Spectral algorithm for pseudospectral methods in optimal control

作     者：Gong, Qi Fahroo, Fariba Ross, I. Michael 

作者机构：Univ Texas San Antonio Dept Elect & Comp Engn San Antonio TX 78249 USA USN Postgrad Sch Dept Appl Math Monterey CA 93943 USA USN Postgrad Sch Dept Mech & Aeronaut Engn Monterey CA 93943 USA 

出 版 物：《JOURNAL OF GUIDANCE CONTROL AND DYNAMICS》 (制导、控制和动力学杂志)

年 卷 期：2008年第31卷第3期

页      面：460-471页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 0804[工学-仪器科学与技术] 0825[工学-航空宇航科学与技术] 

主　　题：FEEDBACK LINEARIZABLE SYSTEMS CONSTRAINED OPTIMAL-CONTROL OPTIMIZATION APPROXIMATIONS CONVERGENCE 

摘      要：Recent convergence results with pseudospectral methods are exploited to design a robust, multigrid, spectral algorithm for computing optimal controls. The design of the algorithm is based on using the pseudospectral differentiation matrix to locate switches, kinks, corners, and other discontinuities that are typical when solving practical optimal control problems. The concept of pseudospectral knots and Gaussian quadrature rules are used to generate a natural spectral mesh that is dense near the points of interest. Several stopping criteria are developed based on new error-estimation formulas and Jackson s theorem. The sequence is terminated when all of the convergence criteria are satisfied. Numerical examples demonstrate the key concepts proposed in the design of the spectral algorithm. Although a vast number of theoretical and algorithmic issues still remain open, this paper advances pseudospectral methods along several new directions and outlines the current theoretical pitfalls in computation and control.