Output Feedback Control and Observer Design for Dynamic Artificial Neural Networks

Artificial neural networks are black-box models widely used to approximate nonlinear dynamical system behavior. This article proposes sufficient design criteria for stabilizing dynamic output error feedback controllers and optimal output observers for systems described by dynamic artificial neural networks (DANNs). DANNs can be written in the standard nonlinear operator form (SNOF) and as diagonal norm-bounded linear differential inclusions (DNLDIs). Expanding on past work on Lyapunov theory and matrix inequalities, criteria are derived for designing two-step observer-based dynamic output feedback controllers for discrete-time DNLDIs. The applicability of the theory is demonstrated for a nonlinear multistep chemical synthesis process modeled by a DANN under the presence of disturbances and parametric uncertainty.