Legendre wavelet collocation method for fractional optimal control problems with fractional Bolza cost
Nitin Kumar, Mani Mehra
Abstract
Abstract This paper exhibits a numerical method for solving general fractional optimal control problems involving a dynamical system described by a nonlinear Caputo fractional differential equation, associated with a fractional Bolza cost composed as the aggregate of a standard Mayer cost and a fractional Lagrange cost given by a Riemann–Liouville fractional integral. By using the Lagrange multiplier within the calculus of variations and by applying integration by part formula, the necessary optimality conditions are derived in terms of a nonlinear two‐point fractional‐order boundary value problem. An operational matrix of fractional order right Riemann–Liouville integration is proposed and by utilizing it, the obtained two‐point fractional‐order boundary value problem is reduced into the solution of an algebraic system. An L 2 ‐error estimate in the approximation of unknown variable by Legendre wavelet is derived and in the last, illustrative examples are included to demonstrate the applicability of the proposed method.