Catastrophes in Optimal Control

A method for tracking control of mechanical systems based on artificial neural networks is presented. The controller consists of a proportional plus derivative controller and a two-layer feedforward neural network. It is shown that the tracking error of the closed-loop system goes to zero while the control effort is minimized. Tuning of the neural networkʹs weights is formulated in terms of a constrained optimization problem. The resulting algorithm has a simple structure and requires a very modest computation effort, in addition, the neural networkʹs learning procedure is implemented on-line.