Indirect Radau pseudospectral method for the receding horizon control problem

作     者：Liao Yuxin Li Huifeng Bao Weimin 

作者机构：School of Astronautics Beihang University Science and Technology Committee China Aerospace Science and Technology Corporation 

出 版 物：《Chinese Journal of Aeronautics》 (中国航空学报（英文版）)

年 卷 期：2016年第29卷第1期

页      面：215-227页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 0802[工学-机械工程] 0825[工学-航空宇航科学与技术] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 0801[工学-力学（可授工学、理学学位）] 071102[理学-系统分析与集成] 081103[工学-系统工程] 

基　　金：supported by the National Natural Science Foundation of China(Nos.61174221 and 61402039) 

主　　题：Indirect Radau pseudospec-tral method Linear time-varying system Nonlinear system Receding horizon control Two-point boundary valueproblem 

摘      要：To solve the receding horizon control （RHC） problem in an online manner, a novel numerical method called the indirect Radau pseudospectral method （IRPM） is proposed in this paper. Based on calculus of variations and the first-order necessary optimality condition, the RHC problem for linear time-varying （LTV） system is transformed into the two-point boundary value problem （TPBVP）. The Radau pseudospectral approximation is employed to discretize the TPBVP into well-posed linear algebraic equations. The resulting linear algebraic equations are solved via a matrix partitioning approach afterwards to obtain the optimal feedback control law. For the nonlinear system, the linearization method or the quasi linearization method is employed to approximate the RHC problem with successive linear approximations. Subsequently, each linear problem is solved via the similar method which is used to solve the RHC problem for LTV system. Simulation results of three examples show that the IRPM is of high accuracy and of high compu- tation efficiency to solve the RHC problem and the stability of closed-loop systems is guaranteed.