Abstract: After a short introduction about Chebyshev polynomial bases, I use them to represent (approximations of) input and output trajectories of a system, and I state a continuous-time version of the “fundamental lemma” frequently used in discrete-time data-driven control. I also show how such Chebyshev representations are useful to extend the informativity approach of van Waarde et al to the continuous-time case.

Abstract: The need for measuring closeness of control systems is basic in control theory. A useful metric for this  in the context of linear control systems was introduced by Vinnicombe in 1993, and is called the $\nu$-metric. But there only systems described by constant coefficient  ordinary differential equations were considered, and  the question of handling partial differential equations, and delay-differential equations was left open.  We address this issue, and define a new $\nu$-metric in control theory  which also covers such systems, and prove its desirable properties.

Abstract: It is known (Jaakkola and Wagener, 2020) that in general there are very many symmetric Nash equilibria in differential games when players are permitted to use discontinuous feedback rules. A detailed analysis of these discontinuous-feedback equilibria can be undertaken in the context of the linear-quadratic game that was proposed by Dockner and Long (1993) as a model for international pollution control. It turns out that it is possible to construct a supremal value function, using a limit procedure that requires the number of discontinuities in the feedback rule used by agents to tend to infinity. When moreover the discount factor in the infinite-horizon objective functional tends to zero, this supremal value function becomes equal to the value function that would be reached by global coordination. The corresponding feedback rule, however, does not converge to the coordinated rule; it remains a discontinuous feedback, be it with only a single jump. Joint work with Jacob Engwerda and Vishwa Reddy. 

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Abstract: Describing a behavior as a steepest-ascent walk in an energy landscape is amongst the most powerful explanatory concepts of science and engineering. But what is a gradient system? My talk will motivate that question in the context of mixed feedback system analysis and spiking control design. Along the way, I will review key systems and control contributions on that question, that all share a tight association with Groningen.

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Abstract: In this seminar we will evaluate different ways for modelling interconnected systems from a data-driven modelling perspective, and discuss the consequences for identifiability and identification. A distinction will be made between systems with topologies characterized by either directed or undirected graphs, reflecting either transfer function (module) representations or diffusively coupled dynamic networks. Specific results for the module framework will be illustrated through the recently released MATLAB Toolbox for identification in dynamic networks.

Abstract: In this presentation we discuss a number of challenges on the modeling of port-Hamiltonian dynamical systems from data, together with numerical approximation methods that preserve the port-Hamiltonian structure of infinite dimensional port-Hamiltonian systems. 

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Abstract: For finite-dimensional systems it is well-known that the system $\dot{x}(t) = A x(t)$, $y(t)= Cx(t)$ is observable if and only if the rank of $[ C \\ sI-A]$ is full for all complex s. This can equivalently be written as there exists an $m>0$ such that for all complex $s$ and for all states $x$ there holds $\|(sI-A)x\|^2 + \|Cx\|^2 \geq m \|x\|^2$. For infinite-dimensional systems such a test is until now unknown. In this presentation we will discuss the progress that has been made until now. In particular, we will focus on the test proposed by D. Russell and G. Weiss in 1994. There they conjecture that the (exponentially stable) infinite-dimensional system $\dot{x}(t) = A x(t)$, $y(t)= Cx(t)$ is (exactly) observable if and only if exists an $m>0$ such that for all complex $s$ with negative real part and for all states $x$ in the domain of $A$ there holds $\|(sI-A)x\|^2 + Re(s) \|Cx\|^2 \geq m Re(s)^2 \|x\|^2$.

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Abstract: We define persistency of excitation and informativity for system identification for a special class of 2D systems, those that are state-representable and autonomous. We characterize informativity for system identification in terms of properties of a matrix constructed from the restrictions of a system trajectory on successive consecutive diagonal lines of Z^2. We state a procedure to compute arbitrary trajectories from a “sufficiently rich” one. (joint work with D. Pal of the Indian Institute of Technology Mumbai)

Abstract: In this talk we will discuss the synergy between two themes from Harry’s oeuvre, namely quadratic difference forms (QDFs) and data-driven control. Quadratic differential forms were introduced by Harry and Jan Willems in 1998 in an effort to develop Lyapunov and dissipativity theory in the context of the behavioral approach to systems and control. These forms serve as Lyapunov functions, storage functions and supply rates for linear systems represented by higher order differential equations. Later on, extensions of the theory to discrete-time systems were developed by Kaneko and Fujii and Kojima and Takaba, using the concept of quadratic difference forms.

In recent years, Harry became interested in the problem of obtaining controllers for dynamical systems directly from measured data, rather than using a given system model. Together with colleagues from Groningen, he developed the so-called informativity approach to data-driven control. Within this approach, one studies the set of dynamical systems that are compatible with a given data set (i.e., all systems that could have generated the data), and the purpose is to come up with a single controller that “works” for all of these systems. If such a controller exists, we say that the data are informative for the specified control task. 

The first contributions to data informativity worked under the assumption that the state of the system can be fully measured. In this talk, however, we will abandon the state-space paradigm. Instead, we will focus on input-output systems represented by autoregressive models, and work with a set of noisy input-output data. In the special case that the system is autonomous, we will provide necessary and sufficient conditions for informativity for quadratic stability, i.e., conditions under which there exists a single Lyapunov function (a QDF) for all systems compatible with the data. For input-output systems, we will provide necessary and sufficient conditions for informativity for quadratic stabilisation, and a recipe to construct a controller from informative data. If time permits, we will also discuss extensions of these results to data-driven dissipativity analysis and synthesis. 

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Abstract: In this talk, 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 of Hankel matrices obtained from the given finite input-output data. In addition, we will introduce a novel state construction from the given measurements.

Abstract: Standard physical systems such as the vibrating string and the transmission line admit different Hamiltonian representations, leading to different sets of boundary variables. The nature of these models, as well as their equivalence, will be discussed. This will make crucially use of the theory of polynomial matrix factorization and the calculus of two-variable polynomial matrices; one of the areas Harry contributed to.

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