鲁棒后退时域控制中HJI方程的数值解法及控制器设计  

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

作　　者：宋崇辉[1] 边春元[1] 张勰[1] 史成龙[1] 

机构地区：[1]东北大学信息科学与工程学院,沈阳110004

出　　处：《中国科学：信息科学》2011年第9期1156-1170,共15页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:60974141,60504006,60621001,60728307,60774093);辽宁省自然科学基金(批准号:20092007);中央高校基本科研业务费专项基金(批准号:N100404015,N100404012)资助项目

摘　　要：本文讨论了由不确定非线性系统鲁棒后退时域控制(robust receding horizon control,RRHC)策略导出的Hamilton-Jacobin-Isaac(HJI)方程的求解,提出了一种新的带反曲变换的有限差分算法计算值函数,所提出算法对HJI方程的求解是一种稳定且收敛的算法.同时提出基于边界值迭代的加速过程,加速优化问题的求解,在花费更少计算时间的前提下,提高计算精度.所求得的值函数可直接应用于一类不确定非线性系统鲁棒后退时域控制器的设计,在控制器设计中,传统鲁棒后退时域控制策略中的有限时域被扩展到无限时域,求得的控制器可实时实现,避免对初始点可解性的依赖以及反复在线优化问题.This paper addresses how to numerically solve the Hamilton-Jacobin-Isaac（HJI） equations derived from 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：动态规划 不确定非线性系统 数值方法 鲁棒后退时域控制 微分对策 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]