A Stability Condition for Neural Network Control of Uncertain Systems

This paper derives a stability condition for neural network control systems which the parameters of the controlled systems are uncertain. The stability condition can be imposed in training processes to guarantee the stability of the control systems. The controller is a single hidden layer, feedforward neural network. The controlled system is assumed to be full-state accessible and can be modeled as a linear uncertain system. The stability is confirmed by the existence of a Lyapunov function of the closed loop systems. A simulation result on Van der Pol’s equation with parametric uncertainty presented to demonstrate an application of the condition. A modified backpropagation algorithm with a model reference technique is used to train the controller.