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

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。

Abstract: 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.