Viability decision of linear discrete-time stochastic systems with probability criterion

In this paper, the optimal viability decision problem of linear discrete-time stochastic systems with probability criterion is investigated. Under the condition of sequence-reachable discrete-time dynamic systems, the existence theorem of optimal viability strategy is given and the solving procedure of the optimal strategy is provided based on dynamic programming. A numerical example shows the effectiveness of the proposed methods.     

Stability analysis of discrete-time switched systems: a switched homogeneous Lyapunov function method

This paper addresses the stability issue of discrete-time switched systems with guaranteed dwell-time. The approach of switched homogeneous Lyapunov function of higher order is formally proposed. By means of this approach, a necessary and sufficient condition is established to check the exponential stability of the considered system. With the observation that switching signal is actually arbitrary if the dwell time is one sample time, a necessary and sufficient condition is also presented to verify the exponential stability of switched systems under arbitrary switching signals. Using the augmented argument, a necessary and sufficient exponential stability criterion is given for discrete-time switched systems with delays. A numerical example is provided to show the advantages of the theoretical results.     

带Markov跳的离散时间随机控制系统的最大值原理

本文研究一类同时含有Markov跳过程和乘性噪声的离散时间非线性随机系统的最优控制问题, 给出并证明了相应的最大值原理. 首先, 利用条件期望的平滑性, 通过引入具有适应解的倒向随机差分方程, 给出了带有线性差分方程约束的线性泛函的表示形式, 并利用Riesz定理证明其唯一性. 其次, 对带Markov跳的非线性随机控制系统, 利用针状变分法, 对状态方程进行一阶变分, 获得其变分所满足的线性差分方程. 然后, 在引入Hamilton函数的基础上, 通过一对由倒向随机差分方程刻画的伴随方程, 给出并证明了带有Markov跳的离散时间非线性随机最优控制问题的最大值原理, 并给出该最优控制问题的一个充分条件和相应的Hamilton-Jacobi-Bellman方程. 最后, 通过 一个实际例子说明了所提理论的实用性和可行性.     

Stability margins of discrete-time nonlinear-non-quadratic optimal regulators

The paper derives guaranteed gain, sector and disk margins for discrete-time nonlinear optimal and inverse optimal regulators that minimize a nonlinear-non-quadratic performance criterion. The proposed results provide a generalization of the classical discrete-time, linear-quadratic optimal regulator gain and phase margins.     

Optimal linear estimators for systems with random measurement delays

This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with random measurement delays. A new model that describes the random delays is constructed where possible the largest delay is bounded. Based on this new model, the optimal linear estimators including filter, predictor and smoother are developed via an innovation analysis approach. The estimators are recursively computed in terms of the solutions of a Riccati difference equation and a Lyapunov difference equation. The steady-state estimators are also investigated. A sufficient condition for the convergence of the optimal linear estimators is given. A simulation example shows the effectiveness of the proposed algorithms.     

Singular linear-quadratic optimal control problem for a class of discrete singular systems with multiple time-delays

The singular linear-quadratic optimal control problem for a class of discrete-time linear singular systems with multiple time-delays is investigated. The equivalent relationship between this problem and the non-singular linear-quadratic problem for standard state-space discrete-time linear systems without time-delay is derived, and the necessary and sufficient condition guaranteeing this equivalent relationship is also given. The optimal control is synthesized as state feedback, and the closed-loop system is regular, impulse-free and without time-delay. An example is given to show the validity of the proposed method.     

Decentralized stabilization of large-scale systems with structured uncertainties

The decentralized stabilization problem of large-scale systems with structured time-varying uncertainties is considered. A new sufficient condition is established for asymptotically stabilizing the large-scale perturbed systems using decentralized state feedback controllers. We also consider the use of optimal Perron weightings to reduce conservatism and the extension of the results to discrete-time large-scale systems with structured uncertainties. An illustrative example is given to demonstrate that the new sufficient condition is less conservative than the one reported recently. Another example is also given to illustrate the use of the sufficient condition for stability robustness of discrete-time large-scale systems.     

Optimal linear estimation for systems with multiple packet dropouts

This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with multiple packet dropouts. Based on a packet dropout model, the optimal linear estimators including filter, predictor and smoother are developed via an innovation analysis approach. The estimators are computed recursively in terms of the solution of a Riccati difference equation of dimension equal to the order of the system state plus that of the measurement output. The steady-state estimators are also investigated. A sufficient condition for the convergence of the optimal linear estimators is given. Simulation results show the effectiveness of the proposed optimal linear estimators.     

Robust LQG optimal controller design for multivariable discrete saturating systems with noise spectral uncertainties and non-linear time-varying unmodelled dynamics

A design procedure is proposed for robust linear-quadratic-gaussian (LQG) optimal controller synthesis against noise spectral uncertainties, non-linear time-varying (NLTV) unmodelled dynamics in discrete saturating systems. A robust stability criterion is derived for multivariable stochastic discrete-time systems with NLTV unmodelled dynamics and constrained actuators. An algorithm based on the robust stabilization creterion is presented for synthesing a robust controller not only to minimize the least favourable cost functional but also to satisfy the robust stabilization criterion by specifying an appropriate weighting scalar in the cost functional. A necessary and sufficient condition for the solvability of such a robust stabilization problem is derived by means of the Nevanlinna-Pick interpolation theory. The Wiener Z-domain solution for controller synthesis, the saddle point theory, and the properties of Schur operator (Class S) are employed to treat this problem. Finally, a numerical example is given to illustrate the results.     

