A novel optimisation strategy for solving optimal control of variable-order fractional dynamic systems with nonlocal boundary conditions

Abstract

This paper presents a general class of the nonlinear variable-order fractional optimal control problems (GCNVOFOCPs) subject to a general class of the nonlinear variable-order fractional dynamical system (GCNVFDS) with nonlocal boundary conditions (NBCs) and an optimisation method for solving the problem under study based on a new family of polynomials namely fractional Abel polynomials (FAPs). Therefore, first, the new operational matrices for FAPs are derived. Then, the GCNVOFOCPs are transformed into a system of algebraic equations. By solving these systems, we can determine the unknown parameters and coefficients. To address the nonlinear system, we employ the Lagrange multipliers to achieve optimal approximations. The convergence of the proposed numerical method is also analysed. Finally, numerical simulations are provided to illustrate the performance of the method.