Numerical optimization method for HJI equations derived from robust receding horizon control schemes and controller design  

作　　者：SONG ChongHui BIAN ChunYuan ZHANG Xie SHI ChengLong 

机构地区：[1]School of Inforvnation Science and Engineering,Northeastern University,Shenyang 110004,China

出　　处：《Science China(Information Sciences)》2012年第1期214-227,共14页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.60974141,60504006,60621001,60728307,60774093);Natural Science Foundation of Liaoning Province(Grant No.20092007);Fundamental Research Funds for the Central Universities(Grant Nos.N100404015,N100404012)

摘　　要：This paper addresses how to numerically solve the Hamilton-Jacobin-Isaac （HJI） equations derived ffom the robust receding horizon control schemes. The developed numerical method, the finite difference scheme with sigmoidal transformation, is a stable and convergent algorithm for HJI equations. A boundary value iteration procedure is developed to increase the calculation accuracy with less time consumption. The obtained value function can be applied to the robust receding horizon controller design of some kind of uncertain nonlinear systems. In the controller design, the finite time horizon is extended into the infinite time horizon and the controller can be implemented in real time. It can avoid the on-line repeated optimization and the dependence on the feasibility of the initial state which are encountered in the traditional robust receding horizon control schemes.This paper addresses how to numerically solve the Hamilton-Jacobin-Isaac （HJI） equations derived ffom the robust receding horizon control schemes. The developed numerical method, the finite difference scheme with sigmoidal transformation, is a stable and convergent algorithm for HJI equations. A boundary value iteration procedure is developed to increase the calculation accuracy with less time consumption. The obtained value function can be applied to the robust receding horizon controller design of some kind of uncertain nonlinear systems. In the controller design, the finite time horizon is extended into the infinite time horizon and the controller can be implemented in real time. It can avoid the on-line repeated optimization and the dependence on the feasibility of the initial state which are encountered in the traditional robust receding horizon control schemes.

关 键 词：dynamic programming uncertain nonlinear systems numerical method robust receding horizoncontrol differential game 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置] TP273.1[自动化与计算机技术—控制科学与工程]