Nonlinear optimal stabilization of unstable periodic orbits

The framework for the optimal stabilization of unstable periodic orbits in nonlinear systems is proposed. First, the stable manifold method for approximately solving Hamilton-Jacobi equations in the optimal control problem is extended to nonlinear periodic systems. Then, this method is applied for optimal stabilization problem of error dynamics around an unstable periodic orbit. The effectiveness of the proposed method is evaluated via numerical simulations for the Rossler chaotic system.