title: Neural network-based control design: an LMI approach.
abstract: In this paper, we address a neural-network-based control design for a discrete-time nonlinear system. Our design approach is to approximate the nonlinear system with a multilayer perceptron of which the activation functions are of the sigmoid type symmetric to the origin. A linear difference inclusion representation is then established for this class of approximating neural networks and is used to design a state-feedback control law for the nonlinear system based on the certainty equivalence principle. The control design equations are shown to be a set of linear matrix inequalities where a convex optimization algorithm can be applied to determine the control signal. Further, the stability of the closed-loop is guaranteed in the sense that there exists a unique global attraction region in the neighborhood of the origin to which every trajectory of the closed-loop system converges. Finally, a simple example is presented so as to illustrate our control design procedure.
authors.affiliation: Department of Electrical Engineering, SSERC, Arizona State University, Tempe, AZ 85287-7606, USA.
authors.forename: S
authors.initials: S
authors.lastname: Limanond
authors.forename: J
authors.initials: J
authors.lastname: Si