Robust targeted exploration for systems with non-stochastic disturbances

TL;DR

This paper introduces a robust targeted exploration method for uncertain linear systems with energy-bounded disturbances, ensuring accurate parameter estimation without distributional assumptions, applicable to nonlinear systems.

Contribution

It develops a semidefinite programming approach for exploration in systems with non-stochastic disturbances, advancing robust system identification techniques.

Findings

Guarantees desired accuracy in parameter estimation.

Applicable to nonlinear system examples.

Robust to initial parametric uncertainty.

Abstract

We propose a novel targeted exploration strategy designed specifically for uncertain linear time-invariant systems with energy-bounded disturbances, i.e., without any assumptions on the distribution of the disturbances. We use classical results characterising the set of non-falsified parameters consistent with energy-bounded disturbances. We derive a semidefinite program which computes an exploration strategy that guarantees a desired accuracy of the parameter estimate. This design is based on sufficient conditions on the spectral content of the exploration data that robustly account for initial parametric uncertainty. Finally, we highlight the applicability of the exploration strategy through a numerical example involving a nonlinear system.