Piecewise affine neural networks and nonlinear control: stability results

Concerns stability properties of artificial neural networks tuned to nonlinear control. The neural networks used are piecewise affine perceptrons (PAP), a subclass of perceptrons. They have properties that can be used to initialize them to control a given nonlinear system. Besides they have the same useful properties as classical perceptrons: the universal approximation property and the generalization property. The stability results given here are obtained by constructing piecewise quadratic Lyapunov functions. This paper will at first establish a result about PAP that will be use to adapt a result about stability of piecewise affine continuous-time systems, then a similar result will be found for discrete-time ones. After that a methodology to tune PAP for control of nonlinear systems will be exposed and finally this will be illustrated by an example: the control of an engine combustion model