Markovian 跳变广义随机切换系统的稳定性及滑模控制与应用研究

The sliding mode control problem of Markovian jump systems has attracted many interests.In fact, it is an open problem and still remain challenging.(1) When the system is in mode 1 (say), the state is attracted tosliding surface 1, what happens if switching occurs BEFORE the state reaches the sliding surface of mode 1? How can your control preventthis to happen? If this happens, there is a possibility that the state will NOT reach any sliding surface.(2) When the system state has reached the sliding surface 1 (say) andundergoes sliding motion, switching to mode 2 will render the state lying outside the sliding surface 2, this situation will happen always whenever a switching occurs (and infinitely frequent), the conclusion is that the state will not stay within one sliding surface all the time. We have found a solution to this question and the results have been submitted to Automatica and are under the third round review. This project is devoted to investitation of sliding mode control for Markovian jump time-delay singular systems with general incomlete transition rates (MJTDSSINTRR) and its applications. We try to find the new sliding-mode design methods and resuts for modeling, analisys and simulation of this kind of singular systems. The focuses in detail are as follows: Basic sliding mode control theory of MJTDSSINTRR,including the existence, reachability problem, robustness and stability of the sliding mode dynamics; The analysis and design of sliding-mode controller for singular stochastic time-delay systems or stochastic time-delay systems with Markovian switching; Establish sliding mode control theory for the large scale stochastic time-delay singular systems; Discuss scattered sliding mode motion law, and present sliding mode motion equation and reachability conditions; Probe the numerical method and computer simulation to sliding mode control, and apply the findings to attitude control of missile and robot systems.

Markovian 跳变随机系统的分析和综合还有许多问题需要解决。 Markovian 跳变随机系统的变结构控制最关键难题就是该类系统的滑模切换面的设计问题。现有文献中针对随机切换系统设计的滑模切换面都是模式依赖的，这使系统从一种模式转移到另一种模式，系统轨线可能根本达不到切换面，从而使滑模控制无效。本项目将力争解决上述问题，研究Markovian 跳变时滞广义随机变结构控制系统的建模、分析与仿真以及滑模设计新方法。内容包括：带有不确定转移概率Markovian 跳变随机广义系统滑模控制的基本理论（滑模的存在性、滑模有限时间可达性、滑模的逼近性、鲁棒性和稳定性）；重点解决目前还没有很好解决的带有Markovian跳变时滞广义系统的滑模切换面设计问题；研究时滞随机系统在实用可达意义下的滑动模控制，给出数值解法和计算仿真，并将得到的理论应用到水下机器人控制系统，导弹和卫星姿态控制等实际系统中。

Markovian 跳变随机系统的变结构控制最关键难题就是该类系统的滑模切换面的设计问题。文献中针对随机跳变系统设计的滑模切换面大都是模式依赖的，这使系统从一种模式转移到另一种模式，系统轨线可能根本达不到切换面，从而使滑模控制无效。本项目研究了Markovian 跳变时滞随机变结构控制系统的建模、分析与仿真以及滑模设计新方法。主要研究了带有不确定转移速率的Markovian 跳变随机广义系统和Markovian 跳变中立型系统滑模控制的基本理论（滑模的存在性、滑模有限时间可达性、滑模的逼近性、鲁棒性和稳定性），重点解决了带有Markovian 跳变系统的滑模切换面设计问题，研究时滞随机系统在实用可达意义下的滑动模控制，给出数值解法和计算仿真，并将得到的理论应用到机器人控制系统等实际系统中。