Control of recurrent neural networks using differential minimax game: The deterministic case

This paper presents a theoretical design of how a minimax equilibrium of differential game is achieved in a class of large-scale nonlinear dynamic systems, namely the recurrent neural networks. In order to realize the equilibrium, we consider the vector of external inputs as a player and the vector of internal noises (or disturbances or modeling errors) as an opposing player. The purpose of this study is to construct a nonlinear H _∞ optimal control for deterministic noisy recurrent neural networks to achieve an optimal-oriented stabilization, as well as to attenuate noise to a prescribed level with stability margins. A numerical example demonstrates the effectiveness of the proposed approach.