随机约束下非齐次Markov跳变系统控制器设计

In modern engineering，a large number of manufacturing systems can be described as Markov jump system, which has both state-evolution and event-driven. The existing major achievements mainly focus on homogeneous Markov jump system whose transition probability matrix is constant. However, in engineering, nonhomogeneous Markov jump system, whose transition probability matrix change over the time period, is widespread. It is necessary to study its related theory. On the other hand, the actual controller design constraints are unavoidable. In the past, the constraints are described in the form of deterministic constraints, however, this form of constraints cannot describe the constraints with random characteristics, which are widespread in practice. The chance constraints are quantified by the probability given in the form of confidence, which include the information of probability . In this way, many problems in engineering can be involved in the scope of representation, and thus it is of broader engineering significance. Therefore, the study of the controller design for nonhomogeneous Markov jump system subject to chance constraints is of great significance. In this project, based on stochastic programming methods, we view nonhomogeneous Markov jump system as a starting point and study the controller design for such systems subject to chance constraints including the potential problems of stability analysis, controller design, calculation and complexity analysis. The project has abundant theoretical connotation and engineering background.

现代工程中大量制造系统可抽象成同时具有状态演化与事件驱动的Markov跳变系统，现有成果主要针对转移概率矩阵为常数的齐次Markov跳变系统，但工程实际中，转移概率矩阵随时间推移而变化的非齐次Markov跳变系统广泛存在，其相关理论有待进一步研究。另一方面，约束条件在实际控制器设计中不可避免，以往对约束条件的刻画，主要考虑确定性约束的描述形式，但这种形式无法刻画工程实际中广泛存在的具有随机特征的约束条件，而随机约束是以概率置信度量化的形式描述，充分体现出约束的概率信息，使得约束条件可表征的范围大大增加，具有更为广泛的工程意义。因此，研究非齐次Markov跳变系统在随机约束条件下的控制器设计具有重要意义。本项目以非齐次Markov跳变系统为切入点，基于随机规划方法，研究其在随机约束下的控制器设计方案，围绕稳定性，控制器设计，计算量与复杂度等问题展开研究，具有较为丰富的理论内涵和工程意义。

针对现代工程中大量制造系统可抽象成同时具有状态演化与事件驱动的Markov跳变系统，其在随机约束下的控制器设计问题仍然有待解决，其主要难点在于随机约束条件下的稳定性定义及描述，进一步，如何求解相应的优化问题成为关键，在此基础之上，进一步深入设计控制器。本项目运用概率置信度量化的形式描述随机约束，充分体现出约束的概率信息，使得约束条件可表征的范围大大增加，具有更为广泛的工程意义。本项目基于随机规划方法，研究其在随机约束下的控制器设计方案，围绕稳定性，控制器设计，计算量与复杂度等问题展开研究，具有较为丰富的理论内涵和工程意义。本项目首先研究随机约束条件下的稳定性描述方法及定义，在此基础上研究其一般的稳定性理论。进一步，深入研究了随机约束条件下跳变系统的控制器设计问题，从而丰富了随机约束下控制器设计的理论及应用。