Optimal Control Computation for Nonlinear Fractional Time-Delay Systems with State Inequality Constraints

Chongyang Liu (), Zhaohua Gong (), Changjun Yu (), Song Wang () and Kok Lay Teo ()
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Chongyang Liu: Shandong Technology and Business University
Zhaohua Gong: Shandong Technology and Business University
Changjun Yu: Shanghai University
Song Wang: Curtin University
Kok Lay Teo: Sunway University

Journal of Optimization Theory and Applications, 2021, vol. 191, issue 1, No 4, 83-117

Abstract: Abstract In this paper, a numerical method is developed for solving a class of delay fractional optimal control problems involving nonlinear time-delay systems and subject to state inequality constraints. The fractional derivatives in this class of problems are described in the sense of Caputo, and they can be of different orders. First, we propose a numerical integration scheme for the fractional time-delay system and prove that the convergence rate of the numerical solution to the exact one is of second order based on Taylor expansion and linear interpolation. This gives rise to a discrete-time optimal control problem. Then, we derive the gradient formulas of the cost and constraint functions with respect to the decision variables and present a gradient computation procedure. On this basis, a gradient-based optimization algorithm is developed to solve the resulting discrete-time optimal control problem. Finally, several example problems are solved to demonstrate the effectiveness of the developed solution approach.

Keywords: Fractional time-delay system; Fractional optimal control; Inequality constraint; Numerical integration; Numerical optimization; 34K37; 49M37; 90C55 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-021-01926-8

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