**Title:** TCP/AQM Congestion Control with Funnel Control

**Abstract:** The congestion control mechanism of the Transmission Control Protocol (TCP) is of great significance to prevent the congestion of the TCP network. Active queue management (AQM) is currently one of the most widely studied congestion solution. In this presentation, we introduced the TCP congestion control principle and algorithm, then we optimized the existing TCP model and applied the funnel control to make the congestion control algorithm play a good role in congestion avoidance and recovery.

*The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.*
**Title:** Inertial Algorithms in optimization, variational inequalities and fixed point problems

**Abstract:** We present an overview of the dynamical aspects of old and new first-order methods used in optimization and variational analysis, and how inertial features and relaxation can help improve their performance. Special attention will be paid to inertial and overrelaxed primal-dual methods, as an illustration.

**Title:** Impulse controllability of system classes of switched DAEs

**Abstract:** In this presentation we consider system classes of switched differential algebraic equations (DAEs). A system class is said to be impulse controllable if every system contained in the class is impulse controllable. In the case that we consider a system class generated by the matrix triplets (E_p, A_p, B_p) and a piecewise continuous switching signal, impulse controllability is not difficult to characterize. However, if we consider a system class generated by some matrix triplets and switching signals that induce the same order modes, the problem of characterizing impulse controllability becomes more complex.

**Title:** The untold story of system identification

**Abstract:** We state necessary and sufficient conditions for one finite length input-output trajectory to determine uniquely (modulo isomorphism of the state-space) a minimal linear, deterministic input-state-output system with given an upper bound on its state dimension. These conditions are in terms of the ranks of a sequence Hankel matrices obtained from the given finite input-output data. In addition, we will introduce a novel state construction from the given measurements.

*The colloquium will also take place online in Google Meet. You can email the organizer for a link to the meeting.*
**Title:** A restart scheme for a dynamic with Hessian damping

**Abstract:** The study of the convergence of optimization algorithms is directly linked to the study of certain differential equations. In [1], it is shown that the convergence of Nesterov’s accelerated gradient method is related to a dynamic involving the gradient of a convex function. Also, a restart scheme is provided, that accelerates the convergence of the function along the solutions of the dynamics. It has been studied that the addition of a term involving the Hessian of the functions stabilizes the convergence, so the main objective is to present the results obtained on the convergence of a new restart scheme for the dynamics with the Hessian term.

[1] W. Su, S. Boyd, and E. Candes, E. “A differential equation for modeling Nesterov’s accelerated gradient method: theory and insights,” *Advances in neural information processing systems*, 2014.

*The colloquium will also take place online in Google Meet. You can email the organizer for a link to the meeting.*

**Title:** Assume-guarantee contracts using simulation

**Abstract:** Contracts can be used to express specifications for dynamical systems. They provide an alternative to common methods for expressing specifications in control, such as dissipativity and set-invariance. In this talk, we will discuss some preliminary work on assume-guarantee contracts similar to the ones introduced in [1]. In contrast to [1], where systems are compared using behaviours, we will compare systems using the notion of *simulation*. We will define contracts and contract implementation for a certain class of linear dynamical systems. Thereafter, we will provide necessary and sufficient conditions for the existence of an implementation, discuss the interpretation of these conditions and whether they can be verified systematically. We will also look into the problem of designing a controller that converts a given system into an implementation of a given contract.

[1] B. M. Shali, A. J. van der Schaft, and B. Besselink, “Behavioural assume-guarantee contracts for linear dynamical systems,” in *IEEE Proceedings of the Conference on Decision and Control*, 2021.

*The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.*

**Title:** Memristor networks, an introduction

**Abstract: ** The emerging field of neuromorphic computing aims to reduce the energy requirements of computing platforms. It draws inspiration from the functioning of the brain and wants to learn from its energy efficiency. For these new neuromorphic technologies dedicated hardware needs to be developed. It is suggested that memristors will play an important role within this new hardware. Memristors, are resistors with a memory storage that can act as non-volatile memory. In addition, because of their dynamical nature, memristors have high potential of mimicking the behavior of certain elements of the brain. In this talk, we introduce a mathematical framework to study the behavior of networks of memristors and we discuss research questions that arise about these networks.

*The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.*

**Title:** Solution Theory for Switched Singular Systems in Discrete Time

**Abstract:** In this talk, solution theory for three sub-classes of linear switched singular systems in discrete time will be presented: jointly index-1, sequentially index-1 and switched index-1. The well-posedness of these sub-classes is guaranteed for an arbitrary switching signal, a fixed mode sequence and a fixed switching signal, respectively. An extension to nonlinear switched singular systems will also be discussed for the jointly index-1 sub-class.

*The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.*

**Title: **Bilevel Aggregator-Prosumers’ Optimization Problem in Real-Time: A Convex Optimization Approach

**Abstract:** This paper proposes a Real-Time Market (RTM) platform for an aggregator and its corresponding prosumers to participate in the electricity wholesale market. The proposed energy market platform is modeled as a bilevel optimization problem where the aggregator and the prosumers are considered as self-interested agents. We present a convex optimization problem which can capture a subset of the set of global optima of the bilevel problem as its optimal solution.

*The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.*

**Title:** Reduced realization and model reduction of switched linear systems with known switching sequence

**Abstract:** We propose a novel reduction approach for switched linear systems with a fixed mode sequence based on subspaces related to the (time-varying) reachable and unobservable spaces. These subspaces are defined in such a way that they can be used to construct a switched weak Kalman decomposition, which is then in turn used to define a reduced switched linear system with an identical input-output behavior. Then we apply a well known balanced truncation approach to each active mode of the reduced realization. The proposed method is illustrated with an example.

*The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.*