Projectional dynamic neural network identifier for chaotic systems: Application to Chua's circuit

Chaotic systems arise in many different fields, being their modeling, synchronization and control, important topics for interested researchers in this kind of systems. The present paper deals with the problem of non-parametric identification (adaptable modeling) of a class of uncertain nonlinear systems with chaotic behavior. A Projectional Dynamic Neural Network (PDNN) is proposed to carry out the identification task. The practical stability of the identification error is proven by the second Lyapunov's method and the Linear Matrix Inequalities approaches. The obtained algorithm is tested by numerical simulations, taking into account the mathematical model of the so-called chaotic Chuas circuit, and compared with a nonlinear observer (Thaus observer). Then, a reported version of the Chua's circuit is constructed to verify the proposed identification scheme under an experimental framework. PDNN is tested with this real data. In both cases, simulation and real measurements, the developed algorithm shows an excellent convergence to the state variables of the chaotic system, fact that is supported by the formal analysis.