AN EFFICIENT PARALLEL PROCESSING OPTIMAL CONTROL SCHEME FOR A CLASS OF NONLINEAR COMPOSITE SYSTEMS  

作　　者：A. JAJARMT M. HAJIPOUR 

机构地区：[1]Department of Electrical Engineering, University of Bojnord, P.O. Box 94531-1339, Bojnord, Iran [2]Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, P.O. Box 51335-1996, Tabriz, Iran

出　　处：《Acta Mathematica Scientia》2017年第3期703-721,共19页数学物理学报（B辑英文版）

摘　　要：This article presents an efficient parallel processing approach for solving the opti- mal control problem of nonlinear composite systems. In this approach, the original high-order coupled nonlinear two-point boundary value problem （TPBVP） derived from the Pontrya- gin＇s maximum principle is first transformed into a sequence of lower-order deeoupled linear time-invariant TPBVPs. Then, an optimal control law which consists of both feedback and forward terms is achieved by using the modal series method for the derived sequence. The feedback term specified by local states of each subsystem is determined by solving a ma- trix Riccati differential equation. The forward term for each subsystem derived from its local information is an infinite sum of adjoint vectors. The convergence analysis and parallel processing capability of the proposed approach are also provided. To achieve an accurate feedforward-feedbaek suboptimal control, we apply a fast iterative algorithm with low com- putational effort. Finally, some comparative results are included to illustrate the effectiveness of the proposed approach.This article presents an efficient parallel processing approach for solving the opti- mal control problem of nonlinear composite systems. In this approach, the original high-order coupled nonlinear two-point boundary value problem （TPBVP） derived from the Pontrya- gin＇s maximum principle is first transformed into a sequence of lower-order deeoupled linear time-invariant TPBVPs. Then, an optimal control law which consists of both feedback and forward terms is achieved by using the modal series method for the derived sequence. The feedback term specified by local states of each subsystem is determined by solving a ma- trix Riccati differential equation. The forward term for each subsystem derived from its local information is an infinite sum of adjoint vectors. The convergence analysis and parallel processing capability of the proposed approach are also provided. To achieve an accurate feedforward-feedbaek suboptimal control, we apply a fast iterative algorithm with low com- putational effort. Finally, some comparative results are included to illustrate the effectiveness of the proposed approach.

关 键 词：Modal series method nonlinear composite system optimal control PARALLELPROCESSING 

分 类 号：O[理学]