Deterministic Learning and Rapid Dynamical Pattern Recognition of Discrete-Time Systems

Recently, a deterministic learning theory was proposed for identification and rapid pattern recognition of uncertain nonlinear dynamical systems. In this paper, we investigate deterministic learning of discrete-time nonlinear systems. For periodic or recurrent dynamical patterns, the persistent excitation (PE) condition can be satisfied by a regression subvector constructed from the neurons near the sequence. With the satisfaction of the PE condition, it is shown that the internal dynamics of an uncertain discrete-time nonlinear system can be accurately learned along the state sequence. Using the learned knowledge, a rapid pattern recognition mechanism can be implemented, in which synchronous errors are taken as the measure of similarity of the dynamical patterns generated from different systems. Compared with the methods based on signal processing, this approach appears to need less time-domain information for recognition and is more effective for high speed applications. Simulation is included to show the effectiveness of the approach.