Signature-Based Time-Series Analysis for System Identification: Methods That Offer Unique Benefits

Nonlinear dynamic models are the essential components of the virtual environments that drive today's design, optimization, control, and automation technology. They are the natural choice for characterizing the behavior of biological, ecological, social, and economic systems, as well as artifacts such as aircraft and manufacturing systems. The art and science of developing models in accordance with the observed input/output data and the corresponding analysis is called system identification [1]. When dynamic systems can be modeled by first principles, the models are in the form of differential equations, defined in terms of physically meaningful variables and parameters (coefficients and exponents). Otherwise, the models are in empirical form as neural networks or autoregressive moving-average models [2]. Regardless of the model form, the output data, acquired in the form of a time series, are the basis of system identification.