ADAPTIVE-CONTROL OF A CLASS OF NONLINEAR DISCRETE-TIME-SYSTEMS USING NEURAL NETWORKS

Layered neural networks are used in a nonlinear self-tuning adaptive c ontrol problem, The plant is an unknown feedback-linearizable discrete -time system,represented by an input-output model. To derive the linea rizing-stabilizing feedback control, a (possibly nonminimal) state-spa ce model of the plant is obtained. This model is used to define the ze ro dynamics, which are assumed to be stable, i.e., the system is assum ed to be minimum phase. A linearizing feedback control is derived in t erms of some unknown nonlinear functions. A layered neural network is used to model the unknown system and generate the feedback control. Ba sed on the error between the plant output and the model output, the we ights of the neural network are updated. A local convergence result is given. The result says that for any bounded initial conditions of the plant, if the neural network model contains enough number of nonlinea r hidden neurons and if the initial guess of the network weights is su fficiently close to the correct weights, then the tracking error betwe en the plant output and the reference command will converge to a bound ed ball, whose size is determined by a dead-zone nonlinearity. Compute r simulations verify the theoretical result.