Adaptive critic neural network-based controller for nonlinear systems with input constraints

A novel adaptive critic-based multilayer neural network (NN) controller in discrete-time is designed to deliver a desired tracking performance for a class of nonlinear systems in the presence of magnitude constraints on the input. Reinforcement learning scheme in discrete-time is proposed for the NN controller, where the action generating NN learning is performed based on a certain performance measure, which is supplied from a critic. Using the Lyapunov approach and with a novel weight updates, the uniform ultimately boundedness (UUB) of the closed-loop tracking error and weight estimates are shown. The adaptive critic NN does not require an offline learning phase and the weights can be initialized at zero or randomly. It is shown via simulation that taking magnitude constraints on the input help reduce transients.