An Efficient Algorithm for the Multi-Scale Solution of Nonlinear Fractional Optimal Control Problems

Abstract

An efficient algorithm based on the wavelet collocation method is introduced in order to solve nonlinear fractional optimal control problems (FOCPs) with inequality constraints. By using the interpolation properties of Hermite cubic spline functions, we construct an operational matrix of the Caputo fractional derivative for the first time. Using this matrix, we reduce the nonlinear fractional optimal control problem to a nonlinear programming problem that can be solved with some suitable optimization algorithms. Illustrative examples are examined to demonstrate the important features of the new method.

Keywords

• fractional-order optimal control
• Caputo fractional derivative
• Riemann–Liouville fractional integration
• biorthogonal Hermite cubic spline multiscaling bases