**Title:** Dissipativity-preserving reduced-order modeling from data

**Abstract:** Reduced-order modeling from data with dissipativity preservation is discussed in this talk. Employing the data informativity framework, the dissipativity of all systems consistent with noisy data can be characterized by a data-based linear matrix inequality (LMI). Furthermore, semi-definite programming duality helps us to prove the existence of minimal and maximal solutions to the LMI. As in the classical bounded-real and positive-real balanced truncation, these extremal solutions play a role in the computation of well-approximating reduced-order models carrying the dissipativity property. As an additional advantage of using this balancing-type method, a priori error bounds of the reduced-order models are available.

**Title:** A speed restart scheme for first order dynamics bearing second order information in time and space

**Abstract:** We present two techniques that can help stabilize otherwise erratic inertial methods. Combined, they can enhance the performance of accelerated methods, especially for functions with quadratic growth, for which the rate of linear convergence is improved.

**Title:** Prescribed-time control

**Abstract:** In terms of the user’s knowledge about the settling time, non-asymptotic controllers can be divided into three major categories of finite-time, fixed-time, and prescribed-time approaches. In finite-time schemes, it is only known that the system non-asymptotically converges at a finite time that is generally a function of the initial conditions. Fixed-time schemes provide an upper bound for the settling time, independently of initial conditions. However, in prescribed-time control, the settling time is commanded to the system, which means that the user is not only aware of the convergence moment but can arbitrarily specify it just by changing a parameter. It turns out that another interesting feature of prescribed-time controllers, apart from having an adjustable settling time, is their robustness to unknown dynamics for which no global bounds exist.

In this talk, after reviewing the state-of-the-art, some new unpublished results on the differential Riccati equation approaches to prescribed-time control are discussed (LQR and SDRE-based designs), and it is shown how they can be used for the stabilization of (partially) unknown nonlinear systems.

**Title:** Singular linear switched systems in discrete time: solution theory, reachability, and duality

**Abstract:** In this talk, solution theory for singular linear switched systems in discreet time with arbitrary switching signals will be presented. Based on the derived solution theory, reachability and controllability characterizations will be discussed for a fixed and known switching signal. Moreover, the duality between reachability and observability of this system class will also be discussed.

**Title:** Model reference Gaussian process regression: data-driven output feedback controller

**Abstract:** Data-driven controls using Gaussian process regression have recently gained much attention. In such approaches, system identification by Gaussian process regression is mostly followed by model-based controller designs. However, the outcomes of Gaussian process regression are often too complicated to apply conventional control designs, which makes the numerical design such as model predictive control employed in many cases. To overcome the restriction, our idea is to perform Gaussian process regression to the inverse of the plant with the same input/output data for the conventional regression. With the inverse, one can design a model reference controller without resorting to numerical control methods. This talk considers single-input single-output (SISO) discrete-time nonlinear systems of minimum phase with relative degree one. It is highlighted that the model reference Gaussian process regression controller is designed directly from pre-collected input/output data without system identification.

**Title:** On the legacy of Jan Willems (talk given before for the Control History Forum, CSS Day, October 2022)

**Abstract:** The list of scientific contributions of Jan Willems spans a whole range of topics, including (input-output) stability theory, dissipativity theory, linear geometric control theory, identification, the behavioral approach to systems and control, physical systems theory, open stochastic systems, .. ; see the website

https://homes.esat.kuleuven.be/~sistawww/smc/jwillems/ for much more information. In this talk I will focus on two of these topics: dissipativity theory, and the behavioral approach to systems and control. Discussion of the first topic will be partly based on:

Introduction by Arjan van der Schaft to Jan C. Willems’, “Dissipative Dynamical Systems,

Part I: General Theory, 50 Years of Dissipativity Theory, IEEE Control Systems Magazine 42 (2), 46-50, 2022,

Part II: Linear Systems With Quadratic Supply Rates, IEEE Control Systems Magazine 42 (3), 32-35, 2022.

**Title:** Scalable controllability analysis of structured systems

**Abstract:** This talk deals with strong structural controllability of structured networks. A structured network is a family of structured systems (called node systems) that are interconnected by means of a structured interconnection law. The node systems and their structured interconnection law are given by pattern matrices. We will show that a structured network is strongly structurally controllable if and only if an associated structured system is. This structured system will in general have a very large state space dimension, and therefore existing tests for verifying strong structural controllability are not tractable. The results we present circumvent this problem. We show that controllability can be tested by replacing the original network by a new network in which all original node systems have been replaced by (auxiliary) node systems with state space dimensions either 1 or 2. Hence, controllability of the original network can be verified by testing controllability of a structured system with state space dimension at most twice the number of node systems, regardless of the state space dimensions of the original node systems.

**Title: **About observers of hybrid systems

**Abstract: **I recently reviewed the very nice paper [1] by Pauline Bernard and Ricardo Sanfelice about an observer design for hybrid systems, whose ideas I would like to share with you. I will briefly recall the hybrid systems framework proposed by Goebel, Sanfelice and Teel [2]. Afterwards I will highlight the difficulties in designing an observer for these kind of systems, in particular, when the jump times cannot be observed directly. Then I explain the actual observer design proposed in [1].

[1] Pauline Bernard and Ricardo Sanfelice, “Semi-global high-gain hybrid observer for a class of hybrid dynamical systems with unknown jump times,”

*Submitted to Transaction on Automatic Control, full version available at https://hal. archives-ouvertes.fr/hal-03736135*, 2022.

[2] R. Goebel, R. Sanfelice, and A. Teel, “Hybrid Dynamical Systems: Modeling, Stability and Robustness,” *Princeton University Press*, 2012

**Title:** System analysis with scaled relative graphs

**Abstract:** Scaled relative graphs (SRGs) were recently introduced by Ryu, Hannah and Yin to analyze the convergence of optimisation algorithms using two dimensional Euclidean geometry. In this seminar, I’ll show how the SRG can be used to study incremental input/output properties of feedback systems. The SRG of an LTI transfer function is closely related to its Nyquist diagram. The SRG may be plotted or approximated for arbitrary nonlinear operators, and allows classical Nyquist techniques to be applied to nonlinear systems. I will give a generalisation of the Nyquist criterion for stable systems, where the Nyquist diagram and the point −1 are replaced by SRGs of two feedback-interconnected nonlinear operators. The distance between the two SRGs is a nonlinear stability margin, and is the reciprocal of the incremental gain of the feedback system. This theorem generalises a range of existing results, and has advantages over classical input/output techniques.