Optimal Control for a Class of Chaotic Systems Using Sum-of-Squares Programming

This paper proposes a new computational approach for optimal control of chaotic systems based on the polynomial model and Hamilton-Jacobi inequality. Firstly, a class of chaotic systems under a state feedback controller are described as a polynomial model. Secondly, the optimal control problem for the class of chaotic systems is transformed into a state-dependent linear matrix inequality (SDLMI) problem using the Hamilton-Jacobi inequality. Then, by using the sum-of-squares programming method, a feasible solution to the SDLMI problem is obtained with an upper bound on the optimal value and the state feedback law. Finally, numerical simulations are given to illustrate the validity of the proposed method.