基于随机凸优化算法的不确定跳变系统概率控制

Controller design for systems with uncertain parameters is one of the active areas in control community. Previous methods for solving such problem are mainly focused on the worst case of uncertainty, and the controllers designed are constrained under all possible values of the uncertainty, however, all the design process is focused on a special “ill” situation (the worst-case plant), which could not be representative of the majority of admissible plants, and it also has difficulty in computating. The controller design under probabilistic meaning does not satisfies all the constraints and a small fraction probability of stability is allowed to be violated. This approach can be seen as a relaxation of the worst-case paradigm and thus makes it easier to solve the problem. On the other hand, controller design for uncertain system under probabilistic meaning are mainly focuses on dynamic systems evolving singly along time, however there are plenty of hybrid systems which involve both time evolving and event triggering, thus it is necessary to develop new control theories for this type of systems. Based on the random convex optimization method, this project is focused on controller design for uncertain Markov jump systems and investigates the problems of probabilistic stability, computational complexity, etc. Therefore, the project is of profound theoretical and practical significance..

不确定参数下系统的控制器设计是控制理论中非常活跃的领域之一。以往对时域不确定系统的研究，主要是考虑在不确定性范数有界的最坏情况下进行的，即要求满足所有不确定性约束，但这样设计出来的控制器在大多数可行的对象中并不具有代表性，且在数值计算上较为困难。而概率意义下的不确定性处理方法，允许有一定的小概率风险不满足系统稳定性的要求，本质上可以看成最坏情况下不确定性处理的一种松弛，以换取算法的可解性与易实现性，具有更好的工程意义。另一方面，目前概率意义下不确定系统控制器设计方法主要针对单一时间演化的动态系统，而现代工程中存在大量同时具有状态时间演化与模态事件驱动的混杂系统，需要新的可以处理概率意义下不确定混杂系统的理论。本项目以不确定参数环境下Markov跳变系统为切入点，基于随机凸优化方法，研究概率意义下的控制器设计问题，围绕概率稳定性，计算复杂度等问题开展研究。项目具有深刻的理论和实际意义。

不确定参数下系统的控制器设计是控制理论中非常活跃的领域之一。以往对时域不确定系统的研究，主要是考虑在不确定性范数有界的最坏情况下进行的，即要求满足所有不确定性约束，但这样设计出来的控制器在大多数可行的对象中并不具有代表性，且在数值计算上较为困难。而概率意义下的不确定性处理方法，允许有一定的小概率风险不满足系统稳定性的要求，本质上可以看成最坏情况下不确定性处理的一种松弛，以换取算法的可解性与易实现性，具有更好的工程意义。.本课题进展期间，针对带有系统参数不确定的跳变系统，考虑稳定性，控制器设计以及故障检测问题，围绕概率稳定性，计算复杂度等问题开展研究并在本领域国际学术期刊发表SCI收录论文数篇。项目具有深刻的理论和实际意义。