Numerical solution of distributed-order fractional 2D optimal control problems using the Bernstein polynomials

In this work, a new class of two-dimensional optimal control problems is introduced with the help of distributed-order fractional derivative in the Caputo form. The orthonormal Bernstein polynomials are used to make a numerical method to solve these problems. Through this way, some operational matrices are obtained for the classical and fractional derivatives of these polynomials to make effective utilisation of them in constructing the proposed method. The main advantage of the established method is that it turns the solution of the problem under consideration into a system of algebraic equations by approximating the state and control variables by the expressed polynomials and applying the method of Lagrange multipliers. The accuracy and capability of the proposed approach are investigated by solving some numerical examples.

Automated summary

In this work, a new class of two-dimensional optimal control problems is introduced using distributed-order fractional derivative in the Caputo form. The orthonormal Bernstein polynomials are utilized to solve these problems numerically. The proposed approach approximates the state and control variables using polynomials and converts the problem into a system of algebraic equations using the method of Lagrange multipliers. The accuracy and capability of this method are demonstrated through numerical examples.