Chaos control and chaos synchronization using the state-dependent Riccati equation techniques

In this paper, the problems of chaos control and chaos synchronization are solved using the state-dependent Riccati equation methods. In the former problem, a nonlinear suboptimal control law is found, which leads to a stable closed-loop system. In the latter, an optimal infinite-time horizon tracking problem is defined and solved using the state-dependent Riccati equation technique. It is shown that the synchronization error between the slave and the master systems converges asymptotically to zero under some mild conditions. Three numerical simulations are provided to demonstrate the design procedure and the flexibility of the methods.