随机非完整动力学系统镇定问题研究

Now, the stabilization of stochastic nonholonomic dynamic systems has not been considered in most of the existing results for stochastic nonholonomic systems in which kinematic systems have been discussed. But, the dynamic parts for practical stochastic nonholonomic systems, for example, mobile robots, cannot usually be omitted. Based on backstepping technique and adaptive control, the feedback stabilization for a class of stochastic nonholonomic dynamic systems will be considered in this subject research. The objective is to find a general design method of controllers for these problems. The main innovation points can be summarized as: Firstly, the state feedback and output feedback stabilization of stochastic lower triangular nonholonomic dynamic systems will be studied, especially, the adaptive output feedback stabilization based on reduced-order observer when systems include uncertain parameters and Markovian swicthing. Secondly, the state feedback and output feedback stabilization for a class of feedforward stochastic nonholonomic dynamic systems, especially, when the systems contain nonlinear drifts terms and uncertain parameters, are discussed. Finally, the stabilization of stochastic nonholonomic dynamic mobile robots is considered. We also extend these results to the case of visual servoing. The experiment for the problems will be carried out. The implements of this project will provide some new ideas and methods for the feedback control of stochastic nonholonomic systems.

目前关于随机非完整系统镇定问题的研究对象主要为运动学系统，大都没有考虑动力学部分，但是实际系统，比如移动机器人，一般是不能忽略动力学部分的. 本项目将研究几类随机非完整动力学系统的镇定问题，基于反步技术和自适应控制，探讨这些问题镇定控制器设计的一般方法. 主要研究特色与创新点是：1) 研究基于下三角结构的随机非完整动力学系统的状态反馈和输出反馈镇定问题，特别当系统含有不确定参数和马尔科夫切换时，基于降阶观测器的自适应输出反馈镇定控制器的设计；2) 讨论随机前馈型非完整动力学系统的镇定问题，包括含有非线性飘移项和不确定参数的状态反馈和输出反馈镇定问题；3) 探讨随机非完整移动机器人动力学系统的镇定问题，然后将结论扩展到视觉伺服的情形，并进行试验. 课题的实施将为随机非完整系统反馈镇定理论研究提供新的思路和方法.

本课题以李雅普诺夫稳定性理论和反步技术为工具，研究了几类随机非完整动力学系统镇定问题，给出了镇定控制器设计的一般方法。探讨了基于任意切换的输出反馈镇定问题，给出了一个简单的输出反馈观测器，能简化设计过程，设计的控制器能使参数的计算更简单；讨论了随机非完整移动机器人的输出反馈镇定问题；基于任意切换的随机非完整移动机器人模型，设计了状态反馈镇定控制器，能使系统依概率镇定到原点；分析了随机非完整系统发展的趋势，给出了6 个可能的研究方向；设计了反步反馈镇定和自适应反馈镇定实例，讨论了随机非完整系统的自适应镇定问题；探讨了基于任意切换的随机非完整时滞系统的状态反馈镇定问题。上述课题的实施将为随机非完整系统反馈镇定理论研究提供新的思路和方法，丰富随机系统控制理论.