Neural network-based control design: an LMI approach

S. Limanond, J. Si
1998 IEEE Transactions on Neural Networks  
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 statefeedback control law for the nonlinear system based on the certainty equivalence
more » ... ciple. 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 closedloop system converges. Finally, a simple example is presented so as to illustrate our control design procedure. Index Terms-Linear matrix inequality, multilayer perceptron, nonlinear control, stability analysis.
doi:10.1109/72.728392 pmid:18255820 fatcat:xpo4ozhdjvf5rmzykfwwwcflua