NLq Theory: A Neural Control Framework with Global Asymptotic Stability Criteria
In this paper a framework for model-based neural control design is presented, consisting of nonlinear state space models and controllers, parametrized by multilayer feedforward neural networks. The models and closed-loop systems are transformed into so-called NLq system form. NLq systems represent a large class of nonlinear dynamical systems consisting of q layers with alternating linear and static nonlinear operators that satisfy a sector condition. For such NLqs sufficient conditions for global asymptotic stability, input/output stability (dissipativity with finite L2-gain) and robust stability and performance are presented. The stability criteria are expressed as linear matrix inequalities. In the analysis problem it is shown how stability of a given controller can be checked. In the synthesis problem two methods for neural control design are discussed. In the first method Narendra's dynamic backpropagation for tracking on a set of specific reference inputs is modified with an NLq stability constraint in order to ensure, e.g., closed-loop stability. In a second method control design is done without tracking on specific reference inputs, but based on the input/output stability criteria itself, within a standard plant framework as this is done, for example, in H? control theory and ? theory.  1997 Elsevier Science Ltd.
neural control global asymptotic stability state space models input/output stability dissipativity linear matrix inequalities dynamic backpropagation multilayer recurrent neutral networks lyapunov function