Data-driven input-to-state stabilization with respect to measurement errors

TL;DR

This paper develops data-driven conditions for ensuring input-to-state stability of nonlinear systems with measurement errors, using convex sum-of-squares programming to design controllers and Lyapunov functions based on experimental data.

Contribution

It introduces a novel data-based approach for input-to-state stabilization considering measurement errors, employing convex sum-of-squares optimization.

Findings

Feasibility demonstrated with a numerical example.

Conditions account for all dynamics consistent with data.

Provides a systematic data-driven control design method.

Abstract

We consider noisy input/state data collected from an experiment on a polynomial input-affine nonlinear system. Motivated by event-triggered control, we provide data-based conditions for input-to-state stability with respect to measurement errors. Such conditions, which take into account all dynamics consistent with data, lead to the design of a feedback controller, an ISS Lyapunov function, and comparison functions ensuring ISS with respect to measurement errors. When solved alternately for two subsets of the decision variables, these conditions become a convex sum-of-squares program. Feasibility of the program is illustrated with a numerical example.