WP descrition: The interaction and the coordination between the partners is favored by the organization
of yearly plenary meetings that bring together the project members. Each meeting typically lasts 1 or 2 days. One part
of the meeting consists of talks given by project members or external guests presenting their most
recent developments in relevant areas for the project. Significant slots are devoted to presentations
given by the students, with the double objective of developing their presentation skills and of obtaining
valuable feedback on their work. The rest of the meeting consists of working sessions, where the
project members spread in groups working on a specific problem related to the project. The
closing session of the meeting summarizes the ideas exchanged in the working groups;
it also defines the research agenda of the project for the following year.

Coordinator:Luca Zaccarian (LAAS)

The HANDY project consists in four WorkPackages organized according to the following diagram.

WP descrition: The area of hybrid dynamical systems will be enriched with
the interconnection tools typical of networked systems, first focusing on input/output characterizations of single units and then moving on to complete interconnections.

Coordinators:Romain Postoyan (CRAN) and Luca Zaccarian (LAAS)

Participants:Marc Jungers (CRAN), Carla De Souza (LAAS), Mohamed Maghenem (Gipsa), Angelo Alessandri (adj-europe), Daniele Astolfi (adj-france), Giorgio Valmorbida (L2S), Antoine Girard (L2S), Christophe Prieur (Gipsa), Simone Mariano (CRAN), Francesco Ferrante (Gipsa), Elena Panteley (L2S), Isabelle Queinnec (LAAS), Sophie Tarbouriech (LAAS), Luca Zaccarian (LAAS), Paolo Frasca (Gipsa), Aneel Tanwani (LAAS), Romain Postoyan (CRAN), Himadri Basu (Gipsa).

Task 1.1: Input-Output properties of stand-alone hybrid systems

Below is a list of research topics investigated in the context of this Task/WorkPackage

Dissipativity of hybrid systems

The goal is to provide novel energetic interpretations of dissipativity, based on their original formulation back in the 60-70’s. Paralleling what has been done for classical nonlinear systems, the links
between storage functions, supply rates and Lyapunov functions will be investigated. Generic conditions will then be derived for an important class of hybrid systems: switched systems, and the
link with optimal control will be investigated. These results are important when studying microgrids
of power converters, which is one of the topics of WP3.

Relevant References:

[J32] E.S. Tognetti, M. Jungers, and T.R. Calliero. Output feedback control for quadratic systems: A lyapunov function approach. International Journal of Robust and Nonlinear Control, 31(17):8373–8389, 2021.

[J77] M. Jungers and C. Oara. Solving parameterized non-symmetric algebraic riccati equations: A matrix sign function approach. Journal of Control Engineering and Applied Informatics, 21(2):3–10, 2019.

[C57] M. Jungers, F. Ferrante, and J. Lohéac. Dissipativeness and dissipativation of discrete-time switched linear systems. In Proceedings of 58th IEEE Conference on Decision and Control, Nice, France, 2019.

Switched Systems

In many engineering models, the evolution of the state is guided by a switching rule/signal that somehow selects, among a finite family, the dynamics that the solution must follow.
This formalism, referred to as switched systems, can be seen as a subclass of hybrid systems, emphasizing the continuous behavior and seeing the discrete events as switching among a prescribed finite family of vector fields. Putting the emphasis on the class of admissible switching rules/signals and exploiting the properties of the individual subsystems opens fruitful paths of research in establishing stability/stabilizability results. In this project, various aspects of hybrid-formulated switched systems are being investigated, with special emphasis towards the instrumental role of this theory towards systems interconnections.

Relevant References:

[J3] M. Serieye, C. Albea-Sanchez, A. Seuret, and M. Jungers. Attractors and limit cycles of discrete-time switching affine systems: nominal and uncertain cases. Automatica, 149:110691, 2023.

[J46] Missie Aguado-Rojas, Trong Biên Hoàng, William Pasillas-Lépine, Antonio Loría, and Witold Respondek. A switching observer for a class of nonuniformly observable systems via singular time-rescaling. IEEE Transactions on Automatic Control, 66(12):6071–6076, 2021.

[J83] Missie Aguado-Rojas, William Pasillas-Lépine, and Antonio Loría. Extended-braking-stiffness estimation under varying road-adherence conditions. IEEE Transactions on Control Systems Technology, 28(5):1964–1971, 2019.

[C16] Georges Aazan, Antoine Girard, Paolo Mason, and Luca Greco. Stability of discrete-time switched linear systems with ω-regular switching sequences. In 25th ACM International Conference on HybridSystems: Computation and Control, pages 1–7, 2022.

[C17] Georges Aazan, Antoine Girard, Luca Greco, and Paolo Mason. On the joint spectral radius of shuffled switched linear systems. In International Symposium on Mathematical Theory of Networks andSystems, 2022.

[C27] Leonardo Cabral, JM Gomes da Silva, and Giorgio Valmorbida. Stabilization of discrete-time piecewise affine systems in implicit representation. In 2021 60th IEEE Conference on Decision andControl (CDC), pages 6049–6054. IEEE, 2021.

[C57] M. Jungers, F. Ferrante, and J. Lohéac. Dissipativeness and dissipativation of discrete-time switched linear systems. In Proceedings of 58th IEEE Conference on Decision and Control, Nice, France, 2019.

[C64] M. Della Rossa, A. Tanwani, and L. Zaccarian. Smooth approximation of patchy Lyapunov functions for switching systems. In Symposium on Nonlinear Control Systems (NOLCOS), pages 518–523, Vienna, Austria, September 2019.

Hybrid Lyapunov techniques

We will study different types of Lyapunov constructions to establish stability of hybrid dynamical systems. As an example, with hybrid dynamics nonsmoothness of the Lyapunov function can be advantageous when patching different functions at the boundary of the flow set (which is typically closed, due to well posedness requirements). The ensuing use of Clarke's generalized directional derivatives can be replaced by more sophisticated concepts providing reduced conservativeness of the Lyapunov conditions.

Relevant References:

[J22] Mirko Fiacchini. Yet another computation-oriented necessary and sufficient condition for stabilizability of switched linear systems. IEEE Transactions on Automatic Control, 67(7):3627–3632, 2022.

[J42] Matteo Della Rossa, Rafal Goebel, Aneel Tanwani, and Luca Zaccarian. Piecewise structure of lyapunov functions and densely checked decrease conditions for hybrid systems. Mathematics of Control,Signals, and Systems, 33:123–149, 2021.

[C7] E. Petri, R. Postoyan, D. Astolfi, D. Nešić, and V. Andrieu. Towards improving the estimation performance of a given nonlinear observer: a multi-observer approach. In Proceedings of the 61st IEEEConference on Decision and Control, pages 583–590, 2022.

