SCO colloquium: Harry Trentelman

Title: A behavioral approach to data-driven control with noisy input-output data

 

Abstract: Data-driven analysis and control is a research topic that has received a lot of attention in the past few years. The idea that lies at the core of this research area is to use data obtained from an unknown dynamical system to verify certain system properties and to design feedback control laws for that system. The main challenge is to do the analysis and design without the usual first step of establishing a mathematical model of the system (for example by using first principles modeling or system identification), but work directly with the data instead. This has been the subject of many recent publications in the area, for the most part in the context of input-output systems in state space form.

 

In this talk, we will abandon the paradigm of systems in state space form, and will, instead, use as model class the set of all input-output systems described by higher order difference equations, also called auto-regressive (AR) systems. The unknown dynamical system that we want to analyse or control is assumed to be a member of this model class of AR systems. We will assume that noisy input-output data on a given finite time-interval have been obtained from this unknown AR system. These data are employed to check stability or to verify whether a dynamic feedback controller exists that stabilizes the unknown system and, if so, to compute a stabilizing controller.

 

We will discuss data-based tests to tackle these analysis and design problems. To do this, we will heavily rely on methods from the behavioral approach to systems and control. In particular, we will adopt the notion of quadratic difference form (QDF) as a framework for Lyapunov functions for autonomous systems described by higher order difference equations. Our main results will be necessary and sufficient condition for data informativity in terms of feasibility of certain linear matrix inequalities (LMIs) obtained from the data. Important tools in deriving these conditions are recent results on quadratic matrix inequalties (QMIs) and a matrix version of Yakubovich’s S-procedure.