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An efficient parallel processing optimal control scheme for a class of nonlinear composite systems
Authors:A JAJARMI  M HAJIPOUR
Institution:Department of Electrical Engineering, University of Bojnord, P.O. Box 94531-1339, Bojnord, Iran;Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, P.O. Box 51335-1996, Tabriz, Iran
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.
Keywords:Modal series method  nonlinear composite system  optimal control  parallel processing  49J15  49N05  93C10
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