Robust Fixed Point Transformations in Chaos synchronization

Due to the technical difficulties related to the practical application of Lyapunov´s 2ⁿd or “direct” method in the adaptive control of nonlinear systems as an alternative approach the use of “Robust Fixed Point Transformations (RFPT)” were suggested on the basis of recent researches. Various application possibilities were revealed for the new controller and design for imprecisely and partially modeled fully and underactuated Classical Mechanical Systems, Electromechanical Systems by direct utilization and within the frames if the “Model Reference Controllers (MRAC)”. In the present paper a novel application, the synchronization of coupled, chaotic systems is considered. It is shown that besides the “traditional” problem tackling normally based on the use of Lyapunov functions the RFPT based approach can be successful, too. This statement is illustrated via simulation results for the synchronization of the Fitz-Hugh-Nagumo (FHN) neuron model.