实际系统中，许多因素会导致系统结构发生随机突变，例如工作环境突然变化、零部件的失效或修复、子系统内部联接的改变等，semi-Markov(SM)跳变系统可以有效描述这类系统。但多模态的频繁跳变会破坏系统稳定性、产生干扰和抖振,给SM跳变系统的控制和综合带来困难。为此，本项目将利用滑模控制算法简单、响应速度快,以及对外界干扰和参数摄动具有鲁棒性的特点，深入研究SM跳变系统滑模控制及状态估计问题，目的是减小SM跳变参数引起的稳态误差、抑制强扰动并提升系统性能。从基本的稳定性分析、滑模面设计入手，拟对转移概率信息进行深入的分析，建立SM跳变系统的低保守稳定性及性能分析条件,进而通过设计合理的积分型滑模面,提出低保守性的滑动模态分析与滑模控制器设计新方法。本项目研究将丰富SM跳变系统滑模控制理论研究体系,也将推动随机系统理论和鲁棒控制的学科交叉发展,具有重要的科学意义和应用价值。

Semi-Markov jump systems (S-MJS) can effectively represent a class of plants with abrupt variations in their structures. These changes can due, for instance in real systems, to sudden environmental disturbances, component failures or repairs, changes in subsystems interconnections, etc. However, frequent shifting between multiple modes would invariably impair system stability, causing disturbances and chattering, thus bringing difficulties to the control and synthesis of S-MJS. Considering the problems mentioned above, we will consider the siding mode control (SMC) and state estimation problems for S-MJS in this project. The main strengths of SMC systems are its robustness to variations of systems parameters and external disturbances, in addition to its fast responsiveness and simple controller structure. Firstly, we will consider the stability analysis and the sliding mode surface design problems. Then, we will intensively study the transformation probabilities information, and build the stability and performance analysis conditions of the S-MJS. Furthermore, by designing reasonable integral sliding mode surface, we will propose new methods of sliding mode control and sliding mode observer design. The research is important to the research on SMC of S-MJS, and also promotes the interdisciplinary development of stochastic systems theory and robust control, which is of great significance in both scientific research and industrial application.