Rate of convergence for the Legendre pseudospectral optimal control of feedback linearizable systems  

作　　者：Wei KANG (Department of Applied Mathematics,Naval Postgraduate School,Monterey CA 93943,USA) 

出　　处：《控制理论与应用（英文版）》2010年第4期391-405,共15页

基　　金：supported by the Air Force Office of Scientific Research(No.F1ATA0-90-4-3G001)and Air Force Research Laboratory

摘　　要：Pseudospectral （PS） computational methods for nonlinear constrained optimal control have been applied to many industrial-strength problems,notably,the recent zero-propellant-maneuvering of the international space station performed by NASA.In this paper,we prove a theorem on the rate of convergence for the optimal cost computed using a Legendre PS method.In addition to the high-order convergence rate,two theorems are proved for the existence and convergence of the approximate solutions.Relative to existing work on PS optimal control as well as some other direct computational methods,the proofs do not use necessary conditions of optimal control.Furthermore,we do not make coercivity type of assumptions.As a result,the theory does not require the local uniqueness of optimal solutions.In addition,a restrictive assumption on the cluster points of discrete solutions made in existing convergence theorems is removed.Pseudospectral （PS） computational methods for nonlinear constrained optimal control have been applied to many industrial-strength problems,notably,the recent zero-propellant-maneuvering of the international space station performed by NASA.In this paper,we prove a theorem on the rate of convergence for the optimal cost computed using a Legendre PS method.In addition to the high-order convergence rate,two theorems are proved for the existence and convergence of the approximate solutions.Relative to existing work on PS optimal control as well as some other direct computational methods,the proofs do not use necessary conditions of optimal control.Furthermore,we do not make coercivity type of assumptions.As a result,the theory does not require the local uniqueness of optimal solutions.In addition,a restrictive assumption on the cluster points of discrete solutions made in existing convergence theorems is removed.

关 键 词：Computational optimal control Pseudospectral method CONVERGENCE 

分 类 号：TP11[自动化与计算机技术—控制理论与控制工程]