Stabilization of nonlinear singularly perturbed systems using multilayered neural networks

Multilayered neural networks are used to construct a nonlinear learning feedback controller for a class of nonlinear time-invariant singularly perturbed systems with fast actuators. The parameters of the networks are updated on-line by using the gradient descent method with a dead-zone function. The feedback-controlled system is proved to be stable by the Lyapunov approach such that the chosen design manifold becomes an exact integral manifold and the trajectories, starting from the bounded initial states, are steered along the integral manifold to a bounded set centered at the origin, whose size can be arbitrarily chosen for all sufficiently small singular perturbation parameter ϵ;. The simulation results are included to complement the theoretical discussions.