The fundamental lemma proposed by Jan Willems and co-authors in 2005 is pivotal for many recent research efforts on data-driven control. It
states that, under suitable assumptions, any input-output trajectory of a linear time-invariant (LTI) system can be described as a linear combination of previously recorded trajectories.
Recently, there have been several extensions of the fundamental lemma, e.g., to linear-parameter varying systems and to nonlinear systems. Moreover, predictive control based on such non-parametric system descriptions is receiving substantial research interest.
In this seminar, Timm will discuss progress of data-driven predictive control with respect to LTI systems in stochastic and descriptor settings.
First, he will consider the question of how to extend the fundamental lemma to regular descriptor systems and subsequently the stochastic setting. To this end, Timm will revisit polynomial chaos expansions (PCE) of L2 random variables, the origins of which date back to Norbert Wiener.
His research shows that under mild assumptions, stochastic extensions to Willems’ fundamental lemma can be derived either in the PCE framework or relying on past realisation trajectories of inputs, states, and process noise. Specifically, the seminar will illustrate that the knowledge of past noise realisations allows the construction of Hankel matrices which, upon leveraging PCE representations of random variables, enable forward propagation of distributions, without knowledge of any parametric system description.
In the final part of the talk, Timm will turn towards data-driven stochastic MPC to show that the proposed non-parametric system description can be used in a stochastic optimal control problem. Timm’s findings will be illustrated by examples from different applications.
About the Aerodynamics & Control Seminar Series
The Aerodynamics & Control Seminars, hosted by the Department of Aeronautics, are a series of talks by internationally renowned academics covering a broad range of topics in fluid mechanics, control, and the intersection of these two areas.