Affiliation:
1. School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Abstract
The Hamilton–Jacobi–Issacs (HJI) inequality is the most basic relation in nonlinear H∞ design, to which no effective analytical solution is currently available. The sum of squares (SOS) method can numerically solve nonlinear problems that are not easy to solve analytically, but it still cannot solve HJI inequalities directly. In this paper, an HJI inequality suitable for SOS is firstly derived to solve the problem of nonconvex optimization. Then, the problems of SOS in nonlinear H∞ design are analyzed in detail. Finally, a two-step iterative design method for solving nonlinear H∞ control is presented. The first step is to design an adjustable nonlinear state feedback of the gain array of the system using SOS. The second step is to solve the L2 gain of the system; the optimization problem is solved by a graphical analytical method. In the iterative design, a diagonally dominant design idea is proposed to reduce the numerical error of SOS. The nonlinear H∞ control design of a polynomial system for large satellite attitude maneuvers is taken as our example. Simulation results show that the SOS method is comparable to the LMI method used for linear systems, and it is expected to find a broad range of applications in the analysis and design of nonlinear systems.
Funder
Fundamental Research Funds for the Central Universities
Subject
Multidisciplinary,General Computer Science
Cited by
69 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献