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

doi:10.1016/S0252-9602(17)30032-2

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (3): 703-721.doi: 10.1016/S0252-9602(17)30032-2

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

A. JAJARMI¹, M. HAJIPOUR²

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

收稿日期:2015-12-12 修回日期:2016-05-26 出版日期:2017-06-25 发布日期:2017-06-25
通讯作者: A. JAJARMI E-mail:a.jajarmi@ub.ac.ir
作者简介:M.HAJIPOUR,E-mail:hajipour@sut.ac.ir

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

A. JAJARMI¹, M. HAJIPOUR²

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

Received:2015-12-12 Revised:2016-05-26 Online:2017-06-25 Published:2017-06-25

摘要/Abstract

摘要： This article presents an efficient parallel processing approach for solving the optimal control problem of nonlinear composite systems. In this approach, the original high-order coupled nonlinear two-point boundary value problem (TPBVP) derived from the Pontryagin's maximum principle is first transformed into a sequence of lower-order decoupled 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 matrix 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-feedback suboptimal control, we apply a fast iterative algorithm with low computational 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, parallel processing

Abstract: This article presents an efficient parallel processing approach for solving the optimal control problem of nonlinear composite systems. In this approach, the original high-order coupled nonlinear two-point boundary value problem (TPBVP) derived from the Pontryagin's maximum principle is first transformed into a sequence of lower-order decoupled 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 matrix 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-feedback suboptimal control, we apply a fast iterative algorithm with low computational effort. Finally, some comparative results are included to illustrate the effectiveness of the proposed approach.

Key words: Modal series method, nonlinear composite system, optimal control, parallel processing

A. JAJARMI, M. HAJIPOUR. AN EFFICIENT PARALLEL PROCESSING OPTIMAL CONTROL SCHEME FOR A CLASS OF NONLINEAR COMPOSITE SYSTEMS[J]. 数学物理学报(英文版), 2017, 37(3): 703-721.

A. JAJARMI, M. HAJIPOUR. AN EFFICIENT PARALLEL PROCESSING OPTIMAL CONTROL SCHEME FOR A CLASS OF NONLINEAR COMPOSITE SYSTEMS[J]. Acta mathematica scientia,Series B, 2017, 37(3): 703-721.

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

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

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