Nonlinear control by formal neural networks: piecewise affine perceptrons.

Summary The aim of this work is to present new results concerning the use of a particular class of formal neural networks (the Piecewise Affine Perceptrons: PAP) in the context of closed loop optimal control. The main results obtained are: several properties of PAPs, concerning the nature of the functions they can emulate, a constructive representation theorem for piecewise affine continuous functions, which allows to explicitly construct a PAP from a collection of affine functions, a set of heuristics for learning the parameters of a perceptron in a closed loop and in an optimal control framework, theoretical results concerning the stability of PAPs used as controllers. The last part is devoted to applications of these results to the automatic construction of car engine combustion controllers, which have led to the filing of two patents by Renault.