Optimal control design for linear time-varying systems by interpolated variational iteration method

Abstract

Optimal control of linear time-varying (LTV) systems is one of the most common problems in engineering, economics, biology, etc. Solving this problem is not always possible, and this motivates us to improve the existing approximate solution methods. In this paper, the optimality conditions are first obtained, and then the well-known variational iteration method, interpolated by B-spline functions, is applied to solve these conditions. The method is also accelerated through the elimination of redundant calculations. Our method provides a feedback controller for LTV optimal control problems and does not need to solve any system of equations or optimization problems at each iteration. The convergence of the proposed method is proved, and the algorithm’s efficiency is illustrated through several examples.