Stable Neural Network Control Systems Using the Multiple-nonlinearity Popov Criterion

This paper introduces a new concept for training a neural network controller which guarantees Lyapunov stability of a closed loop controlled system. A modified backpropagation algorithm is derived, where the usual minimization problem is constrained to satisfy the multiple-nonlinearity Popov stability condition. The generalized Kalman-Yakubovich condition is used to provide necessaty and sufficient conditions for satisfying the Popov criterion.