Solution of the discrete-time stochastic optimal control problem in the 2-domain

The design of discrete-time optimal multivariate systems is considered in the z-domain. The constant plant can be non-square, unstable and/or non-minimum phase and feedback system dynamics can be modelled. The stationary coloured noise processes are assumed to be represented by discrete rational spectral densities. The system can contain transport delay elements and the effects of plant saturation can be limited by the choice of performance criterion. The system inputs are assumed to contain both stochastic and deterministic components.

The two-stage design procedure is original and it enables the stochastic and deterministic control functions to be separated, A performance criterion is first defined which is insensitive to the deterministic signals and this defines the closed-loop optimal controller. The resulting closed-loop system acts as an optimum regulator to minimize the effects of stochastic disturbances. A second tracking error performance criterion is then specified which determines the optimal reference input to the closed-loop system. This reference signal is generated by two further discrete-time controllers. The first controller ensures that the plant is following a desired trajectory and the second acts as a feedforward controller to counteract measurable disturbances. The minimum variance regulators of Astrom (1970) and Peterka (1972) are also derived from these results.     

控制系统最优降阶技术与应用

本文给出一种新的控制系统最优降阶技术并介绍其在控制系统设计中的应用，文中引入的最优降阶的准则是在指定输入信号时，对降阶模型与原始模型之间误差的加权最小积分方差。广西重点讨论连续系统的降阶算法，但结论同样适合于离散时间系统，文中还将通过一个例子来淙本方法和其它传统方法相比的优越性。     

On the robustness of LQ regulators for discrete-time systems

A sufficient condition for quadratic stabilizability of uncertain linear discrete-time systems using LQ regulators is presented. The true system is represented by a nominal model plus additive terms representing the most common types of uncertainties in the state and input matrices. Sufficient robustness bounds as well as a robustification procedure for discrete-time LQ regulators are presented and the conservativeness of the proposed condition is discussed     

Optimal full-Order filtering for discrete-time systems with random measurement delays and multiple packet dropouts

This paper is concerned with the estimation problem for discrete-time stochastic linear systems with possible single unit delay and multiple packet dropouts. Based on a proposed uncertain model in data transmission, an optimal full-order filter for the state of the system is presented, which is shown to be of the form of employing the received outputs at the current and last time instants. The solution to the optimal filter is given in terms of a Riccati difference equation governed by two binary random variables. The optimal filter is reduced to the standard Kalman filter when there are no random delays and packet dropouts. The steady-state filter is also investigated. A sufficient condition for the existence of the steady-state filter is given. The asymptotic stability of the optimal filter is analyzed.     

Discrete-time optimal feedback controllers with time-multiplied performance indexes

A class of optimal state and output feedback control laws for discrete-time time-invariant linear systems which minimizes a class of discrete-time time-multiplied performance indexes is presented. A necessary condition, an existence condition, and a sufficient condition for the control laws are derived. A simple example is given to illustrate the effectiveness of the proposed control laws.     

Stochastic optimal linear discrete-time feedback control system using available measurements

The stochastic optimal feedback control of linear discrete-time systems with partially observable parameters is synthesized. A quadratic performance criterion is used with discrete noisy measurements. The structure of the regulator is given and the optimal solution is reduced to a two-point boundary-value problem. Comments on the numerical solution schemes are included.     

Minimax指标最优定常输出反馈调节器设计方法

本文在T. Yahagia工作的基础上进一步讨论了minimax指标最优输出反馈设计方法,并将该方法推广到离散系统。给出了计算方法,研制了适用于多种指标函数的CSCAD应用软件。     

Partially observed non-linear risk-sensitive optimal stopping control for non-linear discrete-time systems

In this paper we introduce and solve the partially observed optimal stopping non-linear risk-sensitive stochastic control problem for discrete-time non-linear systems. The presented results are closely related to previous results for finite horizon partially observed risk-sensitive stochastic control problem. An information state approach is used and a new (three-way) separation principle established that leads to a forward dynamic programming equation and a backward dynamic programming inequality equation (both infinite dimensional). A verification theorem is given that establishes the optimal control and optimal stopping time. The risk-neutral optimal stopping stochastic control problem is also discussed.     

Optimal design of PID regulators

Tuning of three-term controllers, a widely popular device for process control, has always been accomplished by semi-empirical rules. The aim of this paper is to establish a link between PID regulators and optimal feedback design for linear systems. After showing how the optimal control theory can be tailored to the design of optimal regulators, the results are extended to the discrete-time case and the feasibility of a microprocessor implementation is assessed with the aid of benchmark tests     

Robust LQG optimal controller synthesis against noise spectral uncertainties and nonlinear time-varying unmodeled dynamics

In this paper, we consider the problem of robust controller synthesis against noise spectral uncertainties and nonlinear time-varying (NLTV) unmodeled dynamics in the discrete LQG (linear-quadratic Gaussian) optimal systems. We derive a necessary and sufficient condition for robust stabilization in multivariable stochastic discrete-time systems with NLTV unmodeled dynamics. Meanwhile, an algorithm based on the robust stabilization criterion is presented for synthesizing a robust controller not only to minimize the least favorable cost functional J but also to satisfy the robust stabilization criterion by specifying an appropriate weighting scalar in the cost functional.     

On variance neutrality of systems within general random parameters

A necessary condition for variance neutrality of discrete-time linear systems within general random parameters and with arbitrary observations is established. It is proved that this condition is sufficient as well if the observations are linear. This result is of importance in connection with separability, of optimal control and state estimation.