[C24] W.P.M.H. Heemels, P. Bernard, K. Scheres, R. Postoyan, and R.G. Sanfelice. Hybrid systems with continuous-time inputs: subtleties in solution concepts and existence results. In Proceedings of the60th IEEE Conference on Decision and Control, pages 5368–5373, 2021.

[C60] Francesco Ferrante and Ricardo G Sanfelice. Certifying optimality in hybrid control systems via lyapunov-like conditions. IFAC-PapersOnLine, 52(16):245–250, 2019.

Harmonic control naturally arises in e.g., electrical engineering, whenever there is a need to regulate given harmonics of the solutions of a dynamical system. For this purpose, harmonic modeling is required, which leads to infinite dimensional systems. The originality of our work is to rigorously design and analyse control strategies for the harmonic model, which can then be converted back to the original finite-dimensional coordinates while preserving the desired properties.

Relevant References:

[J13] P. Riedinger and J. Daafouz. Solving infinite-dimensional harmonic lyapunov and riccati equations. IEEE Transactions on Automatic Control, 2022.

[J44] N. Blin, P. Riedinger, J. Daafouz, L. Grimaud, and P. Feyel. Necessary and sufficient conditions for harmonic control in continuous time. IEEE Transactions on Automatic Control, 67(8):4013–4028, 2021.

[C6] P. Riedinger and J. Daafouz. Harmonic pole placement. In Proceedings of the 61st IEEE Conferenceon Decision and Control, pages 5505–5510, 2022.

Task 1.2: Stability and performance of interconnected hybrid systems

Below is a list of research topics investigated in the context of this Task/WorkPackage

Reset control mechanisms in hybrid interconnections

A certain class of interconnected hybrid systems is the one obtained when combining (hybrid
or non-hybrid) plants with reset controllers. The advantages of using reset elements in control
loops are numerous like flexibility, performance improvement, dwell-time constraint, and
also comprise improvement of multi-objective goals involving L2 gains and convergence rates. We study different classes of reset elements available in the literature and to propose constructive reset designs exploiting the input/output properties established in Task 1.1, thereby generalizing and extending existing SISO ideas.

Relevant References:

[J28] R Bertollo, AR Teel, and L Zaccarian. Soft-reset control with max-of-quadratics lyapunov certificates. IEEE Transactions on Automatic Control, 2022.

[C30] R Bertollo, Michael Schwegel, Andreas Kugi, and Luca Zaccarian. Reset-control-based current tracking for a solenoid with unknown parameters. IFAC-PapersOnLine, 54(5):199–204, 2021.

[C50] L. Zaccarian. Lyapunov-based reset control. In Symposium on Nonlinear Control Systems(NOLCOS), pages 272–273, Vienna, Austria, September 2019.

[C61] F. Ferrante and L. Zaccarian. Dynamic reset output feedback with guaranteed convergence rate. In Symposium on Nonlinear Control Systems (NOLCOS), pages 134–139, Vienna, Austria, September 2019.

[C70] A. Bisoffi, R. Beerens, L. Zaccarian, M. Heemels, H. Nijmeijer, and N. van de Wouw. Hybrid model formulation and stability of a PID-controlled motion system with Coulomb friction. In Symposiumon Nonlinear Control Systems (NOLCOS), pages 116–121, Vienna, Austria, September 2019.

Event-triggered control

The goal here is to provide design methods for event-triggered control systems. These are systems
for which the data transmissions between the plant and the controller are triggered whenever a
state-dependent criterion is satisfied. This sampling paradigm can be modeled as a hybrid system for which a jump corresponds to a sampling instant. The objective is to investigate
general types of stability and dissipativity properties.

Relevant References:

[J6] C. de Souza, S. Tarbouriech, and A. Girard. Event-triggered neural network control for lti systems. IEEE Control Systems Letters, 7:1381–1386, 2023.

[J16] R. Postoyan, R.G. Sanfelice, and W.P.M.H. Heemels. Explaining the “mystery” of periodicity in inter-transmission times in two-dimensional event-triggered controlled system. IEEE Transactions onAutomatic Control, 2022.

[J17] A.I. Maass, W. Wang, D. Nešić, R. Postoyan, and W.P.M.H. Heemels. Event-triggered control through the eyes of a hybrid small-gain theorem. IEEE Transactions on Automatic Control, 2022.

[J18] Y. Lei, Y.-W. Wang, I.-C. Morărescu, and R. Postoyan. Event-triggered fixed-time stabilization of two time scales linear systems. IEEE Transactions on Automatic Control, 68(3):1722–1729, 2022.

[J54] Luciano G Moreira, Joao M Gomes da Silva Jr, Sophie Tarbouriech, and Alexandre Seuret. Observer-based event-triggered control for systems with slope-restricted nonlinearities. InternationalJournal of Robust and Nonlinear Control, 30(17):7409–7428, 2020.

[J61] Y. Lei, Y.-W. Wang, I.-C. Morărescu, and J.-W. Xiao. Guaranteed cost for an event-triggered consensus strategy for interconnected two time-scales systems with structured uncertainty. IEEETransactions on Cybernetics, 52(6):4370–4380, 2020.

[C4] K.J.A. Scheres, V.S. Dolk, M.S. Chong, R. Postoyan, and W.P.M.H. Heemels. Distributed periodic event-triggered control of nonlinear multi-agent systems. IFAC-PapersOnLine, 55(13):168–173, 2022.

[C22] K.J.A. Scheres, M.S.T. Chong, R. Postoyan, and W.P.M.H. Heemels. Event-triggered state estimation with multiple noisy sensor nodes. In Proceedings of the 60th IEEE Conference on Decisionand Control, pages 558–563, 2021.

[C23] E. Petri, R. Postoyan, D. Astolfi, D. Nešić, and W.P.M.H. Heemels. Event-triggered observer design for linear systems. In Proceedings of the 60th IEEE Conference on Decision and Control, pages 546–551, 2021.

[C34] W. Wang, D. Nešić, R. Postoyan, and W.P.M.H. Heemels. A unifying event-triggered control framework based on a hybrid small-gain theorem. In Proceedings of 59th IEEE Conference on Decisionand Control, pages 4979–4984, Jeju Island, South Korea, 2020.

[C38] K. Scheres, R. Postoyan, and W.P.M.H. Heemels. Event-triggered control in presence of measurement noise: a space-regularization approach. In Proceedings of 59th IEEE Conference onDecision and Control, pages 6234–6239, Jeju Island, South Korea, 2020.

