Robust adaptive nonlinear system identification and trajectory tracking by dynamic neural networks

We analyze adaptive nonlinear identification and trajectory tracking using a dynamic neural network, with the same state space dimension as the system. We assume the system space state completely measurable. By means of a Lyapunov-like analysis we determine stability conditions for the identification error. We then analyze the trajectory tracking error when the adaptive controller is utilized. For the identification analysis we use an algebraic Riccati equation and for the tracking error a differential one using online adapted parameters of the neural network. The structure of our scheme is composed-by two parts: the neural network identifier and the tracking controller. As our main contributions, we establish two theorems: the first one gives a bound for the identification error, and the second one establish a bound for the tracking error