A class of optimal control problems governed by singular systems via Balakrishnan’s method

Author:

Makreloufi Abed1,Benharrat Mohammed1

Affiliation:

1. Laboratory of Fundamental and Applicable Mathematics of Oran (LMFAO), Department of Systems Engineering (Ex. Department of Mathematics and Informatics), National Polytechnic School of Oran-Maurice Audin (Ex. ENSET of Oran), BP 1523 Oran-El M’naouar, 31000 Oran, Algeria

Abstract

Abstract The purpose of this paper is to discuss, by the use of the Balakrishnan’s epsilon method, a class of optimal control problems governed by continuous linear time invariant singular systems which have only a finite dynamic mode. The linear differential algebraic equation is handled using the epsilon technique to obtain a sequence of the calculus of variations problems. A convergence theorem is given to obtain approximate and, in the limit, an optimal solution of this class of optimal control problem by the use of the necessary optimality conditions of Euler–Lagrange type. A correspondence has been also shown between this penalty function and duality for this class of optimal control problems considered. As an application, an example of optimal linear quadratic problem is also given.

Funder

Algerian Research Project: PRFU

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Control and Optimization,Control and Systems Engineering

Reference27 articles.

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2. The linear quadratic optimal regulator for descriptor systems;Bender;IEEE Trans. Autom. Control,1987

3. Exterior penalty in optimal control problem with state-control constraints;Benharrat;Rend. Circ. Mat. Palermo,2010

4. Optimal control with time delays via the penalty method;Benharrat;Math. Prob. Eng.,2014

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