不确定非线性切换系统的自适应无源化方法的研究

Switched control systems which is an important class of hybrid systems have been receiving much attention in the control area, due to many engineering applications. On the other hand, passivity theory which is an effective tool for the analysis and design of nonlinear systems forms a system of theory system. For switched nonlinear systems, especially for uncertain switched nonlinear systems, there are few results on quasi-passivity. This project will study adaptive quasi-passification and control design problem for uncertain switched nonlinear system. The research contents include: First, for a class of switched nonlinear systems with unknown nonlinearities, the problem of adaptive quasi-passification is described by using multiple storage functions and multiple supply rates. Then, the stability is obtained for the corresponding closed-systems. Second, the condition and the dual design method of adaptive controllers and switching signal for the adaptive quasi-passification, stabilization and disturbance rejection problems of uncertain switched nonlinear systems with unknown nonlinearities are proposed by combining the adaptive backstepping design technique with intelligent control method. Furthermore, the results on adaptive quasi-passification and stabilization for a class of uncertain switched nonlinear systems with unknown nonlinearities and unmodeled dynamics are obtained. Finally, the adaptive quasi-passification and stabilization problems for uncertain switched systems are solved by the average dwell time method. The research results of project will provide effective methods of analysis and design for the study of uncertain switched nonlinear systems. Moreover, the results will develop and improve passivity theory of switched systems.

切换系统是一类重要的混杂系统。因其广泛的应用背景而备受关注。另一方面，无源性理论是非线性系统分析和设计有力工具，已形成比较系统的理论体系。但对非线性切换系统无源性的研究，特别是对不确定非线性切换系统拟无源性的研究，几乎没有结果。本项目主要研究不确定非线性切换系统的自适应拟无源化及控制设计问题。研究内容包括：针对一类含有未知函数的非线性切换系统，首先，采用多存储函数与多供给率描述自适应拟无源化问题，并得到相应闭环系统的稳定性；其次，结合反步递推设计方法、智能控制方法，提出自适应拟无源化、镇定、干扰抑制等问题的条件及自适应控制器和切换信号双重设计方法；进一步考虑未建模动态，获得自适应拟无源化及镇定结果。最后，利用平均驻留时间方法解决不确定非线性切换系统的自适应拟无源化及镇定问题。项目的研究成果为不确定非线性切换系统的研究提供有效的分析和设计方法，丰富和发展非线性切换系统无源性理论体系。

作为一类特殊的混杂系统，切换系统具有较强的实际应用背景。因而受到了学者们的广泛关注。另一方面，无源理论是系统分析与设计的有力工具。受到较大不确定性影响，无法实现系统的精确反馈无源化，只能实现在球以外是反馈无源的，也就是几乎处处无源或拟无源；因此，本项目主要研究了不确定切换非线性系统的自适应拟无源化及控制设计问题。首先，研究不确定切换非线性系统的自适应无源化；提出了切换律和自适应控制器的设计方法；利用无源化方法解决了切换非线性系统的镇定、输出跟踪、输出调节、干扰抑制等问题；其次，研究不确定切换非线性系统的自适应拟无源化及控制设计问题；建立了一般切换非线性系统拟无源理论框架；提出了切换非线性系统拟无源概念及条件；获得了闭环系统解的最终有界性；并针对一类含有未知函数的切换非线性系统，结合反步递推设计方法、智能控制方法，解决了自适应拟无源化、镇定、 跟踪等问题，提出了自适应控制器和切换信号双重设计方法；最后，进一步考虑未建模动态，获得了自适应拟无源化及镇定结果。项目的研究成果为不确定切换非线性系统的研究提供有效的分析和设计方法，丰富和发展切换非线性系统无源性理论体系。.本项目取得的研究成果发表在《International Journal of Robust and Nonlinear Control》,《International Journal of Control》,《Nonlinear Analysis: Hybrid Systems》,《Journal of the Franklin Institute》等国际控制领域重要学术期刊和《Control Theory and Applications,l》、《Journal of Control and Decision》等国内期刊及国内重要会议上，其中SCI检索源论文13篇；EI检索论文3篇,中文核心论文1篇。