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 understandin g of the stability behavior of the closed-loop system. In this paper, we pr opose, from an adaptive control perspective, a neural controller for a clas s of unknown, minimum phase, feedback linearizable nonlinear system with kn own relative degree, The control scheme is based on the backstepping design technique in conjunction with a linearly parameterized neural-network stru cture. The resulting controller, however, moves the complex mechanics invol ved in a typical backstepping design from offline to online. With appropria te choice of the network size and neural basis functions, the same controll er can be trained online to control different nonlinear plants with the sam e relative degree, with semiglobal stability as shown by simple Lyapunov an alysis, Meanwhile, the controller also preserves some of the performance pr operties of the standard backstepping controllers. Simulation results are s hown to demonstrate these properties and to compare the neural controller w ith a standard backstepping controller.