[C43] L. G. Moreira, J. M. Gomes da Silva Jr, D. Coutinho, and S. Tarbouriech. Event-triggered control co-design for rational systems. In IFAC World Congress, Berlin, Germany, July 2020.

[C47] H. Ichihara, K. Sawada, K. Kobayashi, and S. Tarbouriech. Event-triggered control for extended plants of discrete-time linear systems. In IFAC World Congress, Berlin, Germany, July 2020.

[C51] W. Wang, D. Nešić, R. Postoyan, I. Shames, and W.P.M.H. Heemels. State-feedback event-holding control for nonlinear systems. In Proceedings of 58th IEEE Conference on Decision andControl, pages 1650–1655, Nice, France, 2019.

[C54] R. Postoyan, R.G. Sanfelice, and W.P.M.H. Heemels. Inter-event times analysis for planar linear event-triggered controlled systems. In Proceedings of 58th IEEE Conference on Decision and Control, pages 1662–1667, Nice, France, 2019.

[C63] V.S. Dolk, R. Postoyan, and W.P.M.H. Heemels. Event-triggered consensus for multi-agent systems with guaranteed robust positive minimum inter-event times. In Proceedings of 58th IEEEConference on Decision and Control, Nice, France, 2019.

Control and Observation in the Presence of Intermittent Measurements

Recent technological advances have enabled the control of dynamical systems using data that is transmitted over communication networks. When the networks are not fully reliable, data can get lost or can only be available intermittently. Within the scope of this project, we develop controller and observer architectures ensuring quantifiable performance, fast rate of convergence, and robustness to noise and perturbations in the presence of intermittently available measurements.

Relevant References:

[J4] Francesco Ferrante and Giorgio Valmorbida. Stability analysis of a class of discontinuous discrete-time systems. IEEE Control Systems Letters, 7:454–459, 2023.

[J5] Francesco Ferrante, Ricardo G Sanfelice, and Sophie Tarbouriech. Control design under actuator saturation and multi-rate sampling. Automatica, 148:110767, 2023.

[J8] Himadri Basu, Francesco Ferrante, and Mirko Fiacchini. Output regulation of stochastic sampled-data systems with post-processing internal model. European Journal of Control, page 100866, 2023.

[J9] Alejandro A.I. Maass, W. Wang, D. Nešić, Y. Tan, and R. Postoyan. A multi-processor implementation for networked control systems. IEEE Control Systems Letters, 2023.

[J11] V.S. Varma, R. Postoyan, D.E. Quevedo, and I.-C. Morărescu. Transmission power policies for energy-efficient wireless control of nonlinear systems. IEEE Transactions on Automatic Control, 2022.

[J23] Francesco Ferrante and Alexandre Seuret. Observer design for linear aperiodic sampled-data systems: A hybrid systems approach. IEEE Control Systems Letters, 6:470–475, 2022.

[J33] Antonino Sferlazza, Sophie Tarbouriech, and Luca Zaccarian. State observer with round-robin aperiodic sampled measurements with jitter. Automatica, 129:109573, 2021.

[J38] Roberto Merco, Francesco Ferrante, and Pierluigi Pisu. A hybrid controller for DOS-resilient string-stable vehicle platoons. IEEE Transactions on Intelligent Transportation Systems, 22(3):1697–1707, 2021.

[J65] A.M. de Oliveira, V.S. Varma, R. Postoyan, I.-C. Morărescu, J. Daafouz, and O.L.V. Costa. Network-aware controller design with performance guarantees for linear wireless systems. IEEETransactions on Automatic Control, 66(9):4297–4302, 2020.

[C8] M. Maghenem, C. Prieur, and E. Witrant. Boundary control of the kuramoto-sivashinsky equation under intermittent data availability. In 2022 American Control Conference (ACC), pages 2227–2232, 2022.

[C9] J. Kreiss, R. Postoyan, D. Nešić, and W.P.M.H. Heemels. Scheduling of over-actuated networked control systems. IFAC-PapersOnLine, 55(13):25–30, 2022.

[C12] Francesco Ferrante and Sophie Tarbouriech. Sampled-data control design for systems with quantized actuators. IFAC-PapersOnLine, 55(34):37–42, 2022.

[C20] M.G. Titton, J.M.G. da Silva, G. Valmórbida, and M. Jungers. Stabilization of sampled-data lure systems with slope-restricted nonlinearities. In Proceedings of the 60th IEEE Conference on Decisionand Control, pages 6782–6787, 2021.

[C35] G. Valmorbida and F. Ferrante. On quantization in discrete-time control systems: Stability analysis of ternary controllers. In 2020 59th IEEE Conference on Decision and Control (CDC), pages 2543–2548, 2020.

[C37] Antonino Sferlazza, Luca Zaccarian, Giovanni Garraffa, and Filippo D’ippolito. Localization from inertial data and sporadic position measurements. IFAC-PapersOnLine, 53(2):5976–5981, 2020.

[C44] R. Merco, F. Ferrante, R. G. Sanfelice, and P. Pisu. Lmi-based output feedback control design in the presence of sporadic measurements. In Proceedings of the American Control Conference, pages –, Denver, CO, July 2020.

[C46] A. I. Maass, D. Nešić, V.S. Varma, R. Postoyan, and S. Lasaulce. Stochastic stabilisation and power control for nonlinear feedback loops communicating over lossy wireless networks. In Proceedingsof 59th IEEE Conference on Decision and Control, pages 1866–1871, Jeju Island, South Korea, 2020.

[C58] S.H.J. Heijmans, R. Postoyan, D. Nešić, and W.P.M.H. Heemels. Reverse average dwell-times for networked control systems. In Proceedings of 58th IEEE Conference on Decision and Control, pages 5480–5485, Nice, France, 2019.

[C62] A.S. Fagundes, J.M.G. da Silva Jr, and M. Jungers. Stability of control systems under aperiodic sampling and input saturation withclock-dependent lyapunov functions. In 5th IFAC Symposium onTelematics Applications, TA, 2019.

Feedback systems with piecewise smooth nonlinearities

Systems involving piecewise smooth nonlinearities in a feedback loop comprise interconnections involving the well-studied input-saturation phenomenon in control systems, but also alternative polytopic approaches involving ReLu elements, namely scalar nonlinear functions that are zero when the argoment is non-negative and identity with positive arguments. Studying stability properties of these interconnections requires methods, often based on convex optimization, such as linear matrix inequalities, to study the multi-fold behavior of the system in the different differentiable regions characterizing the piecewise smooth nonlinearity.

Relevant References:

[J2] Alexandre Seuret and Sophie Tarbouriech. A data-driven approach to the l2 stabilization of linear systems subject to input saturations. IEEE Control Systems Letters, 2023.

