Numerical Assessment of Optimal Control Problems with Variable Order Fractional Integro-Differential Equation Based on Laguerre Wavelets Functions

‎This paper deals with a general form of fractional optimal control problems involving variable-order fractional integro differential equation using orthonormal Laguerre wavelets expansions. By effectively employing these ‎functions,‎ product variable-order operational matrices have been obtained. By using these fractional operational matrices and collocation points, the study transforms the original continuous-time optimal control problems of variable-order fractional integro-differential equations into a system of linear or non-linear algebraic equations. ‎Attempts have been made to use the collocation method with a joint application of Lagrange multiplier technique, to obtain the approximate cost function based on determining the state and control functions. ‎The ‎main ‎components ‎for ‎applying ‎these ‎wavelets ‎is ‎to ‎have ‎viable ‎solutions ‎due ‎to ‎their ‎orthogonality.‎ ‎In addition‎, ‎the convergence analysis is presented with respect to the operational matrices of this scheme‎. Simulation results indicate that the proposed method works well and provides satisfactory results with regard to accuracy and computational effort.

کلیدواژه ها:

Integro-differential equation ، Variable-order fractional calculus ، Optimal control problem ، Laguerre wavelet ، Collocation method