基于观测器的半马尔可夫跳变系统模型参考跟踪控制

Observer-based Mode Reference Tracking Control for semi-Markov Jump Systems

摘要:

针对具有外部扰动的半马尔可夫跳变系统,研究了基于状态观测器的模型参考输出跟踪控制。具体来说,当系统状态信息不可测量时,提出通过模态依赖的状态观测器去估计系统的状态。为了获得良好的跟踪效果,采用前馈-反馈复合控制思想,提出基于状态观测器的模型参考输出跟踪控制器,其中反馈镇定控制器用于保证闭环系统稳定,前馈补偿控制器用以实现对参考模型输出信号的跟踪。进而将半马尔可夫跳变系统的模型参考跟踪控制问题转化为闭环增广系统稳定性问题,推导出闭环系统随机稳定并满足跟踪性能的充分条件,同时借助凸优化技术可求得相应观测器和控制器。通过一个数值仿真和对比实验验证了所提方法的可行性和优越性。

Abstract:

For semi-Markov jump systems with external disturbances, an observer-based model reference H∞ output tracking control is studied in this paper. Specifically, when the system state information is unmeasurable, a mode-dependent state observer is proposed to estimate the state of the system. In order to obtain a good tracking effect, a model reference output tracking controller based on state observer is proposed by using the feedforward-feedback composite control idea, in which the feed-back stabilization controller is used to ensure the stability of the closed-loop system, and the feedforward compensation controller is used to track the output signal of the reference model. Furthermore, the model reference tracking control problem for semi-Markov jump systems is transformed into a stability problem for closed-loop augmented systems, and sufficient conditions for asymptotic stability of the closed-loop system to meet H∞ tracking performance are derived. At the same time, the corresponding observer and controller can be obtained by using convex optimization techniques. A numerical simulation and comparative experiment verify the feasibility and superiority of the proposed method.