[J5] Francesco Ferrante, Ricardo G Sanfelice, and Sophie Tarbouriech. Control design under actuator saturation and multi-rate sampling. Automatica, 148:110767, 2023.

[J7] Valentina Breschi, Luca Zaccarian, and Simone Formentin. Data-driven stabilization of input-saturated systems. IEEE Control Systems Letters, 2023.

[J12] Sophie Tarbouriech, Angelo Alessandri, Daniele Astolfi, and Luca Zaccarian. Lmi-based stubborn and dead-zone redesign in linear dynamic output feedback. IEEE Control Systems Letters, 7:187–192, 2022.

[J15] Alberto Priuli, Sophie Tarbouriech, and Luca Zaccarian. Static linear anti-windup design with sign-indefinite quadratic forms. IEEE Control Systems Letters, 6:3158–3163, 2022.

[J25] Franco Blanchini, Giulia Giordano, Francesco Riz, and Luca Zaccarian. Solving nonlinear algebraic loops arising in input-saturated feedbacks. IEEE Transactions on Automatic Control, 2022.

[J35] Isabelle Queinnec, Sophie Tarbouriech, Giorgio Valmorbida, and Luca Zaccarian. Design of saturating state feedback with sign-indefinite quadratic forms. IEEE Transactions on AutomaticControl, 67(7):3507–3520, 2021.

[J43] Philipp Braun, Giulia Giordano, Christopher M Kellett, and Luca Zaccarian. An asymmetric stabilizer based on scheduling shifted coordinates for single-input linear systems with asymmetric saturation. IEEE Control Systems Letters, 6:746–751, 2021.

[J56] Simone Mariano, Franco Blanchini, Simone Formentin, and Luca Zaccarian. Asymmetric state feedback for linear plants with asymmetric input saturation. IEEE Control Systems Letters, 4(3):608–613, 2020.

[J70] Daniele Astolfi, Angelo Alessandri, and Luca Zaccarian. Stubborn and dead-zone redesign for nonlinear observers and filters. IEEE Transactions on Automatic Control, 66(2):667–682, 2020.

[C1] P. Braun, M. Jungers, and L. Zaccarian. Stabilization using shifted equilibria for saturated discrete-time linear systems. In Proceedings of the 12th IFAC Symposium on Nonlinear Control Systems, 2023.

[C36] S. Tarbouriech, I. Queinnec, G. Garcia, and M. Mazerolles. Dead-zone observer-based control for anesthesia subject to noisy BIS measurement. In IFAC World Congress, Berlin, Germany, July 2020.

[C62] A.S. Fagundes, J.M.G. da Silva Jr, and M. Jungers. Stability of control systems under aperiodic sampling and input saturation withclock-dependent lyapunov functions. In 5th IFAC Symposium onTelematics Applications, TA, 2019.

Verification and Symbolic Control

We developed approaches based on formal methods and symbolic control for designing networks of interconnected systems. We established a small gain theorem for symbolic models, making it possible to design compositionally controllers for attractivity specifications. We also considered more complex specifications given by contracts which formalize guarantees that a system must enforce when some assumptions on its environment (possibly made of other systems) are met. In particular, we showed that satisfaction of an assume-guarantee contract can be recasted as an invariance property for a lifted system, making it possible to use a variety of off-the-shelf computational tools for verifying contracts.

Relevant References:

[C10] Antoine Girard, Alessio Iovine, and Sofiane Benberkane. Invariant sets for assume-guarantee contracts. In 2022 IEEE 61st Conference on Decision and Control (CDC), pages 2190–2195. IEEE, 2022.

[C33] W Alejandro Apaza-Perez and Antoine Girard. Compositional synthesis of symbolic controllers for attractivity specifications. In 2021 60th IEEE Conference on Decision and Control (CDC), pages 2008–2013. IEEE, 2021.

Hybrid observers

The purpose of this task is to design hybrid observers for dynamical systems, hybrid or not, which naturally lead to an overall hybrid interconnected system. Motivations go from performance improvement of existing (continuous-time) designs, implementation over networks, distributed designs, and simply the state estimation of a hybrid dynamical system.

Relevant References:

[J23] Francesco Ferrante and Alexandre Seuret. Observer design for linear aperiodic sampled-data systems: A hybrid systems approach. IEEE Control Systems Letters, 6:470–475, 2022.

[J27] Riccardo Bertollo, Pablo Millán, Luis Orihuela, Alexandre Seuret, and Luca Zaccarian. Distributed hybrid observer with prescribed convergence rate for a linear plant using multi-hop decomposition. IEEE Control Systems Letters, 7:331–336, 2022.

[J33] Antonino Sferlazza, Sophie Tarbouriech, and Luca Zaccarian. State observer with round-robin aperiodic sampled measurements with jitter. Automatica, 129:109573, 2021.

[J46] Missie Aguado-Rojas, Trong Biên Hoàng, William Pasillas-Lépine, Antonio Loría, and Witold Respondek. A switching observer for a class of nonuniformly observable systems via singular time-rescaling. IEEE Transactions on Automatic Control, 66(12):6071–6076, 2021.

[J54] Luciano G Moreira, Joao M Gomes da Silva Jr, Sophie Tarbouriech, and Alexandre Seuret. Observer-based event-triggered control for systems with slope-restricted nonlinearities. InternationalJournal of Robust and Nonlinear Control, 30(17):7409–7428, 2020.

[J83] Missie Aguado-Rojas, William Pasillas-Lépine, and Antonio Loría. Extended-braking-stiffness estimation under varying road-adherence conditions. IEEE Transactions on Control Systems Technology, 28(5):1964–1971, 2019.

[C7] E. Petri, R. Postoyan, D. Astolfi, D. Nešić, and V. Andrieu. Towards improving the estimation performance of a given nonlinear observer: a multi-observer approach. In Proceedings of the 61st IEEEConference on Decision and Control, pages 583–590, 2022.

[C19] Gian Marco Vinco, Philipp Braun, and Luca Zaccarian. A modular architecture for mobile robots equipped with continuous-discrete observers. In 2021 IEEE International Conference on Mechatronics(ICM), pages 1–6. IEEE, 2021.

[C23] E. Petri, R. Postoyan, D. Astolfi, D. Nešić, and W.P.M.H. Heemels. Event-triggered observer design for linear systems. In Proceedings of the 60th IEEE Conference on Decision and Control, pages 546–551, 2021.

WP descrition: Systems whose interconnections can be described by directed or
undirected graphs will be considered, going beyond the existing result by leveraging the presence of
multiple time scales and of hybrid dynamics whose input-output properties are characterized in WP1.

