Markov跳变系统的输出反馈鲁棒预测控制

Robust predictive control via output feedback for Markov jump systems

中文关键词  模型预测控制  输出控制  Markov跳变系统  准线性参数时变  二次有界  鲁棒稳定性

英文关键词  model predictive control  output control  Markov jump systems  quasi-linear time-varying parameter  quadratic boundedness  robust stability

中文摘要

      对离散时间Markov跳变系统, 当系统状态不完全可测时, 研究了一类基于输出反馈的鲁棒模型预测控制问题. 所研究系统为准线性参数时变的, 考虑在当前时刻系统的时变参数是已知的, 将来时刻未知的情况. 综合考虑系统存在多胞不确定性和有界噪声等因素, 通过运用线性矩阵不等式方法及变量变换思想, 将无穷时域性能指标的最小最大鲁棒预测控制问题转化为具有线性矩阵不等式约束的凸优化问题, 得到了系统的输出反馈控制律. 引入二次有界概念, 在满足输入输出约束的情况下, 保证闭环系统的随机稳定性. 数值算例验证了方法的有效性.

英文摘要

      For the discrete-time Markov jump system, when the states are not all measurable, we develop a robust modelpredictive control with output feedback for the system with polytopic uncertainty as well as bounded disturbance. The quasi-linear time-varying parameters of this system are known in values at the current time, but unknown in the future time. By using the linear matrix inequalities and the variable transformation, we convert the min-max robust predictive control problem for infinite horizon performance cost into the optimization problem with linear matrix inequality constraints. By solving this problem, we obtain the output feedback law for closed-loop system. Under the conditions for the input and output, the closed-loop system is stochastically stable in the sense of quadratic boundedness as we defined. Finally, a numerical example is provided to illustrate the effectiveness of the controller.