Observer-based echo-state neural network control for a class of nonlinear systems

The echo-state network is a new structure of recurrent neural networks. Based on the echo-state network, this paper develops an adaptive output feedback control method for a class of perturbed Sngle-Input Single-Output (SISO) nonlinear system in which only the system output is measured. The echo-state network is developed to approximate the control law based on the certainty equivalent approach. A Luenberger like observer is used to estimate the state signals. The echo-state network controller’s parameters are updated on-line using the gradient of descent method. The overall adaptive scheme guarantees that all signals involved are bounded and the output of the closed-loop system will asymptotically track the desired output trajectory without using a supervisory control term. Two nonlinear systems are used to verify the effectiveness of the proposed method.