Receding horizon H_∞ control for discrete-time Markovian jump linear systems  

作　　者：Jiwei Wen Fei Liu 

机构地区：[1]Key Laboratory of Advanced Process Control for Light Industry,Institute of Automation, Jiangnan University, Wuxi 214122, P. R. China

出　　处：《Journal of Systems Engineering and Electronics》2011年第2期292-299,共8页系统工程与电子技术（英文版）

基　　金：supported by the National Natural Science Foundation of China (60974001);Jiangsu "Six Personnel Peak" Talent-Funded Projects

摘　　要：Receding horizon H∞ control scheme which can deal with both the H∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given quadratic performance criteria. First, a control law is established for jump systems based on pontryagin’s minimum principle and it can be constructed through numerical solution of iterative equations. The aim of this control strategy is to obtain an optimal control which can minimize the cost function under the worst disturbance at every sampling time. Due to the difficulty of the assurance of stability, then the above mentioned approach is improved by determining terminal weighting matrix which satisfies cost monotonicity condition. The control move which is calculated by using this type of terminal weighting matrix as boundary condition naturally guarantees the mean square stability of the closed-loop system. A sufficient condition for the existence of the terminal weighting matrix is presented in linear matrix inequality （LMI） form which can be solved efficiently by available software toolbox. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.Receding horizon H∞ control scheme which can deal with both the H∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given quadratic performance criteria. First, a control law is established for jump systems based on pontryagin’s minimum principle and it can be constructed through numerical solution of iterative equations. The aim of this control strategy is to obtain an optimal control which can minimize the cost function under the worst disturbance at every sampling time. Due to the difficulty of the assurance of stability, then the above mentioned approach is improved by determining terminal weighting matrix which satisfies cost monotonicity condition. The control move which is calculated by using this type of terminal weighting matrix as boundary condition naturally guarantees the mean square stability of the closed-loop system. A sufficient condition for the existence of the terminal weighting matrix is presented in linear matrix inequality （LMI） form which can be solved efficiently by available software toolbox. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.

关 键 词：Marker jump linear systems receding horizon H∞ control mean square stability terminal weighting matrix pontrya-gin＇s minimum principle current time jump mode. 

分 类 号：TP271[自动化与计算机技术—检测技术与自动化装置] F273.2[自动化与计算机技术—控制科学与工程]