Coordinators:Paolo Frasca (GIPSA) and Elena Panteley (L2S)

Participants:Riccardo Bertollo (adj-europe), Carla De Souza (LAAS), Mohamed Maghenem (Gipsa), Antonio Loria (L2S), Antoine Girard (L2S), Irinel-Constantin Morărescu (CRAN), Christophe Prieur (Gipsa), Simone Mariano (CRAN), Giacomo Casadei (adj-france), Francesco Ferrante (Gipsa), Federica Garin (Gipsa), Mirko Fiacchini (Gipsa), Elena Panteley (L2S), Isabelle Queinnec (LAAS), Sophie Tarbouriech (LAAS), Luca Zaccarian (LAAS), Paolo Frasca (Gipsa), Romain Postoyan (CRAN), Jamal Daafouz (CRAN).

Task 2.1: Hybrid phenomena in multi-agent systems

Below is a list of research topics investigated in the context of this Task/WorkPackage

Synchronization of Networks

It has long been known that oscillators that are linked to each other eventually synchronize. These observations have developed into a large literature that explores whether and how networks of systems synchronize. The purpose of this task is to contribute to this literature by developing system-theoretic tools with a focus on hybrid phenomena, multiple time-scales, heterogeneity, and the development of design methods.

Relevant References:

[J50] E. Nuno, I. Sarras, A. Loria, M. Maghenem, E. Cruz-Zavala, and E. Panteley. Strict lyapunov–krasovskiĭ functionals for undirected networks of euler–lagrange systems with time-varying delays. Systems & Control Letters, 135:104579, 2020.

[J58] M. Maghenem, R. Postoyan, A. Loria, and E. Panteley. Lyapunov-based synchronization of networked systems: From continuous-time to hybrid dynamics. Annual Reviews in Control, 2020.

[J61] Y. Lei, Y.-W. Wang, I.-C. Morărescu, and J.-W. Xiao. Guaranteed cost for an event-triggered consensus strategy for interconnected two time-scales systems with structured uncertainty. IEEETransactions on Cybernetics, 52(6):4370–4380, 2020.

[C14] D.R. Alkhorshid, E.S. Tognetti, and I.-C. Morarescu. A bilinear system approach with input saturation to control the agreement value of multi-agent systems. In Proceedings of the European ControlConference, pages 01–06, 2022.

[C21] M. Serieye, C. Albea, A. Seuret, and M. Jungers. Synchronization on a limit cycle of multi-agent systems governed by discrete-time switched affine dynamics. IFAC-PapersOnLine, 54(5):295–300, 2021.

[C29] Alessandro Bosso, Ilario A Azzollini, Simone Baldi, and Luca Zaccarian. A hybrid distributed strategy for robust global phase synchronization of second-order kuramoto oscillators. In 2021 60thIEEE Conference on Decision and Control (CDC), pages 1212–1217. IEEE, 2021.

[C55] M. Maghenem, H. Lekefouet, A. Loría, and E. Panteley. Decentralized synchronization of time-varying oscillators under time-varying bidirectional graphs. In 2019 American Control Conference(ACC), pages 4018–4023. IEEE, 2019.

[C67] G. Casadei, D. Astolfi, A. Alessandri, and L. Zaccarian. Synchronization of interconnected linear systems via dynamic saturation redesign. In Symposium on Nonlinear Control Systems (NOLCOS), pages 1097–1102, Vienna, Austria, September 2019.

[C71] V. Andrieu and S. Tarbouriech. LMI conditions for contraction and synchronization. In Symposium on Nonlinear Control Systems (NOLCOS), Vienna, Austria, September 2019.

Sensor Networks

When considering large-scale plants, such as factories,
water irrigation channels or solar fields, the problem of
state estimation becomes harder to solve than in small-size systems. The fact that the information from these
systems is collected by many individual agents deployed
in geographically remote locations complicates the design
of estimators. Furthermore, these agents require to com-
municate with each other to achieve system-wide goals,
which incurs in problems derived from network topology
as well as communication drawbacks: delays, quantization,
limited bandwidth, etc.

Relevant References:

[J27] Riccardo Bertollo, Pablo Millán, Luis Orihuela, Alexandre Seuret, and Luca Zaccarian. Distributed hybrid observer with prescribed convergence rate for a linear plant using multi-hop decomposition. IEEE Control Systems Letters, 7:331–336, 2022.

[C39] A. Rodríguez, L. Orihuela Espina, P. Millan Gata, A. Seuret, and L. Zaccarian. Distributed state estimation for LTI systems facing communication failures. In IFAC World Congress, Berlin, Germany, July 2020.

[C40] A Rodríguez del Nozal, L Orihuela, P Millan, Alexandre Seuret, and Luca Zaccarian. Results on distributed state estimation for lti systems facing communication failures. IFAC-PapersOnLine, 53(2):3248–3253, 2020.

Open Multi-Agent Systems

Most literature on multi-agent systems considers networks of fixed size, i.e., number of agents, and then considers several kinds of scenarios such as time-varying network topologies. In this project, we explicitly consider a more radical scenario of open multi-agent systems where the set of agents is time-varying, i.e., agents may join or leave the network at any time. This situation is common to numerous applications, including the Internet of Things, smart power grids, social networks, vehicle platooning and robotic teams.

Relevant References:

[J29] Renato Vizuete, Federica Garin, and Paolo Frasca. The Laplacian spectrum of large graphs sampled from graphons. IEEE Transactions on Network Science and Engineering, 8(2):1711–1721, 2021.

[J41] M. Franceschelli and P. Frasca. Stability of open multi-agent systems and applications to dynamic consensus. IEEE Transactions on Automatic Control, 66(5):2326–2331, 2021.

[C2] Renato Vizuete, Paolo Frasca, and Elena Panteley. Gradient descent for resource allocation with packet loss. IFAC-PapersOnLine, 55(13):109–114, 2022.

[C3] Renato Vizuete, Charles Monnoyer de Galland, Julien M. Hendrickx, Paolo Frasca, and Elena Panteley. Resource allocation in open multi-agent systems: an online optimization analysis. In 2022IEEE 61st Conference on Decision and Control (CDC), pages 5185–5191, 2022.

[C25] Charles Monnoyer de Galland, Renato Vizuete, Julien M. Hendrickx, Paolo Frasca, and Elena Panteley. Random coordinate descent algorithm for open multi-agent systems with complete topology and homogeneous agents. In 2021 60th IEEE Conference on Decision and Control (CDC), pages 1701–1708, 2021.

Distributed event-triggered control

Compared to Task 1.2, where event-triggered control is also addressed, the aim here is to provide distributed solutions, which are adapted to multi-agent systems. The main motivation is to reduce communications between agents, while ensuring the desired global control objective.

