A wavelet-based approach for solving fractional optimal control problems with inequality constraints

Abstract

This article presents a robust and efficient numerical framework for solving fractional optimal control problems (FOCPs) with inequality constraints, leveraging the analytical and computational strengths of wavelet-based methods. The operational matrices (OMs) of fractional integral and the product OM for Jacobi wavelets and Taylor wavelets are constructed. In the proposed method, these OMs of fractional integral and multiplication, along with the Lagrange multiplier method for the constrained extremum are employed for reducing the FOCPs into those consisting of systems of algebraic equations. By solving these systems, the solutions of the FOCPs have been achieved. Convergence analysis of the proposed method has been rigorously examined and some results concerning error analysis are also established. In addition, to demonstrate the validity and applicability of the proposed method, several illustrative examples are presented. In cases where exact solutions are available, comparisons between the numerical and exact solutions show the efficiency of the proposed approach. Furthermore, the results are compared with those obtained using other wavelet methods, which further confirm the accuracy and effectiveness of the proposed technique.