Stable neural-network-based adaptive control for sampled-data nonlinear systems

For a class of MIMO sampled-data nonlinear systems with unknown dynamic nonlinearities, a stable neural-network (NN)-based adaptive control approach which is an integration of an NN approach and the adaptive implementation of the variable structure control with a sector, is developed. The sampled-data nonlinear system is assumed to be controllable and its state vector is available for measurement. The variable structure control with a sector serves two purposes. One is to force the system state to be within the state region in which the NN's are used when the system goes out of neural control; and the other is to provide an additional control until the system tracking error metric is controlled inside the sector within the network approximation region. The proof of a complete stability and a tracking error convergence is given and the setting of the sector and the NN parameters is discussed. It is demonstrated that the asymptotic error of the system can be made dependent only on inherent network approximation errors and the frequency range of unmodeled dynamics. Simulation studies of a two-link manipulator show the effectiveness of the proposed control approach.