Efficient scheme for a category of variable-order optimal control problems based on the sixth-kind Chebyshev polynomials

Abstract

The main goal of the present study is to introduce an operational collocation scheme based on sixth-kind Chebyshev polynomials (SCPs) to solve a category of optimal control problems involving a variable-order dynamical system (VODS). To achieve this goal, the collocation method based on SCPs, the pseudo-operational matrix for the fractional integral operator, and the dual operational matrix are adopted. More precisely, an algebraic equation is obtained instead of the objective function and a system of algebraic equation is derived instead of the VODS. The constrained equations obtained from joining the objective function to the VODS are ultimately optimized using the method of the Lagrange multipliers. Detailed convergence analysis of the suggested method is given as well. Four illustrative examples along with several tables and figures are formally provided to support the efficiency and preciseness of the numerical scheme.