Discrete-Time Adaptive Neural Backstepping

This chapter deals with adaptive tracking for a class of MIMO discrete-time nonlinear systems in presence of bounded disturbances. In this chapter, a high order neural network structure is used to approximate a control law designed by the backstepping technique, applied to a block strict feedback form (BSFF). It also presents the respective stability analysis, on the basis of the Lyapunov approach, for the whole scheme including the extended Kalman filter (EKF)-based NN learning algorithm. Applicability of this scheme is illustrated via simulation for a discrete-time nonlinear model of an electric induction motor.

In recent adaptive and robust control literature, numerous approaches have been proposed for the design of nonlinear control systems. Among these, adaptive backstepping constitutes a major design methodology [6, 9]. The idea behind backstepping design is that some appropriate functions of state variables are selected recursively as virtual control inputs for lower dimension subsystems of the overall system [12]. Each backstepping stage results in a new virtual control designs from the preceding design stages. When the procedure ends, a feedback design for the true control input results, which achieves the original design objective. The backstepping technique provides a systematic framework for the design of tracking and regulation strategies, suitable for a large class of state feedback linearizable nonlinear systems [1, 9–11].