Stable neural controller design for unknown nonlinear systems using backstepping

Despite the vast development of neural controllers in the literature, their stability properties are usually addressed inadequately. With most neural control schemes, the choices of neural-network structure, initial weights, and training speed are often nonsystematic, due to the lack of understanding of the stability behavior of the closed-loop system. In this paper, we propose, from an adaptive control perspective, a neural controller for a class of unknown, minimum phase, feedback linearizable nonlinear system with known relative degree. The control scheme is based on the backstepping design technique in conjunction with a linearly parameterized neural-network structure. The resulting controller, however, moves the complex mechanics involved in a typical backstepping design from offline to online. With appropriate choice of the network size and neural basis functions, the same controller can be trained online to control different nonlinear plants with the same relative degree, with semiglobal stability as shown by simple Lyapunov analysis. Meanwhile, the controller also preserves some of the performance properties of the standard backstepping controllers. Simulation results are shown to demonstrate these properties and to compare the neural controller with a standard backstepping controller.