‎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, 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 P approximates the optimal solution of the original problem 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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AUT Journal of Mathematics and Computing

Articles in Press, Accepted Manuscript
Available Online from 17 November 2024

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