Asymptotic stability and disturbance attenuation properties for a class of networked control systems

In this paper, stability and disturbance attenuation issues for a class of Networked Control Systems (NCSs) under uncertain access delay and packet dropout effects are considered. Our aim is to find conditions on the delay and packet dropout rate, under which the system stability and H∞ disturbance attenuation properties are preserved to a desired level. The basic idea in this paper is to formulate such Networked Control System as a discrete-time switched system. Then the NCSs’ stability and performance problems can be reduced to the corresponding problems for switched systems, which have been studied for decades and for which a number of results are available in the literature. The techniques in this paper are based on recent progress in the discrete-time switched systems and piecewise Lyapunov functions.     

不确定离散时滞分段系统的广义H2弹性控制

针对一类不确定离散时滞分段系统,研究了广义H2稳定性分析和带有时滞的状态反馈弹性控制器设计问题.通过构造适当的离散分段二次李亚普诺夫函数,利用分段二次李亚普诺夫稳定性理论,给出了对于所有的容许参数不确定性,闭环系统是广义H2稳定的充分条件;在此基础上,基于线性矩阵不等式(LMI)处理方法,提出了带有时滞的状态反馈弹性控制器增益阵的设计方案.仿真实例验证了所提方法的有效性.     

Stability of sampled-data piecewise affine systems: A time-delay approach

This paper addresses the stability analysis of sampled-data piecewise-affine (PWA) systems consisting of a continuous-time plant in feedback connection with a discrete-time emulation of a continuous-time state feedback controller. The sampled-data system is first considered as a continuous-time system with a variable time delay. Conditions under which the trajectories of the sampled-data closed-loop system will converge to an attracting invariant set are then presented. It is also shown that when the sampling period converges to zero, these conditions coincide with sufficient conditions for non-fragility of the stabilizing continuous-time PWA state feedback controller. The results are successfully applied to a helicopter example.     

A unified dissipativity approach for stability analysis of piecewise smooth systems

The main objective of this paper is to present a unified dissipativity approach for stability analysis of piecewise smooth (PWS) systems with continuous and discontinuous vector fields. The Filippov definition is considered for the solution of these systems. Using the concept of generalized gradients for nonsmooth functions, sufficient conditions for the stability of a PWS system are formulated based on Lyapunov theory. The importance of the proposed approach is that it does not need any a-priori information about attractive sliding modes on switching surfaces, which is in general difficult to obtain. A section on application of the main results to piecewise affine (PWA) systems followed by a section with extensive examples clearly show the usefulness of the proposed unified methodology. In particular, we present an example with a stable sliding mode where the proposed method works and previously suggested methods fail.     

基于切换模糊模型和分段Lyapunov函数的T-S模糊系统时滞依赖H∞控制

研究了离散时滞T-S模糊系统的H无穷控制问题. 首先, T-S模糊系统被转换成等价的切换模糊系统, 基于分段Lyapunov函数, 给出了该系统带有H无穷性能的时滞依赖稳定化控制方法. 所得结论可以用一组线性矩阵不等式表示. 由于考虑了子系统间的相互关系, 因此所得结论较以往结果具有更小的保守性. 最后, 仿真例子说明了所提方法的有效性.     

基于异步观测器的离散分段仿射系统控制: LMI方法

基于分段二次Lyapunov函数为离散分段仿射系统提出了一种基于观测器的控制律. 考虑的主要问题是原系统当前所在作用域未知, 且无法根据测量输出推断. 通过将凸多面体作用域用椭球体外逼近, 并将矩阵等式约束用奇异值分解技术予以处理, 所提控制方法能够被转化为线性矩阵不等式(LMI)描述, 比现有的只能转化为双线性矩阵不等式的方法更容易求解. 最后, 将所提方法应用到混沌系统控制.     

Quadratic stability and stabilization of bimodal piecewise linear systems

This paper deals with quadratic stability and feedback stabilization problems for continuous bimodal piecewise linear systems. First, we provide necessary and sufficient conditions in terms of linear matrix inequalities for quadratic stability and stabilization of this class of systems. Later, these conditions are investigated from a geometric control point of view and a set of sufficient conditions (in terms of the zero dynamics of one of the two linear subsystems) for feedback stabilization are obtained.     

