一类含扰动的非线性切换系统稳定性分析

首先在非零扰动情况下,利用平均滞留时间的方法给出保证切换系统一致有界或一致终极有界的条件以及最终边界.当切换系统中含有不稳定子系统时,证明了当切换规则满足一定条件时,仍可保证切换系统是有界的.然后在零扰动情况下,给出了扰动非线性切换系统稳定的充分条件.最后通过仿真算例说明了所得结果的有效性.     

随动定向战斗部模糊-单神经元PID控制

防空导弹随动战斗部在高速转动时存在干扰和大过载情况,伺服电机摩擦的产生,系统具有严重的非线性特点,现有的PID和模糊神经元自适应PID控制难以满足快速准确的控制要求,针对上述问题,提出了一种模糊-单神经元PID切换控制策略,结合了传统PID、单神经元网络和模糊控制的优点,在控制前期误差较大的时候采用模糊控制,在控制后期采用单神经元PID控制,并引入切换因子函数来减小了切换冲击.仿真结果显示,改进控制策略提高了随动系统的跟踪精度和速度,克服了非线性问题,满足了随动定向战斗部的工作要求.     

一类非线性切换系统输出与扰动的解耦

研究了一类单输入单输出非线性切换系统输出与扰动的完全解耦的可解性问题,提出了此类非线性切换系统输出与扰动的完全解耦的充要条件,并进一步给出了干扰可测并且能够用于反馈控制律的设计的情况下系统输出与扰动的完全解耦的条件.最后给出了仿真实例说明了本文结果的有效性.     

非线性切换系统的二次镇定

研究多输入多输出非线性切换系统在任意切换律下的二次镇定问题.当非线性切换系统有一致规范型,且一致规范型的零动态在任意切换律是渐近稳定时,设计出状态反馈控制律,并构造出所有闭环子系统的共同二次Lyapunov函数,实现了这类多输入多输出非线性切换系统在任意切换策略下的二次可镇定性,所得结果也适用于线性切换系统。     

一类非线性时变不确定系统的镇定

讨论含时变在数和内部结构不确定性的时变仿射非线性系统的反馈镇定问题，通过引用时变非线性系统的标准形和零动态概念，构造出变结构型的具有状态反馈形式的控制规律。该控制规律使相应闭环系统局部一致渐近稳定。     

基于未建模动态补偿的非线性自适应切换控制方法

针对一类不确定的离散时间零动态不稳定的单输入-单输出(Single-input single-output, SISO)非线性系统,提出了一种基于未建模动态补偿的非线性控制器. 采用自适应神经模糊推理系统(Adaptive-network-based fuzzy inference system, ANFIS)和一一映射相结合的方法估计未建模动态.在此基础上,提出了由线性自 适应控制器、非线性自适应控制器以及切换机制组成的自适应切换控制方法.该方法通过对上述两种控制器的切换, 保证闭环系统输入输出信号有界的同时,改善系统性能.本文将要求未建模动态全局有界的条件放宽为线性增长, 建立了所提自适应控制方法的稳定性和收敛性分析.通过仿真比较和水箱的液位控制实验,验证了所提方法的有效性.     

不确定非线性时滞切换广义系统的鲁棒无源控制

将无源的概念从广义系统扩散到切换广义系统之中,进而研究了一类带有非线性扰动项和时滞不确定项的切换广义系统的无源控制问题。并且系统中的不确定性要满足有界条件。首先,基于一类广义Lyapunov函数结合线性矩阵不等式,获得了使非线性切换广义系统能够渐近稳定且严格无源的充分条件。然后,根据已给的条件设计出鲁棒无源控制器,使得闭环广义切换系统对于所有容许的不确定性是严格无源的。最后运用Matlab中的LMI工具箱具体给出实例,证明其可行性。     

非线性随机多智能体系统的固定时间一致性

本文研究了在固定拓扑和切换拓扑下,非线性随机多智能体系统的固定时间一致性问题.首先针对固定拓扑,设计了一种非线性控制协议,利用随机Lyapunov稳定性理论和代数图论给出了实现固定时间一致性的充分条件和收敛时间的上界值,随后将结论推广至切换拓扑,设计的切换拓扑子图的并集只需要满足连通条件,即可实现固定时间一致,模型更具一般性.最后,两个仿真实例进一步验证了理论结果的有效性.     

基于神经网络和多模型的非线性离散自适应控制

针对一类非线性离散时间单变量系统,提出了基于多模型切换策略的非线性自适应控制方法.首先将被控系统划分为多个工作区间,然后在每个工作区间内建立1个线性自适应控制器和1个非线性神经网络自适应控制器.线性控制器可以保证系统的稳定性,神经网络非线性控制器可以有效的改善系统的暂态性能,采用有效的切换策略可以在保证系统稳定的情况下很好的改善系统的性能.仿真结果验证了所提出方法的有效性.     

