This paper proposes the optimal control methods for a class of chaotic systems via state feedback. By converting the chaotic systems to the form of uncertain piecewise linear systems, we can obtain the optimal controller minimizing the upper bound on cost function by virtue of the robust optimal control method of piecewise linear systems, which is cast as an optimization problem under constraints of bilinear matrix inequalities (BMIs). In addition, the lower bound on cost function can be achieved by solving a semidefinite programming (SDP). Finally, numerical examples are given to illustrate the results.
Jianxiong Zhang. Wansheng Tang. "Optimal Control for a Class of Chaotic Systems." J. Appl. Math. 2012 (SI10) 1 - 20, 2012. https://doi.org/10.1155/2012/859542