基于LMI方法的离散分段线性系统静态输出反馈控制

研究了离散分段线性系统静态输出反馈控制问题. 基于分段二次李亚普诺夫函数, 给出了静态输出反馈镇定控制器综合的新的充分的线性矩阵不等式条件. 同时, 通过使用Finsler引理, 引入一组具有特殊结构的松弛变量以减少设计保守性. 与以后方法相比, 所提出的方法具有好的性能, 并且在已有方法失效的情况下仍可用. 文中还将此方法推广到H无穷控制. 最后给出三个例子说明方法的有效性.     

一类受限线性系统的最优控制

研究了一类受限线性系统的最优控制问题.对于输入和状态联合受限线性系统的最优控制,引入多参数二次规划方法进行求解;首先将控制问题转化为标准的多参数二次规划问题,然后应用多参数二次规划方法求得系统的可行状态空间及其子空间,并对每个子空间的求出其时变最优控制率,最后归纳上述过程得到一般性结论.方法不仅能使系统约束的处理更加系统化和透明化,还可以获得系统的显式分段仿射控制率.仿真结果表明了该方法的有效性.     

An efficient algorithm for optimal control of PWA systems with polyhedral performance indices

We present an algorithm for the computation of explicit optimal control laws for piecewise affine (PWA) systems with polyhedral performance indices. The algorithm is based on dynamic programming (DP) and represents an extension of ideas initially proposed in Kerrigan and Mayne [(2003). Optimal control of constrained, piecewise affine systems with bounded disturbances. In Proceedings of the 41st IEEE conference on decision and control, Las Vegas, Nevada, USA, December], and Baoti? et al. [(2003). A new algorithm for constrained finite time optimal control of hybrid systems with a linear performance index. In Proceedings of European control conference, Cambridge, UK, September]. Specifically, we show how to exploit the underlying geometric structure of the optimization problem in order to significantly improve the efficiency of the off-line computations. An extensive case study is provided, which clearly indicates that the algorithm proposed in this paper may be preferable to other schemes published in the literature.     

A duality-based convex optimization approach to L2 -gain control of piecewise affine slab differential inclusions

This paper introduces the dual parameter set of a piecewise affine (PWA) system. This is a key concept to enable a convex formulation of PWA controller synthesis for PWA slab differential inclusions using a new convex relaxation. Another important contribution of the paper is to present PWA L₂-gain analysis and synthesis results for PWA systems whose output is also a PWA function of the state (as opposed to a piecewise-linear (PWL) function). Unlike other results existing in the literature, the sufficient LMI conditions in this paper are valid for synthesis, even when the PWA systems include sliding modes. A numerical example with sliding modes illustrates the new approach.     

基于分段Lyapunov 函数的Hammerstein-Wiener 非线性预测控制

针对输入和输出受约束的Hammerstein-Wiener型非线性系统,建立T-S模糊模型,并提出一种基于分段Lyapunov函数的非线性预测控制算法.通过构造分段二次Lyapunov函数,分析非线性系统的稳定性,降低普通二次Lyapunov函数的保守性;通过离线设计分段反馈控制律,在线实施符合条件的反馈控制律,极大程度地提高了在线计算效率.仿真结果验证了该方法的有效性.     

Exponential stabilization of discrete-time switched linear systems

This article studies the exponential stabilization problem for discrete-time switched linear systems based on a control-Lyapunov function approach. It is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise quadratic control-Lyapunov function. Such a converse control-Lyapunov function theorem justifies many of the earlier synthesis methods that have adopted piecewise quadratic Lyapunov functions for convenience or heuristic reasons. In addition, it is also proved that if a switched linear system is exponentially stabilizable, then it must be stabilizable by a stationary suboptimal policy of a related switched linear-quadratic regulator (LQR) problem. Motivated by some recent results of the switched LQR problem, an efficient algorithm is proposed, which is guaranteed to yield a control-Lyapunov function and a stabilizing policy whenever the system is exponentially stabilizable.