Simulation of Nonlinear Systems Trajectories: between Models and Behaviors

TL;DR

This paper explores the relationship between model-based and behavioral approaches to simulating nonlinear system trajectories, extending results from deterministic to stochastic frameworks.

Contribution

It establishes equivalences between the two frameworks for trajectory simulation and extends existing deterministic results to stochastic systems.

Findings

Established equivalence between model-based and behavioral representations.

Extended trajectory simulation results to stochastic nonlinear systems.

Provided theoretical foundations for future research in nonlinear system simulation.

Abstract

In this paper, we study connections between the classical model-based approach to nonlinear system theory, where systems are represented by equations, and the nonlinear behavioral approach, where systems are defined as sets of trajectories. In particular, we focus on equivalent representations of the systems in the two frameworks for the problem of simulating a future nonlinear system trajectory starting from a given set of noisy data. The goal also includes extending some existing results from the deterministic to the stochastic setting.