基于状态观测器的Markov跳变系统的有效预测控制  

Efficient Model Predictive Control for Markovian Jump Systems: An Observer-Based Approach

作　　者：牛寅 宋燕[2] 

机构地区：[1]上海理工大学理学院,上海 [2]上海理工大学控制科学与工程系,上海

出　　处：《建模与仿真》2023年第2期1207-1226,共20页Modeling and Simulation

摘　　要：研究了一类具有多面体参数不确定性和状态和输入硬约束的Markov跳变系统的基于观测器的有效模型预测控制问题。考虑到实际应用中系统状态难以获得,该问题的目的是在EMPC框架下设计基于估计状态的控制器,从而在计算量、初始可行域和控制性能之间取得良好的平衡。通过类Lyapunov函数法、引入自由加权矩阵和不等式技术,解决了变量间耦合引起的非凸性问题。随后,利用“最小–最大”策略,建立了一些模态相关的优化问题,以促进EMPC算法的形成,其中反馈增益和观测器增益是离线设计的,摄动量是通过求解模态相关的在线优化问题得到的。并给出了严格保证EMPC算法可行性和Markov跳变系统均方稳定性的充分条件。最后,通过算例验证了所提方法的有效性。This paper is concerned with the observer-based efficient model predictive control (EMPC) problem for a class of Markovian jump systems (MJSs) subject to polytopic parameter uncertainties and hard constraints on states and inputs. Considering the difficulty of obtaining the system state in the prac-tice, the aim of the proposed problem is to design the estimate state-based controller in the frame-work of EMPC so as to obtain a good balance among the computation burden, the initial feasible re-gion and the control performance. By means of the Lyapunov-like function approach, the introduc-tion of free weighting matrices and inequality techniques, the non-convexity problem caused by couplings between variables is solved. Subsequently, by using the “min-max” strategy, some mode-dependent optimizations are established to facilitate the formation of EMPC algorithm, where the feedback gain and the observer gain are designed off-line and the perturbation is calculated by solving an online optimization dependent of the mode. Furthermore, sufficient conditions are pre-sented to rigidly guarantee the feasibility of the proposed EMPC algorithm and the mean-square stability of the underlying MJSs. Finally, an illustrative example is used to demonstrate the validity of the proposed methods.

关 键 词：状态观测器 加权矩阵 模型预测控制 反馈增益 在线优化 可行域 硬约束 多面体 

分 类 号：G63[文化科学—教育学]