广义Markov跳变系统的非同步控制

Singular Markov jump system model exists widely in a lot of practical systems, such as circuit systems,economic systems and power systems. Thus, the study on singular Markov jump systems is important both in theory and in practice and has already attracted a great deal of attention. Up to now, most existing results on control problem for singular Markov jump systems require an indispensable assumption that the system modes are synchronous with the controller modes. In many practical situations, however, this ideal assumption is difficult to be satisfied. In this project, the control problem is studied for singular Markov jump systems under the situation that the system modes are asychronous with the controller modes. Hidden Markov model is introduced to model the asynchronous phenomenon between the system modes and controller modes. Correspondingly, the resultant closed-loop system is modeled as a singular hidden Markov jump system. The sufficient condition is given to ensure the existence and uniqueness of a solution to singular hidden Markov jump system. Based on the condition, the problems of stochastic stability,H∞ performance analysis and dissipativity are investigated for the closed-loop systems, and the design problem of asynchronous controllers including state feedback controller, dynamic output feedback controller, and static output feedback controller is addressed.The obtained results are applied to robot control systems.

广义Markov跳变系统模型普遍存在于许多实际系统中，比如电路系统、经济系统和电力系统。因此,广义Markov跳变系统的研究具有重要的理论意义和应用价值，并已引起了广泛的关注。迄今为止，关于广义Markov跳变系统控制问题的研究结果大多假设系统模态和控制器模态是同步的。然而，这个理想化的假设在很多时候是很难成立的。本项目在系统模态和控制器模态非同步的情形下，研究广义Markov跳变系统的控制问题。引入隐Markov模型描述系统模态与控制器模态之间的非同步现象。相应地，将闭环系统建模成广义隐Markov跳变系统。给出保证广义隐Markov跳变系统解存在且唯一的充分条件。在此基础上，研究闭环系统的随机稳定性、H∞性能分析和耗散性问题；探讨非同步控制器（包括状态反馈控制器、动态输出反馈控制器和静态输出反馈控制器）的设计问题；最后将所提出的理论用于机器人控制系统。

在系统模态和控制器模态非同步的情形下，本项目研究了广义Markov 跳变系统的控制问题。引入了隐Markov 模型描述系统模态与控制器模态之间的非同步现象。相应地，将闭环系统建模成了广义隐Markov 跳变系统。给出了保证广义隐Markov 跳变系统解存在且唯一的充分条件。在此基础上，研究了闭环系统的随机稳定性、H∞性能分析和耗散性问题；探讨了非同步控制器（包括状态反馈控制器、动态输出反馈控制器和静态输出反馈控制器）的设计问题；最后将所提出的理论用到了机器人控制系统。本项目共发表（含录用）SCI论文28篇，EI论文3篇，其中1篇论文被评为2014年中国百篇最具影响国际学术论文，ESI高被引论文3篇。本项目的完成进一步丰富和发展了广义Markov跳变系统的控制理论，也为相关的实际应用提供更多的理论支持。