Data-Driven System Analysis of Nonlinear Systems Using Polynomial Approximation

doi:10.1109/TAC.2023.3321212

2024-07-01

Tim Martin *

Frank Allgöwer

DOI：10.1109/TAC.2023.3321212

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摘要

En 中文

In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we establish a polynomial representation of nonlinear functions based on a polynomial sector by Taylor's theorem and a set-membership for Taylor polynomials. The latter is obtained from finite noisy samples. By incorporating the measurement noise, the error of polynomial approximation, and potentially given prior knowledge on the structure of the system dynamics, we achieve computationally tractable conditions by sum of squares relaxation to verify dissipativity of nonlinear dynamical systems with rigorous guarantees. The framework is extended by combining multiple Taylor polynomial approximations, which yields a less conservative piecewise polynomial system representation. The proposed approach is applied for an experimental example. There it is compared with a least-squares-error model including knowledge from first principle.

Keyword:

Noise measurement

System dynamics

Nonlinear dynamical systems

Trajectory

Linear matrix inequalities

Control theory

Upper bound

Data-driven system analysis

dissipativity

nonlinear systems

polynomial approximation