Synchronization of chaotic electronic circuits using nonlinear optimal control

A nonlinear optimal (H-infinity) control method is developed for control and synchronization of chaotic electric circuits, using as test case Chua’s circuit. Although this electronic circuit is deterministic, for specific values of its parameters its phase diagrams may change in a random-like manner, thus exhibiting a chaotic behavior. In the article’s control approach, the dynamic model of the circuit undergoes first an approximate linearization, around a temporary operating point which is recomputed at each iteration of the control method. The linearization makes use of Taylor series expansion and of the computation of the system’s Jacobian matrices. For the approximately linearized model of the circuit an H-infinity feedback controller is found. This is achieved after solving an algebraic Riccati equation at each step of the control method. The stability properties of the control scheme and the elimination of the synchronization error is proven through Lyapunov analysis. First it is demonstrated that the proposed control scheme satisfies the H-infinity tracking performance condition and this signifies elevated robustness against model uncertainty and external perturbations. Besides, under moderate conditions, the global asymptotic properties of the control method are proven.