## Workshop Dedicated to

## Arjan Van Der Schaft's retirement

**ORGANIZERS**

Kanat Camlibel, Jacquelien Scherpen (University of Groningen)

Correspondence: m.k.camlibel@rug.nl

We are pleased to invite you to the one-day workshop dedicated to the retirement of Arjan van der Schaft. The workshop will be held in Bayreuth, Germany on September 11 (Sunday) just before MTNS.

The participation will be free of charge for MTNS participants.

**Location: **The workshop will take place at the conference venue of MTNS 2022 in the lecture room “H17” in the building “Naturwissenschaften II” (NW 2).

**PROGRAM**

9:50 - 10:00: Opening

10:00 - 10:30: Monotone port-Hamiltonian systems

**Rodolphe Sepulchre** (Cambridge University)

The physical property of passivity is a foundation of port-hamiltonian modeling and its success in control. The talk will briefly review some key contributions of Arjan in that area and their impact on the field. Motivated by the electrical models of biophysical neural networks, we will then ask why it has proven elusive to extend the theory to monotonicity, the incremental form of passivity. We will discuss to what extent monotonicity is still physical and instrumental to the analysis and control of non-equilibrium physical systems.

10:30 - 11:00: Port variables in port Hamiltonian systems

**Bernhard Maschke** (Université de Lyon)

Port variables are at the heart of Port Hamiltonian Systems. In this talk we shall review their definition from the origin, as a generalization of input-output Hamiltonian Systems, until most recent advances including port variables for Irreversible Thermodynamic Systems, for Distributed Parameter Systems and their discretization, as well as Port Variables associated with an implicit definition of the energy.

11:00 - 11:30: Coffee break

11:30 - 12:00: DAE’s everywhere

**Hans Zwart** (University of Twente)

DAE, or Differential Algebraic Equations, may be considered as a (very) special case of differential equations, but in this talk we will show that many models can be regarded coming from DAE’s. This identification enables us to prove existence of solutions for several partial differential equations, by proving it for one DAE first. For instance, as a consequence of this result we, show that the existence of solutions for the beam and diffusion equation follows from that of the wave equation. Furthermore, the result of Weiss and Tucsnak on the Maxwell class falls within this theory. A second general result covers the case of partial differential equations with a state constraint, such as divergence free-ness in the Oseen equation.

12:00 - 12:30: Model reduction for nonlinear control systems based on differential balancing and data

**Jacquelien Scherpen** (University of Groningen)

We present a balancing theory for nonlinear systems in the contraction framework. We use prolonged systems to define the controllability and observability functions which can be used for a simultaneous diagonalization procedure, providing a measure for importance of the states. In addition, we propose a data-based model reduction method based on differential balancing for nonlinear systems whose input vector fields are constants by utilizing its variational system. For a fixed state trajectory, it is possible to compute the values of the differential Gramians by using impulse and initial state responses of the variational system. Therefore, balanced truncation is doable along state trajectories without solving nonlinear partial differential equations. The work presented is joint work with Yu Kawano.

12:30 - 14:00: Lunch

14:00 - 14:30: Into the future with a flux capacitor (or not?)

**Dimitri Jeltsema (HAN University of Applied Sciences)**

The term flux capacitor originates from the movie Back to the Future (1985) in which Dr. Emmett "Doc" Brown (Christopher Lloyd) builds a time machine based on a DeLorean DMC-1 car. While the movie did not provide a precise explanation of how the flux capacitor works, it required 1.21 GW of electrical power to operate. Intuitively, this would suggest that this is a passive device. Passivity (in fact, losslessness) was also suggested by Chua and Szeto (1983), where an ideal flux-based capacitor actually explicitly appears in the periodic table of so-called higher-order elements. A few decades later, Di Ventra, Pershin and Chua (2009) coined the term "memcapacitor" for the same element. Recent years also witnessed the invention of several of its analogies. One such analogy is the patented mechanical mem-inerter. In this talk, I will present a critical analysis of the flux capacitor (and beyond) as one of the many fruitful collaborations of Arjan and myself in the context of our ongoing quest to understand thermodynamics from a systems-theoretic perspective.

14:30 - 15:00: From data to state trajectory via energy

**Pa****o****lo ****Rapisarda** (University of Southampton)

One of the Grundthemen in Arjan van der Schaft’s scientific work is how the exchange of energy between a system and the environment is related to the structure of the system itself. In this talk I present a couple of variations related to system identification on this Leitmotiv of Arjan’s. I was lucky enough to work on some of these with the Meister himself. Starting from the case of linear, time-invariant systems, and proceeding through 2D-systems to 1-D time-varying linear ones, I will illustrate how power conservation laws can be used to compute state trajectories from input-output data. From the given i-o data and the identified state trajectory, one can then compute a state model in a straightforward way. An “energy-based” point of view offers an appealing alternative to standard system identification methods in those cases where shift-invariance cannot be exploited (as is the case for time-varying systems), or where it is inconvenient to do so (as in the case of 2D systems), thus opening the possibility of performing system, rather than parametric, identification also for non-linear systems.

15:00 - 15:30: Manipulator end-effector distance-based distributed formation control

**Bayu Jayawardhana** (University of Groningen)

Energy and electro-mechanical systems have been key components in the scientific life of Arjan van der Schaft. Motivated by the use of virtual springs in Vos, van der Schaft and Scherpen (2016), we present distributed formation control for manipulator end-effectors that achieve and maintain a desired 2D/3D formation shape of networked end-effectors. The formation control objective is achieved by assigning virtual springs between end-effectors and by adding damping terms at joints, which provides a clear physical interpretation of the proposed solution. Subsequently, we extend it to the case where manipulator kinematic and system parameters are not exactly known. This is a joint work with Haiwen Wu (the Chinese University of Hong Kong), Hector Garcia de Marina (University of Granada) and Dabo Xu (South China University of Technology).

15:30 - 16:00: Coffee break

16:00 - 16:30: Computation of (control-)Lyapunov functions via deep neural networks: what can dissipativity tell us?

**Lars Grüne** (Universität Bayreuth)

Deep neural networks have the potential to approximate nonlinear functions with good accuracy even in high dimensions. This means that they have the potential to circumvent the curse of dimensionality. However, this will not work for arbitrary nonlinear functions but only for particular classes thereof. On of these classes are the so-called compositional functions. In this talk, we will present recent dissipativity-based findings that reveal situations in which (control-)Lyapunov functions have - or do not have - such a compositional form (based on joint work with Mario Sperl, Bayreuth).

16:30 - 17:00: Linearization of mechanical control systems

**Witold Respondek** (Normandie Université)

For mechanical control systems we present the problem of linearization that preserves the mechanical structure of the system. We give necessary and sufficient conditions for the mechanical state-space-linearization and mechanical feedback-linearization using geometric tools, like covariant derivatives and the Riemann tensor, that have an immediate mechanical interpretation. In contrast with linearization of general nonlinear systems, conditions for its mechanical counterpart can be given for both, controllable and noncontrollable, cases. We illustrate our results by examples of linearizable mechanical systems. The talk is based on joint research with Marcin Nowicki (Politechnika Poznanska, Poland).

17:00 - 17:30: A port-Hamiltonian mechanism

**Henk Nijmeijer** (TU Eindhoven)

17:30 - 17:50: Closing remarks

**Jacquelien Scherpen **and **Arjan van der Schaft**