A "deterministic learning" theory was recently proposed for identification, representation and rapid recognition of multi-variable dynamical patterns with full-state measurements. In this paper, it will be shown that for a class of single-variable dynamical patterns with only output measurements, identification, representation and rapid recognition can be achieved via the deterministic learning theory and state observation techniques. Firstly, the system dynamics of a set of training single-variable dynamical pattern can be locally-accurately identified through high-gain observation and deterministic learning. Secondly, a single-variable dynamical pattern is represented in a time-invariant and spatially-distributed manner via deterministic learning. This representation is a kind of static, graph-based representation. A set of nonlinear observers are then constructed as dynamic representatives of the training dynamical patterns. Thirdly, rapid recognition of a test single-variable dynamical pattern can be implemented when non-high-gain state observation is achieved according to a kind of internal and dynamical matching on system dynamics. The observation errors can be taken as the measure of similarity between the test and training dynamical patterns.
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