基于耗散性理论的切换随机时滞系统输出跟踪与调节问题研究

Due to more objective and proper characterization of actual systems dynamic behaviors, analysis and synthesis of switched stochastic time-delay systems have recently gained considerable attention in the field of switched systems. However, dissipativity, and output tracking and regulation for switched stochastic time-delay systems, as the desirable properties linking inputs and outputs, remain open and challenging problems. This motivates us to investigate the dissipativity and use of dissipativity in solution of output tracking and regulation problems for switched systems subject to stochastic disturbance and time-delay. The adoption of multiple/piecewise supply rates, multiple/piecewise storage functions and cross-supply rates are exploited to properly describe energy changing across individual subsystems and dissipativity concept for switched stochastic time-delay systems. Criteria and design schemes on switching rule are put forward to assure switched stochastic time-delay systems to be dissipative. Once the dissipativity is guaranteed, the output tracking and regulation problems of switched stochastic time-delay systems are solvable via designed feedback controllers. The corresponding issues are also involved under asynchronous switching. This project presents a framework of output tracking and regulation for switched stochastic time-delay systems, which is also an improvement and development of the dissipativity theory and output tracking and regulation problems for switched systems.

切换随机时滞系统因能够更客观、恰当地刻画实际系统的动态行为，近年来在切换系统领域引起了广泛的关注。然而作为联系系统输入输出关系的重要性质，切换随机时滞系统的耗散性和输出跟踪与调节控制问题的研究结果尚不多见。这启发了本项目考虑切换随机时滞系统的耗散性以及基于耗散性理论探讨切换随机时滞系统的输出跟踪与调节问题。本项目通过引入多/分段存储函数、多/分段供给率和交叉供给率来描述系统能量的变化规律，给出切换随机时滞系统的耗散性定义,得到使得系统耗散的切换信号设计方案和判据，并将耗散性用于处理系统的输出跟踪与调节问题，进而在异步切换条件下探讨基于耗散性理论的切换随机时滞系统的输出跟踪与调节问题，构建切换随机时滞系统的输出跟踪与调节控制问题的理论框架，发展和完善切换系统的耗散性理论和输出跟踪与调节问题的设计理论。

作为联系系统输入输出关系的重要性质，切换随机时滞系统的无源性/耗散性和基于无源性/耗散性的输出跟踪与调节控制问题的研究近年来在切换系统领域引起了广泛的关注。本项目从时滞模型、切换时滞系统的输出跟踪和调节问题、切换时滞系统的异步切换控制方法、基于无源性理论的切换随机时滞系统的输出调节问题、以及基于耗散性理论的切换随机时滞系统的输出调节问题五个方面由浅入深地展开课题的研究。最终，本项目分别在同步/异步切换情况下，通过引入多/分段存储函数、多/分段供给率和交叉供给率来描述系统能量的变化规律，给出切换随机时滞系统的无源性/耗散性的定义，得到使得系统无源/耗散的切换信号设计方案和判据，并将无源性/耗散性用于处理系统的输出跟踪与调节问题。本项目构建了切换随机时滞系统的输出跟踪与调节控制问题的理论框架，发展和完善了切换系统的无源性/耗散性理论和输出跟踪与调节问题的设计理论。