Abstract
In this paper, Homotopy perturbation method is used to find the approximate solution of the optimal control of linear systems. In this method the initial approximations are freely chosen, and a Homotopy is constructed with an embedding parameter , which is considered as a “small parameter”. Some examples are given in order to find the approximate solution and verify the efficiency of the proposed method.
Highlights
Homotopy perturbation method is used to find the approximate solution of the optimal control of linear systems
Optimal control problems arise in a wide variety of disciplines. optimal control theory has been used with great success in areas as diverse as economics to biomedicine [1]
We know that generally optimal control problems are difficult to solve. their analytical solutions are in many cases are not questionable
Summary
Optimal control problems arise in a wide variety of disciplines. optimal control theory has been used with great success in areas as diverse as economics to biomedicine [1]. In this paper we solve the optimal control problem by combine perturbation method. To this end, there are quite a few fundamentally diverse approaches, some of which can be found in [18,19]. The Belgian mathematician Lahaye was the first to use the homotopy method for the numerical solution of equations. He considered the case of a single equation. The homotopy method has been developed for optimal control problems by Avvakumov [27], Since the 1980s.
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