SCO colloquium: Paul Wijnbergen

Title: Optimal control of switched differential algebraic equations and more…
 
Abstract: The first part of this presentation will be concerned with linear quadratic regulator (LQR) problem for switched differential algebraic equations (sDAEs). Due to the linearity of the dynamics and the quadratic cost functional it can be shown that the optimal cost is a quadratic function of the initial value and the optimal controller is linear in the state. Taking dynamic programming approach it will be shown that the LQR problem for sDAEs can be reduced to a repeated finite horizon LQR problem for non-switched DAEs. However, as this LQR problem is considered in the context of sDAEs additional constraints on the terminal state and the terminal cost matrix have to be imposed. As a consequence of these constraints, there generally does not exist an optimal solution for all initial values, but only for initial values contained in a certain subspace. As a main result, it is shown how to characterize this subspace and how to compute an optimal control if it exists. This part of the presentation will be concluded with some simulations to illustrate the results.

In the second part of the presentation, the platooning problem will briefly be addressed. It will be shown that if a leader-follower structure is adopted, the problem of finding a decentralized controller can be posed as a disturbance decoupling problem combined with output stabilization. Within this geometrical context, string stability follows from the spacing policy. Necessary and sufficient conditions on the existence of a decentralized controller are given and the results are illustrated through simulation results.

 

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.

SCO colloquium: Julian Koellermeier

Title: Control problems and stability of hierarchical moment models for fluid dynamics
 
Abstract: Applications of atmospheric re-entry and geophysical flows are characterized by a large variety of separate models for specific tasks. This model variety poses significant difficulties both for the analysis and for the numerical solution. We thus need to rethink mathematical modelling for future numerical simulations. In this talk, I will introduce hierarchical moment models as a flexible way to derive hierarchies of models in fluid dynamics and other applications. The general derivation procedure results in structural similarities of the models, which facilitate physical insight, model adaptivity, and the development of suitable numerical methods. Based on rarefied gases and shallow flows, I will exemplify the hierarchical moment approach and highlight runtime and accuracy improvements. From a control theory perspective, I will discuss problems for the future extension towards adaptive self-learning models that make use of the hierarchical structure of the models. Lastly, I will discuss the derivation and stability analysis of a hierarchical model for a linear delay differential equation with uncertain parameters.

SCO colloquium: Di Liu

Title: On Structural and Safety Properties of Head-to-tail String Stability in Mixed Platoons
 
Abstract: The interaction between automated and human-driven vehicles in mixed (human/automated) platoons is far from understood. To study this interaction, the notion of head-to-tail string stability was proposed in the literature. Head-to-tail string stability is an extension of the standard string stability concept where, instead of asking every vehicle to achieve string stability, a lack of string stability is allowed due to human drivers, provided it can be suitably compensated by automated vehicles sparsely inserted in the platoon. This work introduces a theoretical framework for the problem of head-to-tail string stability of mixed platoons: it discusses a suitable vehicle-following human driver model to study mixed platoons, and it gives a reduced-order design strategy for head-to-tail string stability only depending on three gains. The work further discusses the safety limitations of the head-to-tail string stability notion, and it shows that safety improvements can be attained by an appropriate reduced-order design strategy only depending on two additional gains. To validate the effectiveness of the design, linear and nonlinear simulations show that the string stability/safety trade-offs of the proposed reduced-order design are comparable with those resulting from full-order designs.
 
The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.

SCO colloquium: Yanxin Li

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.

SCO colloquium: Juan Peypouquet

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.
 

SCO colloquium: Paul Wijnbergen

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.

SCO colloquium: Kanat Camlibel

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.

SCO colloquium: Juan José Maulén Muñoz

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.

SCO colloquium: Brayan Shali

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.