Relevant References:

[C38] K. Scheres, R. Postoyan, and W.P.M.H. Heemels. Event-triggered control in presence of measurement noise: a space-regularization approach. In Proceedings of 59th IEEE Conference onDecision and Control, pages 6234–6239, Jeju Island, South Korea, 2020.

[C63] V.S. Dolk, R. Postoyan, and W.P.M.H. Heemels. Event-triggered consensus for multi-agent systems with guaranteed robust positive minimum inter-event times. In Proceedings of 58th IEEEConference on Decision and Control, Nice, France, 2019.

Task 2.2: Multi-time scales

Below is a list of research topics investigated in the context of this Task/WorkPackage

Lyapunov Methods for networks

Lyapunov methods for networked systems play an important role in their analysis, also in the case of singularly perturbed systems. Lyapunov techniques are used to analyze a network of two time-scales systems synchronised under an event-triggering protocol with a guaranteed cost for undirected graph topologies. We also addressed the design of Lyapunov functions under a general directed graph topology for the analysis of network consensus for linear systems. We formulated a spanning-tree condition for directed graphs in terms of a Lyapunov equation involving the graph’s Laplacian that served as a base for Lyapunov analysis of networked systems and applied these results for the study of networked linear systems in several scenarios.

Relevant References:

[J14] Esteban Restrepo, Antonio Loria, Ioannis Sarras, and Julien Marzat. Stability and robustness of edge-agreement-based consensus protocols for undirected proximity graphs. International Journal ofControl, 95(2):526–534, 2022.

[J24] Maitreyee Dutta, Elena Panteley, Antonio Loría, and Srikant Sukumar. Strict lyapunov functions for dynamic consensus in linear systems interconnected over directed graphs. IEEE Control SystemsLetters, 6:2323–2328, 2022.

[J34] Esteban Restrepo, Antonio Loría, Ioannis Sarras, and Julien Marzat. Edge-based strict lyapunov functions for consensus with connectivity preservation over directed graphs. Automatica, 132:109812, 2021.

[J36] Emmanuel Nuño, Antonio Loría, and Elena Panteley. Leaderless consensus formation control of cooperative multi-agent vehicles without velocity measurements. IEEE Control Systems Letters, 6:902–907, 2021.

[J41] M. Franceschelli and P. Frasca. Stability of open multi-agent systems and applications to dynamic consensus. IEEE Transactions on Automatic Control, 66(5):2326–2331, 2021.

[J49] Esteban Restrepo, Antonio Loria, Ioannis Sarras, and Julien Marzat. Robust consensus and connectivity-maintenance under edge-agreement-based protocols for directed spanning tree graphs. IFAC-PapersOnLine, 53(2):2988–2993, 2020.

[J61] Y. Lei, Y.-W. Wang, I.-C. Morărescu, and J.-W. Xiao. Guaranteed cost for an event-triggered consensus strategy for interconnected two time-scales systems with structured uncertainty. IEEETransactions on Cybernetics, 52(6):4370–4380, 2020.

[C41] E. Restrepo, A. Loria, I. Sarras, and J. Marzat. Robust consensus and connectivity-maintenance under edge-agreement-based protocols for directed spanning tree graphs. In 21st IFAC World Congress(VIRTUEL), 2020.

[C42] E. Panteley, A. Loría, and S. Sukumar. Strict lyapunov functions for consensus under directed connected graphs. In 2020 European Control Conference (ECC), pages 935–940. IEEE, 2020.

[C56] Antonio Loria, Elena Panteley, and Mohamed Maghenem. Strict lyapunov functions for model-reference adaptive control based on the mazenc construction. In Congreso Nacional de ControlAutomático (CNCA 2019), pages 407–412. Asociación de México de Control Automático, 2019.

[C63] V.S. Dolk, R. Postoyan, and W.P.M.H. Heemels. Event-triggered consensus for multi-agent systems with guaranteed robust positive minimum inter-event times. In Proceedings of 58th IEEEConference on Decision and Control, Nice, France, 2019.

Cluster control

Many of the existing networks have a modular structure characterized by multiple links within the same module (cluster) and a few links between different clusters. A practical way of dealing with such large-scale networks is to reduce their dimension by collapsing the states of nodes belonging to densely connected agents into aggregate variables. Then such networks can be viewed as multiple time scales systems, where the states of the agents in the clusters converge fast towards local agreements represented by the aggregate variables, which in turn slowly converge to consensus. To complement the existing stability analysis studies of two-time scales systems, we propose a controller design approach composed of two terms. The first term is common to all the nodes of a cluster and can be computed by a supervisory entity of that cluster. The second one, regulating the fast dynamics inside the cluster, is computed at the node level, taking into account its neighbors.

[C15] B. Adhikari, E. Panteley, and I.-C. Morărescu. Three time scales modeling of the undirected clustered network. In Proceedings of the 61st IEEE Conference on Decision and Control, pages 987–992, 2022.

Emergent Dynamics

Heterogeneous networks with nonlinear nodes dynamics and/or interconnections are often characterized by the appearance of common non-trivial behavior, such networks can be viewed as the dichotomy of two related processes: the emergence of a common behavior (emergent dynamics) and the synchronization of the individual systems relative to the latter. We use this approach to approximate the synchronized behavior in large networks of interconnected systems with linear coupling. We assume that the networks are heterogeneous, but the states of all systems are of the same dimension. The goal is to show that, in the case of sufficiently large coupling gains, the network is synchronized in some sense (asymptotically or practically), and its’ synchronized behavior can be approximated by a reduced order system, whose dynamics is independent of the coupling gains.

Relevant References:

[J24] Maitreyee Dutta, Elena Panteley, Antonio Loría, and Srikant Sukumar. Strict lyapunov functions for dynamic consensus in linear systems interconnected over directed graphs. IEEE Control SystemsLetters, 6:2323–2328, 2022.

[C15] B. Adhikari, E. Panteley, and I.-C. Morărescu. Three time scales modeling of the undirected clustered network. In Proceedings of the 61st IEEE Conference on Decision and Control, pages 987–992, 2022.

Singular Perturbations tools for network analysis

Many physical systems are characterized by two features. The first one is that they are composed of multiple interconnected entities/agents and the second one is that the dynamics of each agent is driven by processes evolving on different time-scales. In both case singular perturbation approach can be used for analysis of the system. On one hand, this approach is used in to analyze such a network behavior in the case of agents with hybrid two time scales dynamics. In particular, the output feedback stabilization of singularly perturbed multi-agent systems is considered in the context of analysis and stabilization of hybrid singularly perturbed multi-agent systems. On the other hand, singular perturbations techniques are used for analysis of heterogeneous networks with nonlinear nodes dynamics and high gain linear interconnections. This approach allows to approximate the synchronized behavior in large networks of interconnected systems by a reduced order switching system independent of the control gains.

