On a Method for Optimizing Controlled Polynomial Systems with Constraints

Alexander Buldaev () and Dmitry Trunin
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Alexander Buldaev: Department of Applied Mathematics, Buryat State University, 670000 Ulan-Ude, Russia
Dmitry Trunin: Buryat State University, 670000 Ulan-Ude, Russia

Mathematics, 2023, vol. 11, issue 7, 1-18

Abstract: A new optimization approach is considered in the class of polynomial in-state optimal control problems with constraints based on nonlocal control improvement conditions, which are constructed in the form of special fixed-point problems in the control space. The proposed method of successive approximations of control retains all constraints at each iteration and does not use the operation of parametric variation of control at each iteration, in contrast to known gradient methods. In addition, the initial approximation of the iterative process may not satisfy the constraints, which is a significant factor in increasing the efficiency of the approach. The comparative efficiency of the proposed method of fixed points in the considered class of problems is illustrated in a model example.

Keywords: polynomial optimal control problem with constraints; control improvement conditions; fixed-point problem; iterative algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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