H-infinity control for cascade minimum-phase switched nonlinear systems

This paper is concerned wi th the H-infinity control problem for a class of cascade switched nonlinear systems.Each switched syste m in this class is composed of a zero-input asymptotically stable nonlinear part,which is also a switched system,and a linearizable part which i s controllable.Conditions under which the H-infinity con trol problem is solvable under arbitrary switching l aw and under some designed switching law are der ived respectively.The nonlinear state feedback and s witching law are designed.We exploit the structural characteristics of the switched nonlinear systems t o construct common Lyapunov functions for arbitrary switching and to find a single Lyapunov function for designed switching law.The proposed methods do not rely on the solutions of Hamilton-Jacobi in equalities.     

H-infinity control for switched and impulsive singular systems

A new model of dynamical systems is proposed which consists of singular systems with impulsive effects, i.e., switched and impulsive singular systems （SISS）. By using the switched Lyapunov functions method, a sufficient condition for the solvability of the H-infinity control problem for SISSs is given which generalizes the H-infinity control theory for singular systems to switched singular systems with impulsive effects. Then the sufficient condition of solvablity of the H-infinity control problem is presented in terms of linear matrix inequalities. Finally, the effectiveness of the developed aooroach for switched and imoulsive singular svstems is illustrated by a numerical example.     

Observer-based robust H-infinity control for uncertain switched systems

The problem of observer-based robust H-infinity control is addressed for a class of linear discrete-time switched systems with time-varying norm-bounded uncertainties by using switched Lyapunov function method. None of the individual subsystems is assumed to be robustly H-infinity solvable. A novel switched Lypunov function matrix with diagonal-block form is devised to overcome the difficulties in designing switching laws. For robust H-infinity stability analysis, two linear-matrix-inequality-based sufficient conditions are derived by only using the smallest region function strategy if some parameters are preselected. Then, the robust H-infinity control synthesis is studied using a switching state feedback and an observer-based switching dynamical output feedback. All the switching laws are simultaneously constructively designed. Finally, a simulation example is given to illustrate the validity of the results.     

驻留概率信息方法的离散切换系统鲁棒H∞控制

本文通过驻留概率信息的方法,研究了一类离散时间切换系统的鲁棒H∞控制问题.通过对切换系统在每个子系统的驻留概率信息加以利用,建立一种新的切换系统模型.通过共同Lyapunov泛函方法,给出切换系统的鲁棒H∞随机稳定的充分条件.然后,利用锥补线性化的方法得到控制器增益.最后,通过仿真算例验证本文所用方法的有效性.     

Stabilization of a class of switched nonlinear systems

The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems con- cerned are of (generalized) switched Byrnes-Isidori canonical form, which has all switched models in (generalized) Byrnes- Isidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization prob- lem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to (generalized) switched Byrnes-Isidori canonical systems are presented. Finally, as an application the stability of switched lorenz systems is investigated.     

Stabilization of a class of switched nonlinear systems

The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of （generalized） switched Byrnes-Isidori canonical form, which has all switched models in （generalized） Byrnes- Isidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to （generalized） switched Byrnes-Isidori canonical systems are presented. Finally, as an application the stability of switched lorenz systems is investigated.     

Control of switched systems with actuator saturation

1 Introduction Switched systems are composed of a set of subsystems and a switching rule designating which subsystem to be actuated at each moment. Switched systems are commonly found in various engineering practice, such as in auto- motive engine control systems, chemical process control, robotic manufacture, multiple-model systems and so on. In the past decade, many literatures have been devoted to the study of switched systems. Stability is an important issue in the analysis and synthesis o…     

Output feedback control of switched nonlinear systems using multiple Lyapunov functions

This work presents a hybrid nonlinear control methodology for a broad class of switched nonlinear systems with input constraints. The key feature of the proposed methodology is the integrated synthesis, via multiple Lyapunov functions, of “lower-level” bounded nonlinear feedback controllers together with “upper-level” switching laws that orchestrate the transitions between the constituent modes and their respective controllers. Both the state and output feedback control problems are addressed. Under the assumption of availability of full state measurements, a family of bounded nonlinear state feedback controllers are initially designed to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding stability region for each mode. A set of switching laws are then designed to track the evolution of the state and orchestrate switching between the stability regions of the constituent modes in a way that guarantees asymptotic stability of the overall switched closed-loop system. When complete state measurements are unavailable, a family of output feedback controllers are synthesized, using a combination of bounded state feedback controllers, high-gain observers and appropriate saturation filters to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding output feedback stability regions in terms of the input constraints and the observer gain. A different set of switching rules, based on the evolution of the state estimates generated by the observers, is designed to orchestrate stabilizing transitions between the output feedback stability regions of the constituent modes. The differences between the state and output feedback switching strategies, and their implications for the switching logic, are discussed and a chemical process example is used to demonstrate the proposed approach.     

Probabilistic sorting and stabilization of switched systems

In this paper, we consider Lyapunov stability of switched linear systems whose switching signal is constrained to a subset of indices. We propose a switching rule that chooses the most stable subsystem among those belonging to the subset. This rule is based on an ordering of the subsystems using a common Lyapunov function. We develop randomized algorithms for finding the ordering as well as for finding a subset of systems for which a common Lyapunov function exists. It is shown that the class of randomized algorithms known as the Las Vegas type is useful in the design procedure. A third-order example illustrating the efficacy of the approach is presented.     

一类大时滞非线性网络控制系统的H∞保成本控制

本文研究一类大时滞不确定非线性网络控制系统的H∞保成本控制问题. 首先将具有随机大时滞的网络控制系统模型化为具有不确定系数的离散时间系统模型. 然后利用Lyapunov稳定性理论和线性矩阵不等式方法, 给出H∞保成本控制律的存在条件和H∞保成本控制器的设计方法. 进而通过求解凸优化问题得到最优鲁棒H∞保成本控制器. 最后仿真结果验证了该控制算法的有效性.     

