Application of the Generalized Hermite Wavelet Technique to Improve Optimal Control Systems

Abstract

This study introduces a novel class of optimal control problems that incorporate the distributed-order derivative operator. The generalized Hermite wavelet is employed to approximate the state and control functions and the distributed-order Riemann–Liouville integral. Subsequently, the Galerkin method combined with the Lagrange multiplier technique is applied to derive the optimal solutions. Several real-world examples demonstrate the proposed approach's effectiveness and accuracy.