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 chaotic system, where all admissible controls are required to satisfy small boundedness constraints. A numerical approach is developed to seek for an optimal feedback control for the optimal control problem. In this approach, the state space is partitioned into subregions, and the controller is approximated by a linear combination of a modified third order B-spline basis functions. The partition points are also taken as decision variables in this formulation. An algorithm based on this approach is proposed. To show the effectiveness of the proposed method, a control problem involving the Lorenz system is solved by the proposed approach. The numerical results demonstrate that the method is efficient in the construction of a robust, near-optimal control.