Adaptive neurocontrol of MIMO systems based on stability theory

In this paper, we prove the input-output stability of a certain class of nonlinear discrete MIMO systems controlled by a multilayer neural net with a simple weight adaptation strategy. The proof is based on the Lyapunov formalism. The stability statement is, however, only valid if the initial weight values are not too far from their optimal values that allow perfect model matching. We therefore propose to initialize the weights with values that solve the linear problem. This extends our previous work (Renders, 1993; Saerens, Renders and Bersini, 1993), where SISO systems were considered