Lyapunov measure and control of periodic orbit

The focus of this paper is on the computation of optimal stabilizing control for the control of complex dynamics in a lower dimensional discrete time dynamical system. Lyapunov measure is used for the purpose of the stabilization. Using the results from [17], optimal stabilization problem is posed as a infinite dimensional linear program. Finite dimensional approximation of the linear program is obtained using set oriented numerical methods. Simulation results are presented to demonstrate the use of Lyapunov measure for the optimal stabilization of periodic orbit in Henon map and Standard map.