Data-driven control of continuous-time systems: A synthesis-operator approach

TL;DR

This paper introduces a novel data-driven control framework for continuous-time systems using synthesis operators, enabling stabilization analysis directly from data without derivatives or sampling.

Contribution

It presents a new synthesis-operator based approach that characterizes data informativity and provides linear matrix inequality conditions for stabilization under noise.

Findings

Characterizes data informativity for system identification and stabilization

Provides necessary and sufficient conditions for quadratic stabilization

Formulates conditions as linear matrix inequalities

Abstract

This paper addresses data-driven control of continuous-time systems. We develop a framework based on synthesis operators associated with input and state trajectories. A key advantage of the proposed method is that it does not require the state derivative and uses continuous-time data directly without sampling or filtering. First, systems compatible with given data are described by the synthesis operators into which data trajectories are embedded. Next, we characterize data informativity properties for system identification and for stabilization. Finally, we establish a necessary and sufficient condition for informativity for quadratic stabilization in the presence of process noise. This condition is formulated as linear matrix inequalities by exploiting the finite-rank structure of the synthesis operators.