On Lyapunov stability of nonlinear adaptive control based on neural networks emulator and controller

This paper addresses a Lyapunov stability analysis of nonlinear systems control. We consider an adaptive control scheme based on recurrent neural networks emulator and controller with decoupled adaptive rates. Lyapunov sufficient stability conditions for decoupled adaptive rates of the emulator and controller are proposed. In order to guarantee the fast convergence, the optimal adaptive rate of controller is derived in the sense of Lyapunov exponential stability taking into account the stability of the emulator. The good performances of the proposed stable control design are shown with numerical simulations results.