H∞ control for a class of cascade switched nonlinear systems

In this paper, we investigate the H_∞ control problem for a class of cascade switched nonlinear systems consisting of two nonlinear parts which are also switched systems using the multiple Lyapunov function method. Firstly, we design the state feedback controller and the switching law, which guarantees that the corresponding closed‐loop system is globally asymptotically stable and has a prescribed H_∞ performance level. This method is suitable for a case where none of the switched subsystems is asymptotically stable. Then, as an application, we study the hybrid H_∞ control problem for a class of nonlinear cascade systems. Finally, an example is given to illustrate the feasibility of our results. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings

This paper is concerned with the global stabilization problem for switched nonlinear systems in lower triangular form under arbitrary switchings. Two classes of state feedback controllers and a common Lyapunov function (CLF) are simultaneously constructed by backstepping. The first class uses the common state feedback controller which is independent of switching signals; the other class utilizes individual state feedback controllers for the subsystems. As an extension of the designed method, the global stabilization problem under arbitrary switchings for switched nonlinear systems in nested lower triangular form is also studied. An example is given to show the effectiveness of the proposed method.     

Convergence rate of nonlinear switched systems

This paper is concerned with the convergence rate of the solutions of nonlinear switched systems.We first consider a switched system which is asymptotically stable for a class of switching signals but not for all switching signals. We show that solutions corresponding to that class of switching signals converge arbitrarily slowly to the origin.Then we consider analytic switched systems for which a common weak quadratic Lyapunov function exists. Under two different sets of assumptions we provide explicit exponential convergence rates for switching signals with a fixed dwell-time.     

Global stabilization for a class of switched nonlinear feedforward systems

The problem of global stabilization for a class of switched nonlinear feedforward systems under arbitrary switchings is investigated in this paper. Based on the integrator forwarding technique and the common Lyapunov function method, we design bounded state feedback controllers of individual subsystems to guarantee asymptotic stability of the closed-loop system. A common coordinate transformation of all subsystems is exploited to avoid individual coordinate transformations for subsystems that are required when applying the forwarding recursive design scheme. An example is provided to demonstrate the effectiveness of the proposed design method.     

Adaptive tracking H-infinity control for switched nonlinear systems with unknown control gain sign

This paper addresses the adaptive tracking control scheme for switched nonlinear systems with unknown control gain sign. The approach relaxes the hypothesis that the upper bound of function control gain is known constant and the bounds of external disturbance and approximation errors of neural networks are known. RBF neural networks (NNs) are used to approximate unknown functions and an H-infinity controller is introduced to enhance robustness. The adaptive updating laws and the admissible switching signals have been derived from switched multiple Lyapunov function method. It’s proved that the resulting closed loop system is asymptotically Lyapunov stable such that the output tracking error performance and H-infinity disturbance attenuation level are well obtained. Finally, a simulation example of Forced Duffing systems is given to illustrate the effectiveness of the proposed control scheme and improve significantly the transient performance.     

一类非线性微分代数系统的L2-增益分析及状态反馈∞控制

分析了一类非线性微分代数系统的L₂增益, 并讨论了一类状态反馈H_∞控制问题. 在一定条件下给出了控制器的设计, 并保证了闭环指数为 1且零解渐近稳定.     

Absolute exponential stability and stabilization of switched nonlinear systems

This paper is concerned with the problems of absolute exponential stability and stabilization for a class of switched nonlinear systems whose system matrices are Metzler. Nonlinearity of the systems is constrained in a sector field, which is bounded by two odd symmetric piecewise linear functions. Multiple Lyapunov functions are introduced to deal with the stability of such nonlinear systems. Compared with some existing results obtained by the common Lyapunov function approach in the literature, the conservatism of our results is reduced. All present conditions can be solved by linear programming. Furthermore, the absolute exponential stabilization for the considered systems is designed by the state-feedback and average dwell time switching strategy. Two examples are also given to illustrate the validity of the theoretical findings.     

一类切换线性奇异系统的H∞控制

研究一类由任意有限多个奇异子系统组成的切换奇异系统的状态反馈和动态输出反馈H∞控制问题.利用共同Lyapunov函数方法和凸组合技术,给出由矩阵不等式表示的控制器存在的充分条件,并设计了相应的子控制器和切换策略.分别采用矩阵变换和消元法,将矩阵不等式分别转化为一组线性矩阵不等式(LMIs).数值算例说明了所提方法的有效性和可行性.     

A converse Lyapunov theorem for nonlinear switched systems

In this paper we present a converse Lyapunov theorem for uniform asymptotic stability of switched nonlinear systems. Its proof is a simple consequence of some results on converse Lyapunov theorems for systems with bounded disturbances obtained by Lin et al. (SIAM J. Control Optim. 34 (1996) 124–160), once an association of the switched system with a nonlinear system with disturbances is established.     

基于干扰观测器的一类不确定非线性系统鲁棒H∞控制

为了降低控制器对干扰的要求,基于干扰观测器提出一类多输入多输出不确定非线性系统的鲁棒H∞控制方法．将系统的内部不确定性和外部干扰组成复合干扰,设计基于小波神经网络的复合干扰观测器,并提出干扰观测器的参数调节方案使观测器能以高精度逼近复合干扰．同时在控制器中引入鲁棒控制项用来抑制观测器误差给系统带来的影响,所设计的控制器能使系统的跟踪误差小于一个给定的性能指标．最后给出一个仿真算例验证了本控制方案的有效性．