**Title:** Feedback system analysis: back to the future

**Abstract:** Feedback system analysis is the backbone of control theory. While the theory was originally developed in an input-output framework, as an offspring of circuit theory, the state-space formalism has become dominant under the drive of robotics, and, more recently, machine learning. Dissipativity theory has played a crucial role in bridging the two approaches, using state-space representations to make the input output theory algorithmic, at least in the special case of linear time-invariant (LTI) systems. The talk will reflect on the fact that the focus of the input-output theory was on *incremental *system properties (e.g. incremental gain) whereas the focus of state-space theory is on* non-incremental* properties. We will discuss why the analysis of incremental properties has disappeared from state-space theory and why this limitation has become a bottleneck of nonlinear control. Finally we will report on current research avenues to bypass state-space representations in an algorithmic input-output analysis of incremental system properties.

**Speaker**: Amirreza Silani

**Title**: Distributed Control, Optimization, Coordination of Smart Microgrids

**Abstract**: Microgrids are power distribution systems which are typically classified by Direct Current (DC) and Alternating Current (AC) networks. Nowadays, renewable generation sources and new loads such as Electric Vehicles (EVs) are largely used in power systems. Thus, due to the increased share of renewable generations and large scale introduction of new loads such as EVs, new control strategies are required to address the uncertainties of power networks.

Due to the random and unpredictable diversity of load patterns, it is more realistic to consider dynamical or stochastic differential load models. In DC networks, in order to guarantee a proper and safe functioning of the overall network, the main goal is the voltage regulation. Thus, we propose controller schemes achieving voltage regulation and ensuring the stability of the overall DC network. Moreover, an important operational objective of AC networks is frequency regulation. Hence, we propose controller schemes achieving frequency regulation and ensuring the stability of the overall AC network.

Furthermore, we propose an Energy Management Strategy (EMS) taking into account the load, power flow, and system operational constraints in a distribution network such that the cost of the Distributed Generations (DGs), Distributed Storages (DSs) and energy purchased from the main grid are minimized and the customers’ demanded load are provided where the loads are considered stochastic generated by time-homogeneous Markov chain. Finally, we solve a microgird optimal control problem with taking into account the social behavior of the EV drivers via a corresponding real data set.

**Speaker**: Daniele Astolfi

**Title**: On the use of dynamic saturation and dead-zone in observer design and synchronization problems

**Abstract**: We propose a redesign paradigm for stable estimators by introducing a saturation or a dead-zone nonlinearity with adaptive thresholds on the output injection term. Such nonlinearities allow improving the sensitivity to measurement noise in different scenarios (impulsive disturbances or persistent noise such as sensor bias), while preserving the asymptotic convergence properties of the original observer in nominal conditions. These redesigns apply to a broad class of state estimators, including linear observers, observers for input-affine systems, observers for Lipschitz systems, observers based on the circle criterion, high-gain observers, standard and extended Kalman filters. Finally, the same philosophy design is then applied in the context of synchronization problems for a network of nonlinear systems with measurement noise affecting the exchange of information.

**Speaker**: Henk van Waarde

**Title**: Data-driven control à la Finsler and Yakubovich

**Abstract**: This talk is about the design of state feedback controllers directly on the basis of (noise-corrupted) data. After stating the problem, I will recall two robust control results, namely Finsler’s lemma and Yakubovich’s S-lemma. I will then provide generalizations of these classical results that are suitable for data-driven control applications. During the talk, I will show that these generalizations can be naturally applied to design state feedback controllers. As we will see, this design method is non-conservative and based on tractable linear matrix inequalities.

**Speaker**: Mattia Giaccagli

**Title**: Toward global nonlinear integral action?

**Abstract**: In this presentation we focus on an output set-point tracking and constant disturbance rejection problem for a class of MIMO nonlinear systems . We allow the references and the disturbances to be arbitrarily large and the initial conditions of the system to range in the full-state space. We rely on the common approach of extending the system with an integral action processing the regulation error and we cast the problem in the contraction framework, without making explicit use of normal forms. We present sufficient conditions for the design of a state-feedback and output-feedback control laws able to make the resulting closed-loop system incrementally stable, uniformly with respect to the references and the disturbances; such property guarantees the existence of an unique attractive equilibrium on which output regulation is achieved. To this end, we develop an incremental version of forwarding control techniques. Then, we show that our assumptions are always satisfied for a class of minimum-phase systems whose zero-dynamics are incrementally stable.

