A Dynamical Systems Approach to Modeling Input-Output Systems

Motivated by practical applications, we generalize theoretical results on the nonlinear modeling of autonomous dynamical systems to input-output systems. The inputs driving the system are assumed to be observed, as well as the outputs. The underlying dynamics coupling inputs to outputs is assumed to be deterministic. We give a definition of chaos for input-output systems, and develop a theoretical framework for state space reconstruction and modeling. Most of the results for autonomous deterministic systems are found to generalize to input-output systems with some modifications, even if the inputs are stochastic.