On-line learning of dynamical systems in the presence of model mismatch and disturbances

This paper is concerned with the on-line learning of unknown dynamical syst ems using a recurrent neural network. The unknown dynamic systems to be lea rned are subject to disturbances and possibly unstable, The neural-network model used has a simple architecture with one layer of adaptive connection weights. Four learning rules are proposed for the cases where the system st ate is measurable in continuous or discrete time. Some of these learning ru les extend the sigma -modification of the standard gradient learning rule. Convergence properties are given to show that the weight parameters of the recurrent neural network are bounded and the state estimation error converg es exponentially to a bounded set, which depends on the modeling error and the disturbance bound. The effectiveness;of the proposed learning rules far the recurrent neural network is demonstrated using an illustrative example of tracking a Brownian motion.