‎Solving the optimum control problem constrained with Volterra integro-differential equations using Chebyshev wavelets and particle swarm optimization

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Ebrahimzadeh Asiyeh

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Journal Paper

Paper Information

Journal: AUT JOURNAL OF MATHEMATICS AND COMPUTING Year:2026 | Volume:7 | Issue:1 Page(s): 45-61

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Information Journal Paper

Title

‎Solving the optimum control problem constrained with Volterra integro-differential equations using Chebyshev wavelets and particle swarm optimization

Author(s)

Ebrahimzadeh Asiyeh | Issue Writer Certificate

Keywords

Chebyshev ‎ wavelet

‎Optimal control

‎Particle ‎s‎warm ‎optimization

Collocation‎ method

Volterra integro-differential equation

Abstract

To handle a type of optimum control problems (OCP) for systems controlled described by Volterra integro-differential equations (VIDE), we introduce in this study a direct Chebyshev wavelet collocation approach, which is utilized in applied science and engineering. The proposed direct approach turns the OCP into a nonlinear programming (NLP) problem, in which the wavelet coefficients are the optimization variables. To solve the resulting NLP, we use the particle swarm optimization (PSO) technique. In addition, we illustrate the suggested method's convergence. Under certain sufficient conditions, it is shown that a sequence of optimal solutions for the finite-dimensional optimization problems corresponding to $\overline{\mathcal{P}}$ approximates the optimal solution of the original problem $\mathcal{P}$ in a desirable manner. To demonstrate the method's applicability and efficiency, we provide several numerical examples that emphasize the PSO algorithm's effectiveness in solving the resulted NLP.

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