Rapid dynamical pattern recognition for sampling sequences

In this paper, based on deterministic learning, we propose a method for rapid recognition of dynamical patterns consisting of sampling sequences. First, for the sequences yielded by sampling a periodic or recurrent trajectory (a dynamical pattern) generated from a nonlinear dynamical system, a sampled-data deterministic learning algorithm is employed for modeling/identification of inherent system dynamics. Second, a definition is formulated to characterize similarities between sampling sequences (dynamical patterns) based on differences in the system dynamics. Third, by constructing a set of discrete-time dynamical estimators based on the learned knowledge, similarities between the test and training patterns are measured by using the average L1 norms of synchronization errors, and general conditions for accurate and rapid recognition of dynamical patterns are given in a sampled-data framework. Finally, numerical examples are discussed to illustrate the effectiveness of the proposed method. We demonstrate that not only a test pattern can be rapidly recognized corresponding to a similar training pattern, but also the proposed recognition conditions can be verified step by step based on historical sampling data. This makes a distinction compared with the previous work on rapid dynamical pattern recognition for continuous-time nonlinear systems, in which the recognition conditions are difficult to be verified by using continuous-time signals.