Construction of suboptimal feedback control for chaotic systems using B-splines with optimally chosen knot points

In this paper we consider a class of optimal control problem involving a ch aotic system, where all admissible controls are required to satisfy small b oundedness constraints. A numerical approach is developed to seek for an op timal feedback control for the optimal control problem. In this approach, t he state space is partitioned into subregions, and the controller is approx imated by a linear combination of a modified third order B-spline basis fun ctions. The partition points are also taken as decision variables in this f ormulation. An algorithm based on this approach is proposed. To show the ef fectiveness of the proposed method, a control problem involving the Lorenz system is solved by the proposed approach. The numerical results demonstrat e that the method is efficient in the construction of a robust, near-optima l control.