一类多输入级联非线性切换系统的全局镇定

研究一类带有部分线性系统的多输入级联非线性切换系统的全局镇定问题. 首先, 给出保证线性部分有一致规范型的充分条件. 其次, 利用一致规范型及其零动态的共同二次Lyapunov函数设计状态反馈使得线性部分在任意切换律下镇定. 最后, 通过构造共同Lyapunov函数能实现闭环系统在任意切换律下的全局渐近稳定性.     

Quadratic stabilization of switched nonlinear systems

In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated. When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law. The results of this paper are also applied to switched linear systems. Supported partially by the National Natural Science Foundation of China (Grant No. 50525721)     

Average dwell time based stability analysis for nonautonomous continuous‐time switched systems

Inspired by the idea of multiple Lyapunov functions and the average dwell time, we address the stability analysis of nonautonomous continuous‐time switched systems. First, we investigate nonautonomous continuous‐time switched nonlinear systems and successively propose sufficient conditions for their (uniform) stability, global (uniform) asymptotic stability, and global (uniform) exponential stability, in which an indefinite scalar function is utilized to release the nonincreasing requirements of the classical multiple Lyapunov functions. Afterwards, by using multiple Lyapunov functions of quadratic form, we obtain the corresponding sufficient conditions for (uniform) stability, global (uniform) asymptotic stability, and global exponential stability of nonautonomous switched linear systems. Finally, we consider the computation issue of our current results for a special class of nonautonomous switched systems (ie, rational nonautonomous switched systems), associated with two illustrative examples.     

Global uniform input-to-state stabilization of large-scale interconnections of MIMO generalized triangular form switched systems

We solve the problem of global uniform input-to-state stabilization with respect to external disturbance signals for a class of large-scale interconnected nonlinear switched systems. The overall system is composed of switched subsystems each of which has the nonlinear MIMO generalized triangular form, which (in contrast to strict-feedback form) has non-invertible input–output maps. The switching signal is an arbitrary unknown piecewise constant function and the feedback constructed does not depend on the switching signal.     

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.     

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.     

Uniform Asymptotic Stability of Nonlinear Switched Systems With an Application to Mobile Robots

This paper is concerned with the study of, both local and global, uniform asymptotic stability for general nonlinear and time-varying switched systems. Two concepts of Lyapunov functions are introduced and used to establish uniform Lyapunov stability and uniform global stability. With the help of output functions, an almost bounded output energy condition and an output persistent excitation condition are then proposed and employed to guarantee uniform local and global asymptotic stability. Based on this result, a generalized version of Krasovskii-LaSalle theorem in time-varying switched systems is proposed. For switched systems with persistent dwell-time, the output persistent excitation condition is guaranteed to hold under a zero-state observability condition. It is shown that several existing results in past literature can be covered as special cases using the proposed criteria. Interestingly, as opposed to previous work, the main results of this paper are applicable to the situation where some switching systems are not asymptotically stable at the origin. The robust practical regulation problem of nonholonomic mobile robots is studied as a way of demonstrating the power of the proposed new criteria. A novel switching controller is proposed with guaranteed robustness to orientation error and unknown parameters in mobile robots.      

A Note on Marginal Stability of Switched Systems

In this note, we present criteria for marginal stability and marginal instability of switched systems. For switched nonlinear systems, we prove that uniform stability is equivalent to the existence of a common weak Lyapunov function (CWLF) that is generally not continuous. For switched linear systems, we present a unified treatment for marginal stability and marginal instability for both continuous-time and discrete-time switched systems. In particular, we prove that any marginally stable system admits a norm as a CWLF. By exploiting the largest invariant set contained in a polyhedron, several insightful algebraic characteristics are revealed for marginal stability and marginal instability.     

带有不稳定子系统的切换非线性系统的积分输入状态稳定

本文针对带有不稳定子系统的切换非线性系统研究了系统的积分输入状态稳定性问题. 应用导数不定的 类Lyapunov函数得出切换非线性系统的积分输入状态稳定. 导数不定的类Lyapunov函数方法比传统的导数正定 的Lyapunov函数的方法更具有一般性. 文中包含两种情况: 当所有子系统为积分输入状态稳定时, 切换非线性系统 是积分输入状态稳定的; 当部分子系统为非积分输入状态稳定时, 本文证明了切换非线性系统的积分输入状态稳 定. 最后应用一个仿真例子描述了所提结果的有效性.