditions for the existence of minimax strategies are proposed. Also, we prove that the values of the finite-horizon problem converge to the values of the infinite-horizon problems. Moreover, for finite-horizon problems an algorithm of calculation of minimax strategies is developed and tested by using time-varying stochastic systems.     

Disturbance localization with dead-beat control for linear periodic discrete-time systems

In this paper the classical notion of a controlled invariant subspace, together with its main properties, is extended to the case of linear periodic discrete-time systems, and used for deriving necessary and sufficient solvability conditions for the disturbance-localization problem and a synthesis procedure for the solution. Moreover, the notions of outer and inner controllable subspaces are introduced and studied for the same class of system, thus allowing the derivation of necessary and sufficient solvability conditions for the disturbance-localization problem with output or state dead-beat control and to give synthesis procedures for the solutions.     

Regulator problem for linear discrete-time systems with non-symmetrical constrained control

The regulator problem is studied for linear discrete-time systems with non-symmetrical constrained control, i.e. systems described by the state equation x _k+1 = Ax _k + Bu _k, where u _k ? Ω, and u _k = Fx _k. Necessary and sufficient conditions allowing us to obtain the largest non-symmetrical polyhedral domain of positive invariance and contractivity with respect to motions of the system in the closed loop are established. The case of symmetrically constrained control is obtained as a particular case.     

Regulator problem for uncertain linear discrete-time systems with constrained control

A necessary and sufficient condition to test the robustness of a regulator of uncertain linear systems with constrained control is given. The candidate regulator for this test is that stabilizing nominal systems. An illustrative example is also given.     

Optimal control of discrete-time systems with time-lag controls

Various optimal control problems for discrete-time systems with time-lag controls are discussed. Some of the basic features of this type of system are noted. A simple example is given for illustrative purpose.     

离散系统多步观测时滞的H∞输出反馈控制

针对一类多观测时滞离散系统,本文提出了基于Krein空间理论解决H∞输出反馈问题的新方法．利用H∞输出反馈控制问题与不定二次型之间的关系,时滞系统的H∞控制问题分解为LQ问题和时滞的H∞估计问题．通过重组观测,时滞的H∞估计问题可转化为无时滞的H∞估计问题,从而给出由两个Riccati方程决定的H∞控制器存在的充要条件．本文的方法不需要增广系统．     

A new admissibility condition of discrete-time singular systems with time-varying delays

This paper gives a novel delay-dependent admissibility condition of discrete-time singular systems with time-varying delays. For convenience, the time-varying delay is assumed to be the sum of delay lower bound and the integral multiples of a constant delay. Specially, if the constant delay is of unit length, the delay is an interval-like time-varying delay. The proposed admissibility condition is presented and expressed in terms of linear matrix inequality (LMI) by Lyapunov approach. Generally, the uncertainty of time-varying delay would lead to conservatism. In this paper, this critical issue is tackled by accurately estimating the time-varying delay. Consequently, the proposed admissibility condition is less conservative than the existing results, which is demonstrated by a numerical example.