An Algorithm for Optimal Control of a Class of Linear Time Varying Systems with Computational Time Reduction and Increasing Its Speed Approach in Engineering Problems
Subject Areas : electrical and computer engineeringMehdi Yousefi Tabari 1 , Zahra Rahmani 2 , Ali Vahidian Kamyad 3 , Seyed Jalil Sadati 4
1 -
2 - عضو هیات علمی
3 - Ferdowsi University of Mashhad
4 - Babol Noshirvani University of Technology
Keywords: Optimal control, time delay systems, Pontryagin's maximum principle,
Abstract :
Time-delay systems have been very much considered in the last few decades. Many of these time-delay systems appear in different systems and branches of science such as engineering, chemistry, physics, disease models. The presence of delay makes the analysis and control of such systems much more complicated. In fact, the application of Pontryagin’s maximum principle to the optimal control problems with time-delay results in boundary value problem involving both delay and advance terms. In this paper, we consider a time-delay optimal control problems. The first section, using the Pontryagin's maximum principle for optimal control problems with time delay, the necessary optimality conditions for this problem, are obtained. Then a new algorithm is proposed to solve this problem numerically. This algorithm is based on an approximation for derivatives and linear interpolation for delayed arguments. Finally, the resulting equations becomes a linear programming problem that can be solved numerically. The efficiency of the proposed method is evaluated by solving several numerical examples.
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