Relevant References:

[J9] Alejandro A.I. Maass, W. Wang, D. Nešić, Y. Tan, and R. Postoyan. A multi-processor implementation for networked control systems. IEEE Control Systems Letters, 2023.

[J18] Y. Lei, Y.-W. Wang, I.-C. Morărescu, and R. Postoyan. Event-triggered fixed-time stabilization of two time scales linear systems. IEEE Transactions on Automatic Control, 68(3):1722–1729, 2022.

[J31] E.S. Tognetti, M. Jungers, and T.R. Calliero. Output feedback control for quadratic systems: A lyapunov function approach. International Journal of Robust and Nonlinear Control, 31(17):8373–8389, 2021.

[C15] B. Adhikari, E. Panteley, and I.-C. Morărescu. Three time scales modeling of the undirected clustered network. In Proceedings of the 61st IEEE Conference on Decision and Control, pages 987–992, 2022.

[C52] E.S. Tognetti, T.R. Calliero, and M. Jungers. Output feedback control for bilinear systems: a polytopic approach. IFAC-PapersOnLine, 52(28):58–63, 2019.

WP descrition: A number of application cases will be considered, which will confirm the effectiveness of the tools produced as research results from the previous workpackages.

Coordinator:Luca Zaccarian (LAAS)

Participants:Mohamed Maghenem (Gipsa), Philipp Braun (adj-world), Antonio Loria (L2S), Antoine Girard (L2S), Irinel-Constantin Morărescu (CRAN), Pierre Riedinger (CRAN), Renato Vizuete (L2S), Isabelle Queinnec (LAAS), Sophie Tarbouriech (LAAS), Luca Zaccarian (LAAS), Paolo Frasca (Gipsa), Jamal Daafouz (CRAN).

Below is a list of research topics investigated in the context of this Task/WorkPackage

Obstacle Avoidance

While global asymptotic stability/stabilization of nonlinear dynamical systems is well understood, also in terms
of possible topological obstructions, stability/stabilization
of dynamical systems subject to state constraints is more difficult. This is particularly true for the so-called obstacle avoidance problem. In particular, to simultaneously achieve global asymptotic stability
of the origin and avoidance of a bounded obstacle, topological obstructions prevent
the possibility of using continuous time-invariant feedback.
The natural approach is then to use discontiuous feedback but the resulting closed-loop system
is highly sensitive to measurement errors so that both stability and avoidance become unrobust.
One way to preserve robustness of GAS with non-continuous feedback laws (which proved to be effective for overcoming topological obstructions in the obstacle-free case
[17]), is to unite local and global controllers with hybrid techniques. In this task we characterize several control solutions using this hybrid paradigm
within a setting where each obstacle can be seen as a component of a network-like
description of the dynamics wherein the different avoidance phases are activated, as required.

[C28] Philipp Braun and Luca Zaccarian. Augmented obstacle avoidance controller design for mobile robots. IFAC-PapersOnLine, 54(5):157–162, 2021.

[C41] E. Restrepo, A. Loria, I. Sarras, and J. Marzat. Robust consensus and connectivity-maintenance under edge-agreement-based protocols for directed spanning tree graphs. In 21st IFAC World Congress(VIRTUEL), 2020.

[C69] P. Braun, C. Kellett, and L. Zaccarian. Complete control Lyapunov functions: Stability under state constraints. In Symposium on Nonlinear Control Systems (NOLCOS), pages 512–517, Vienna, Austria, September 2019.

Unmanned Aerial Vehicles

Trajectory tracking control
for underactuated unmanned aerial vehicles (UAVs) is an active field of research. According to the different actuation mechanisms, the most common
UAV platforms can achieve only a partial decoupling of attitude and
position tasks. Since position tracking is of utmost importance for
applications involving aerial vehicles, attitude tracking can be seen
as a secondary objective, which can be realized as long as the desired trajectory is compliant with the position tracking goal. Nonetheless, well-known intrinsic limitations of stabilization on compact manifolds limits the capabilities of smooth continuous-time feedback and hybrid architectures provide significant advantages in terms of uniformity of convergence to the desired motion. The generalization of classical continuous-time solutions to this hybrid setting makes use of theoretical results on interconnected hybrid systems.

Relevant References:

[J19] Davide Invernizzi, Marco Lovera, and Luca Zaccarian. Global robust attitude tracking with torque disturbance rejection via dynamic hybrid feedback. Automatica, 144:110462, 2022.

[J78] Michele Furci, Carlo Nainer, Luca Zaccarian, and Antonio Franchi. Input allocation for the propeller-based overactuated platform rospo. IEEE Transactions on Control Systems Technology, 28(6):2720–2727, 2019.

[C5] Florian Sansou and Luca Zaccarian. On local-global hysteresis-based hovering stabilization of the darko convertible uav. In 2022 European Control Conference (ECC), pages 40–45. IEEE, 2022.

Nanoscale Positioning Systems

The reset control solutions developed in the project can be effectively employed to
induce stability and performance of PID-controlled positioning systems suffering from nonlinear frictional effects. With Coulomb-only effect, PID feedback produces a nontrivial set of equilibria whose asymptotic (but not exponential) stability can be certified by using a discontinuous Lyapunov-like function. With velocity weakening effects (the so-called Stribeck friction), the set of equilibria becomes unstable with PID feedback and the so-called "hunting phenomenon" (persistent oscillations) is experienced. Resetting laws can be used in both scenarios. With Coulomb friction only, the discontinuous Lyapunov-like function immediately suggests a reset action providing extreme performance improvement, preserving stability and increasing the convergence speed. With Stribeck, a more sophisticated set of logic-based reset rules recovers global asymptotic stability of the set of equilibria, providing an effective solution to the hunting instability. The theoretical results have been tested on an industrial nano-positioning system, showing the experimental advantages arising from the novel reset PID controllers developed in the project.

Relevant References:

[J45] Ruud Beerens, Andrea Bisoffi, Luca Zaccarian, Henk Nijmeijer, Maurice Heemels, and Nathan van de Wouw. Reset pid design for motion systems with stribeck friction. IEEE Transactions on ControlSystems Technology, 30(1):294–310, 2021.

[C70] A. Bisoffi, R. Beerens, L. Zaccarian, M. Heemels, H. Nijmeijer, and N. van de Wouw. Hybrid model formulation and stability of a PID-controlled motion system with Coulomb friction. In Symposiumon Nonlinear Control Systems (NOLCOS), pages 116–121, Vienna, Austria, September 2019.

