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

Document Type : Original Article

Author

Department of Mathematics Education, Farhangian University, P. O. Box 14665-889, Tehran, Iran

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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References

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AUT Journal of Mathematics and Computing
Volume 7, Issue 1
January 2026
Pages 45-61

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