**Speaker**: Prof. Juan G. Peypouquet, Bernoulli Institute

**Title: **A fast convergent first-order method bearing second-order information

**Abstract:** We propose a model for a class of first-order methods as an inertial system with Hessian-driven damping. The model combines several features of the Levenberg-Marquardt algorithm and Nesterov’s acceleration scheme for first-order algorithms. We obtain a second-order system (in time and space), which can be interpreted as a first-order one by an appropriate transformation. The resulting method is easily implementable, more stable than classical accelerated methods, and just as fast.

**Abstract:** When only part of the state of a control system is known, a state stabilizing feedback can not be directly implemented. One must achieve output feedback stabilization instead. A sufficient condition for a (globally) state feedback stabilizable control system to be (semi-globally) output feedback stabilizable is the uniform observability of the system, that is observability for all inputs. However, some systems present an observability singularity at the target: the value of control at the target point is an input making the system unobservable. Then, the challenge lies in according the antagonistic nature of the state estimation and stabilization. While the system approaches the target, observability properties vanish, hence the state estimation is getting worse, which in turn prevents stabilization.

On examples of systems with linear conservative dynamics and nonlinear output, we illustrate two main guidelines to tackle this problem:

– using well chosen perturbations of the state feedback law can yield new observability properties of the closed-loop system;

– embedding the original control system into a new (finite or infinite-dimensional) system admitting an observer with dissipative error allows to mitigate the observability issues.

**Speaker:** Lucas Brivadis (Univ. de Lyon)

**Abstract:**

While model-based techniques for cyber-physical systems design have been the subject of a large amount of research in the last decade, scalability of these techniques remains an issue. In this talk, we present some contributions to make such approaches more scalable. In the first part of the talk, we present a general framework for compositional reasoning using assume-guarantee contracts. This framework applies to very general systems with arbitrary interconnections, and makes it possible to reason on very general properties. We introduce weak and strong semantics and show that the weak semantics are sufficient to reason on acyclic interconnections and strong semantics are necessary for cyclic interconnections. In the second part, this framework is combined with symbolic control techniques and applied to synthesis problems. Given a system made of interconnected components, each component is equipped with a sampled-data controller (with its own sampling period), and the controller of a component can receive partial information on the state of other components through a given information structure. The considered global system can be seen as distributed, multiperiodic and with partial information. Assume guarantee contracts are used to decompose the global problem into local sub-problems that can be solved independently, then symbolic control techniques are used to synthesize controllers enforcing the local control objectives. Finally, theoretical results are applied to a vehicle platooning problem on a circular road, to show the effectiveness of the proposed approach.

**Biography:**

Adnane SAOUD is a Postdoctoral Research Fellow in the Electrical and Computer Engineering Department at the University of California, Berkeley Since February 2021. Between February 2020 and January 2021, he was a Postdoctoral Research Fellow in the Electrical and Computer Engineering Department at the University of California, Santa Cruz. He received the Ph.D. degree in Control from CentraleSupelec, France, in 2019. During his Ph.D. studies, he was selected as one of the top three finalists for the Best student paper award at the European Control Conference, ECC, 2018. He obtained the M.Sc. degree in control from University Paris-Saclay, France, in 2016, and Electrical Engineering degree from Ecole Mohammadia d’ingénieurs, (EMI), Morocco, in 2014. His current research interests include formal methods for cyber–physical systems, compositional analysis and synthesis of interconnected system and learning-based control of dynamical systems.

Speaker website: https://sites.google.com/view/adnanesaoud/

##### Speaker: Prof. Giacomo Como, Politecnico di Torino, Italy

**Abstract:** In the last months the interest in dynamic models of network epidemics and their control has surged and many new works have appeared motivated by applications to the current situation. In this talk I will review some of the most used models and recent results with particular focus on the network SIR model.

**About the speaker:** Giacomo Como received the B.Sc., M.S., and Ph.D. degrees in applied mathematics from the Politecnico di Torino, Italy, in 2002, 2004, and 2008, respectively. He was a Visiting Assistant in research at Yale University from 2006 to 2007, and a Post-Doctoral Associate at the Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, from 2008 to 2011. He is currently an Associate Professor with the Department of Mathematical Sciences, Politecnico di Torino, and at the Automatic Control Department, Lund University, Sweden. His research interests are in dynamics, information, and control in network systems with applications to cyber-physical systems, infrastructure networks, as well as social and economic networks. He is a recipient of the 2015 George S. Axelby Outstanding Paper Award. He currently serves as an Associate Editor of the IEEE-TCNS and IEEE-TNSE and as the Chair of the IEEE-CSS Technical Committee on Networks and Communications. He was the IPC Chair of the IFAC Workshop NecSys’15 and a Semiplenary Speaker at the International Symposium MTNS’16.

*This seminar will be carried out online via zoom, please contact the organizer to obtain the login details.*