Data-Driven Simulation for NARX Systems

Nonlinear phenomena can be represented as nonlinear autoregressive exogenous (NARX) systems. NARX systems can be seen as a nonlinear version of linear infinite impulse response filter. Data-driven approaches are witnessing considerable interests in recent times and they are well-flourished for linear time-invariant systems. However, for nonlinear systems, they are still limited and attempts have been made to generalize the results for linear systems to nonlinear systems. In this paper, we study the problem of data-driven simulation for NARX systems: compute the output trajectory from a given input trajectory and initial conditions without explicitly identifying the parametric model; the model is implicitly identified by observed trajectory. Next, we develop an algorithm for the implementation of our approach. Finally, we illustrate the developed algorithm by numerical experiments.