Shooting continuous Runge–Kutta method for delay optimal control problems

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Jabbari Khanbehbin T.; Gachpazan M.; Effati S.; Miri S.M.

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Journal Paper

Paper Information

Journal: IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION Year:2022 | Volume:12 | Issue:3 Page(s): 680-703

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Information Journal Paper

Title

Shooting continuous Runge–Kutta method for delay optimal control problems

Author(s)

Jabbari Khanbehbin T. | Gachpazan M. | Effati S. | Miri S.M. | Issue Writer Certificate

Keywords

Pontryagin maximum principle

Time-delay two-point bound-ary value problems

Time-delay optimal control problems

Continuous Runge–Kutta methods

Shooting Method

Abstract

In this paper, we present an eﬀicient method to solve linear Time-delay optimal control problems with a quadratic cost function. In this regard, first, by employing the Pontryagin maximum principle to time-delay systems, the original problem is converted into a sequence of two-point boundary value problems (TPBVPs) that have both advance and delay terms. Then, using the continuous Runge–Kutta (CRK) method, the resulting sequences are recursively solved by the Shooting Method to obtain an optimal control law. This obtained optimal control consists of a linear feedback term, which is obtained by solving a Riccati matrix differential equation, and a forward term, which is an infinite sum of adjoint vectors, that can be obtained by solving sequences of delay TPBVPs by the shooting CRK method. Finally, numerical results and their comparison with other available results illustrate the high accuracy and eﬀiciency of our proposed method.

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