Solving of time varying quadratic optimal control problems by using Bezier control points

In this paper, linear quadratic optimal control problems are solved by applying least square method based on Bezier control points. We divide the interval which includes t, into k subintervals and approximate the trajectory and control functions by Bezier curves. We have chosen the Bezier curves as piacewise polynomials of degree three, and determined Bezier curves on any subinterval by four control points. By using least square method, we introduce an optimization problem and compute the control points by solving this optimization problem. Numerical experiments are presented to illustrate the proposed method.