New Results on Rapid Dynamical Pattern Recognition via Deterministic Learning From Sampling Sequences

Rapid dynamical pattern recognition based on the deterministic learning method (DLM-based RDPR) aims to rapidly recognize the most similar dynamical pattern pair from perspectives of differences in inherent system dynamics. The basic mechanism is to use available recognition errors to reflect the differences in the dynamics of dynamical pattern pairs and then to make a decision based on a minimal recognition error (MRE) principle. This article focuses on providing a rigorous theoretical analysis of the MRE principle in DLM-based RDPR under the sampled-data framework. Specifically, we seek a unified methodology from the similarity definition to the measure implementation and then to derive general sufficient conditions and necessary conditions for the MRE principle. The main idea is to: 1) from the average signal energy aspect, define a time-dependent dynamics-based similarity in dynamical pattern pairs and reestablish the measure of recognition errors generated from the DLM-based RDPR; 2) introduce the energy-based Lyapunov method to establish the interrelation between the dynamical distance and the recognition error; and 3) derive sufficient conditions and necessary conditions from two directions of the interrelation. The proposed conditions distinguish themselves from virtually all of the existing DLM-based RDPR works with only sufficient conditions in the sense that it is shown in a rigorous analysis that under what conditions, the pattern pair recognized based on the MRE principle is indeed the most similar one. Therefore, the proposed work makes the DLM-based RDPR possess good interpretability and provides strong theoretical guidance in engineering applications.