A numerical technique for solving fractional optimal control problems using fractional wavelet method

Abstract

This manuscript presents an efficient numerical method for solving fractional optimal control problems using an operational matrix for a fractional wavelet. Using well-known formulae such as Caputo and Riemann-Liouville operators to determine fractional derivatives and integral fractional wavelets, operational matrices were devised and utilized to solve fractional optimal control problems. The proposed method reduced the fractional optimal control problems into a system of algebraic equations and apply the Lagrange multiplier technique for determining the cost value. The convergence analysis and error bound of the proposed scheme have been established. To validate the effectiveness of the presented numerical approach, some illustrative examples were solved using fractional Taylor and Taylor wavelets, and the approximate cost function value derived by approximating state and control functions was compared. MSC Classification: 49J15 , 49N10 , 65T60 , 26A33.