随机非完整系统镇定问题研究
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摘要
反馈控制是随机非线性系统镇定中的基本问题之一，它主要包括状态反馈镇定和输出反馈镇定两种。本文主要讨论了随机非完整系统的镇定问题。首先论述了研究对象的背景和目前的研究现状，引入了一类带有随机扰动的非完整移动机器人模型，并给出了随机非完整链式系统的一般形式，简要介绍了本文需要的基础知识；然后探讨了三类不确定随机非完整链式系统的状态反馈镇定问题；对于带有马尔科夫切换的随机非完整系统，设计了状态反馈和输出反馈镇定器；最后研究了一类随机非完整移动机器人的状态反馈镇定问题。主要研究内容可分为以下几个方面：
1、针对三类不确定随机非完整系统，基于Backstepping技术，设计了自适应状态反馈控制器，给出了切换策略，它们能够保证闭环系统是依概率渐进稳定的；
2、对于带有马尔科夫切换和漂移项的随机非完整系统，当部分状态不可测时，设计了输出反馈控制器，该控制器能够使闭环系统是大范围依概率渐进稳定的，并给出了随机非线性系统解几乎必然有界的一个充分条件；
3、当全部状态可测时，讨论了带有马尔科夫切换的随机非完整系统的状态反馈镇定问题。
4、给出了视觉伺服随机非完整移动机器人的模型，该模型不是严格满足三角结构，针对该模型设计了状态反馈控制器和切换策略，它们能保证系统状态依概率渐进镇定到平衡点。
5、对上述研究结果，结合Matlab给出了仿真实例，特别是非完整移动机器人，仿真结果验证了控制器的有效性。
Feedback control, which mainly contains state-feedback control and output-feedback control, is one of the basic problems for the stabilization of stochasticnonlinear systems. This paper is largely concerned with the stabilization problems ofstochastic noholonomic systems. Firstly, the backgrounds and developments ofnonholonomic control systems, stochastic nonlinear systems and stochasticnonholonomic systems are introduced. A model of stochastic nonholonomic mobilerobots is given and the general form of stochastic nonholonomic chained systems isintroduced. Some basic concepts and results are briefly given. The problems ofstate-feedback stabilization for three types of uncertain stochastic nonholonomicsystems are discussed. Then, for stochastic nonhlonomic systems with Markovianswitching, we design state-feedback and output-feedback controllers. In the end, theproblem of state-feedback stabilization for stochastic nonhlonomic mobile robots isstudied. The main results and innovative points can be summarized as follows:
1．For three types of uncertain stochastic nonholonomic systems, based onbackstepping method, we design the adaptive state-feedback controllers and switchinglaw, which guarantee that the closed systems are asymptotically stabilized inprobability.
2．When parts of the states are unmeasured, the output-feedback stabilization forstochastic nonhlonomic systems with Markovian switching is discussed. A Sufficientcondition for almost surely bounded solution of stochastic nonholonomic systems withMarkovian switching is given. The designed controllers and switching law guaranteethat the closed systems are largly asymptotically stabilized in probability.
3．If all states can be measured, we studied the state-feedback stabilization forstochastic nonhlonomic systems with Markovian switching.
4．We establish the model of stochastic nonholonomic mobile robots based onvisual servoing, which are not strict triangle structure. The state-feedback controllers and switching law, which guarantee that the closed systems are asymptoticallystabilized in probability, are presented for stochastic nonhlonomic systems.
5．Based on the research results mentioned above, some simulation examples,especially, stochastic nonholonomic mobile robots, are given. These simulation resultswith MATLAB show the effectiveness of designed controllers.
1、针对三类不确定随机非完整系统，基于Backstepping技术，设计了自适应状态反馈控制器，给出了切换策略，它们能够保证闭环系统是依概率渐进稳定的；
2、对于带有马尔科夫切换和漂移项的随机非完整系统，当部分状态不可测时，设计了输出反馈控制器，该控制器能够使闭环系统是大范围依概率渐进稳定的，并给出了随机非线性系统解几乎必然有界的一个充分条件；
3、当全部状态可测时，讨论了带有马尔科夫切换的随机非完整系统的状态反馈镇定问题。
4、给出了视觉伺服随机非完整移动机器人的模型，该模型不是严格满足三角结构，针对该模型设计了状态反馈控制器和切换策略，它们能保证系统状态依概率渐进镇定到平衡点。
5、对上述研究结果，结合Matlab给出了仿真实例，特别是非完整移动机器人，仿真结果验证了控制器的有效性。
Feedback control, which mainly contains state-feedback control and output-feedback control, is one of the basic problems for the stabilization of stochasticnonlinear systems. This paper is largely concerned with the stabilization problems ofstochastic noholonomic systems. Firstly, the backgrounds and developments ofnonholonomic control systems, stochastic nonlinear systems and stochasticnonholonomic systems are introduced. A model of stochastic nonholonomic mobilerobots is given and the general form of stochastic nonholonomic chained systems isintroduced. Some basic concepts and results are briefly given. The problems ofstate-feedback stabilization for three types of uncertain stochastic nonholonomicsystems are discussed. Then, for stochastic nonhlonomic systems with Markovianswitching, we design state-feedback and output-feedback controllers. In the end, theproblem of state-feedback stabilization for stochastic nonhlonomic mobile robots isstudied. The main results and innovative points can be summarized as follows:
1．For three types of uncertain stochastic nonholonomic systems, based onbackstepping method, we design the adaptive state-feedback controllers and switchinglaw, which guarantee that the closed systems are asymptotically stabilized inprobability.
2．When parts of the states are unmeasured, the output-feedback stabilization forstochastic nonhlonomic systems with Markovian switching is discussed. A Sufficientcondition for almost surely bounded solution of stochastic nonholonomic systems withMarkovian switching is given. The designed controllers and switching law guaranteethat the closed systems are largly asymptotically stabilized in probability.
3．If all states can be measured, we studied the state-feedback stabilization forstochastic nonhlonomic systems with Markovian switching.
4．We establish the model of stochastic nonholonomic mobile robots based onvisual servoing, which are not strict triangle structure. The state-feedback controllers and switching law, which guarantee that the closed systems are asymptoticallystabilized in probability, are presented for stochastic nonhlonomic systems.
5．Based on the research results mentioned above, some simulation examples,especially, stochastic nonholonomic mobile robots, are given. These simulation resultswith MATLAB show the effectiveness of designed controllers.
引文
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