Modeling of Dynamical Systems via Successive Graph Approximations

TL;DR

This paper introduces a non-parametric, iterative method for online modeling of unknown nonlinear systems using graph approximations with quadratic constraints, demonstrated on control applications like bounds and invariant sets.

Contribution

It presents a novel successive graph approximation technique for real-time modeling of nonlinear Lipschitz systems, enabling better control analysis.

Findings

Effective in approximating unknown nonlinear dynamics

Provides tractable bounds for unmodeled dynamics

Computes positive invariant sets efficiently

Abstract

In this work, we propose a non-parametric technique for online modeling of systems with unknown nonlinear Lipschitz dynamics. The key idea is to successively utilize measurements to approximate the graph of the state-update function using envelopes described by quadratic constraints. The proposed approach is then demonstrated on two control applications: (i) computation of tractable bounds for unmodeled dynamics, and (ii) computation of positive invariant sets. We further highlight the efficacy of the proposed approach via a detailed numerical example.