On the numerical scheme of a 2D optimal control problem with the hyperbolic system via Bernstein polynomial basis

A numerical method for solving a 2D optimal control problem (2DOCP) governed by a linear time-varying constraint is presented in this paper. The method is based upon the Bernstein polynomial basis. The properties of Bernstein polynomial functions are presented. These properties, together with the Ritz method, are then utilized to reduce the given 2DOCP to the solution of an algebraic system of equations. By solving this system, the solution of the proposed problem is achieved. The main advantage of this scheme is that the approximate solutions satisfy all initial and boundary conditions of the problem. We extensively discuss the convergence of the method. Finally, an illustrative example is included to demonstrate the validity and applicability of the new technique.