Data-driven input-to-state stabilization

TL;DR

This paper develops a data-driven method using sum-of-squares programming to design controllers that stabilize nonlinear polynomial systems against disturbances, even when the system dynamics are unknown but data is available.

Contribution

It introduces a novel data-based approach for input-to-state stabilization of nonlinear systems using sum-of-squares programs, applicable without explicit system models.

Findings

Successfully designed stabilizing controllers from data.

Validated the approach with a numerical example.

Applicable to both data-driven and model-based scenarios.

Abstract

For the class of nonlinear input-affine systems with polynomial dynamics, we consider the problem of designing an input-to-state stabilizing controller with respect to typical exogenous signals in a feedback control system, such as actuator and process disturbances. We address this problem in a data-based setting when we cannot avail ourselves of the dynamics of the actual system, but only of data generated by it under unknown bounded noise. For all dynamics consistent with data, we derive sum-of-squares programs to design an input-to-state stabilizing controller, an input-to-state Lyapunov function and the corresponding comparison functions. This numerical design for input-to-state stabilization seems to be relevant not only in the considered data-based setting, but also in a model-based setting. Illustration of feasibility of the provided sum-of-squares programs is provided on a numerical example.