中文摘要：

针对一类带有扰动、多重状态时滞的凸多面体不确定离散非线性系统,基于预测控制理论提出一种min-max鲁棒预测控制算法。将模型预测控制问题描述为一类无限时域min-max优化问题;采用LMI技术把此问题转变为一类采用LMI描述的约束问题,设计了状态反馈控制器;运用所给信息构造一个改进的Lyapunov-Krasovskii泛函,根据模型预测控制基本原理来求解此优化问题,同时给出了控制器存在的定理及相关证明,进而获得所设计控制器存在的新判据及状态反馈矩阵构造方法,在此基础上给出了鲁棒模型预测控制算法流程。最后,给出了闭环系统渐进鲁棒稳定定理,理论及仿真分析验证了控制器设计的可行性及系统的鲁棒渐近稳定性。

英文摘要：

For a class of convex polyhedron uncertain discrete nonlinear systems with disturbance and multi-state time delays, a min-max robust predictive control algorithm is proposed based on the predictive control theorem.Firstly, the model prediction control problem is described as a class of min-max problems for an infinite time-do-main. Then, using liner matrix inequalitie（LMI） technology, the problem is transformed into a constraint problem and a state feedback controller designed. An improved Lyapunov-Krasovskii function is constructed using informa-tion provided, and the optimization problem is solved based on model predictive control theory. At the same time,the theorem and its proofs for the existence of the designed controller are also given. Thus, new evidence for the ex-istence of a designed controller and a design method for the state feedback matrix were obtained. Based on this, a flowchart of the robust model predictive controller is given. Finally, a robust asymptotic stable theory of the closed-loop system is given. Theoretical analysis and simulation demonstrate the feasibility of the controller and the robust asymptotic stability of the system.