Solving infinite-horizon optimal control problems of the time-delayed systems by Haar wavelet collocation method

Abstract

A numerical method using Haar wavelets for solving infinite-horizon time-delayed optimal control problems is studied. The problem is first transformed, using a Pade approximation, to one without a time-delayed argument. By a suitable change of variable, the obtained non-delay infinite-horizon optimal control problem is converted to a finite-horizon non-linear optimal control problem. An approximation scheme based on Haar wavelets in the time domain is then proposed for solving the obtained optimal control problem. Haar wavelets integral operational matrix and direct collocation method are used to find the approximated optimal trajectory and the optimal control law of the original problem. Two illustrative examples are provided to show the feasibility and the efficiency of the proposed method.