Opinion Dynamics

As a general trend, the attention of the control community is expanding beyond industrial applications to include the social and economic sciences. Hybrid phenomena are plentiful in social networks, as they may originate either from changes in the network that describes the society, or from the nature of the interaction itself. However, the literature on rigorous analysis of mathematical models of social dynamics has largely disregarded hybrid phenomena, with very few notable exceptions. This project thus appears to be the ideal venue to further pursue these efforts in a number of relevant directions including opinion dynamics and related fields.

Relevant References:

[J21] Floriana Gargiulo, Maria Castaldo, Tommaso Venturini, and Paolo Frasca. Distribution of labor, productivity and innovation in collaborative science. Applied Network Science, 7(1):19, 2022.

[J26] Massimo Bini, Paolo Frasca, Chiara Ravazzi, and Fabrizio Dabbene. Graph structure-based heuristics for optimal targeting in social networks. IEEE Transactions on Control of Network Systems, 9(3):1189–1201, 2022.

[C11] Paolo Frasca and Francesco Rossi. Caratheodory solutions and their associated graphs in opinion dynamics with topological interactions. IFAC-PapersOnLine, 55(30):436–441, 2022.

[C26] Francesca Ceragioli, Paolo Frasca, and Wilbert Samuel Rossi. Modeling limited attention in opinion dynamics by topological interactions. In Network Games, Control and Optimization: 10thInternational Conference, NetGCooP 2020, France, September 22–24, 2021, Proceedings 10, pages 272–281. Springer, 2021.

Coordinated Control of Vehicle Networks

We address the problems of consensus and formation control of nonholonomic systems via distributed control under the assumption that each vehicle receives measured states from a set of neighbors, with a bounded, time-varying, but necessarly differentiable delay. The controllers that we propose guarantee either partial or full consensus, in both cases a common consensus point is reached in the Cartesian positions on the plane; in the case of full consensus orientations on the plane converge to a common orientation. Uniform global asymptotic stability is established for the closed-loop system in each case.

Relevant References:

[J14] Esteban Restrepo, Antonio Loria, Ioannis Sarras, and Julien Marzat. Stability and robustness of edge-agreement-based consensus protocols for undirected proximity graphs. International Journal ofControl, 95(2):526–534, 2022.

[J34] Esteban Restrepo, Antonio Loría, Ioannis Sarras, and Julien Marzat. Edge-based strict lyapunov functions for consensus with connectivity preservation over directed graphs. Automatica, 132:109812, 2021.

[J36] Emmanuel Nuño, Antonio Loría, and Elena Panteley. Leaderless consensus formation control of cooperative multi-agent vehicles without velocity measurements. IEEE Control Systems Letters, 6:902–907, 2021.

[J40] V. Giammarino, S. Baldi, P. Frasca, and M. L. D. Monache. Traffic flow on a ring with a single autonomous vehicle: An interconnected stability perspective. IEEE Transactions on IntelligentTransportation Systems, 22(8):4998–5008, 2021.

[J49] Esteban Restrepo, Antonio Loria, Ioannis Sarras, and Julien Marzat. Robust consensus and connectivity-maintenance under edge-agreement-based protocols for directed spanning tree graphs. IFAC-PapersOnLine, 53(2):2988–2993, 2020.

[J51] E. Nuno, A. Loria, T. Hernández, M. Maghenem, and E. Panteley. Distributed consensus-formation of force-controlled nonholonomic robots with time-varying delays. Automatica, 120:109114, 2020.

[J59] M. Maghenem, A. Loria, E. Nuno, and E. Panteley. Distributed full-consensus control of nonholonomic vehicles under non-differentiable measurement delays. IEEE Control Systems Letters, 5(1):97–102, 2020.

[J60] M. Maghenem, A. Loria, E. Nuno, and E. Panteley. Consensus-based formation control of networked nonholonomic vehicles with delayed communications. IEEE Transactions on AutomaticControl, 2020.

[J75] M. A. Maghenem, A. Loria, and E. Panteley. Cascades-based leader-follower formation-tracking and stabilization of multiple nonholonomic vehicles. IEEE Transactions on Automatic Control, 2019.

[C19] Gian Marco Vinco, Philipp Braun, and Luca Zaccarian. A modular architecture for mobile robots equipped with continuous-discrete observers. In 2021 IEEE International Conference on Mechatronics(ICM), pages 1–6. IEEE, 2021.

[C45] M. Maghenem, A. Loria, E. Nuno, and E. Panteley. Decentralized partial-consensus control of nonholonomic vehicles over networks with interconnection delays. In 2020 American Control Conference(ACC), pages 2106–2111. IEEE, 2020.

[C48] T. Hernández, A. Loría, E. Nuño, and E. Panteley. Consensus-based formation control of nonholonomic robots without velocity measurements. In 2020 European Control Conference (ECC), pages 674–679. IEEE, 2020.

A microgrid is a group of interconnected loads and distributed energy resources within clearly deﬁned electrical boundaries, which acts as a single controllable entity with respect to the grid. Control of the microgrid is achieved through switching devices, such as power converters and interconnection ﬁlters, which are by nature hybrid. The goal of this task is both to develop suitable hybrid control laws for power converters, to be then combined in a collective behavior in a microgrid, and also to develop control strategies allowing for optimal operation of the microgrid as well as optimal design of the architecture in terms of storage or interconnection ﬁlter elements.

Relevant References:

[J1] Nicola Zaupa, Carlos Olalla, Isabelle Queinnec, Luis Martínez-Salamero, and Luca Zaccarian. Hybrid control of self-oscillating resonant converters with three-level input. IEEE Control SystemsLetters, 7:1375–1380, 2023.

[J10] Nicola Zaupa, Luis Martínez-Salamero, Carlos Olalla, and Luca Zaccarian. Hybrid control of self-oscillating resonant converters. IEEE Transactions on Control Systems Technology, 2022.

[J37] Giacomo Moretti, Luca Zaccarian, and Franco Blanchini. Quadratic constrained periodic optimization for bandlimited linear systems via the fourier-based method. Journal of Dynamic Systems,Measurement, and Control, 143(6), 2021.

[C18] Nicola Zaupa, Luis Martínez-Salamero, Carlos Olalla, and Luca Zaccarian. Results on hybrid control of self-oscillating resonant converters. IFAC-PapersOnLine, 54(5):211–216, 2021.

[C31] S. Benahmed, P. Riedinger, and S. Pierfederici. Distributed static state feedback control for current sharing and average voltage regulation in dc microgrids. In 24th International Symposium onMathematical Theory of Networks and Systems, Cambridge, UK, 2021.

[C32] S. Benahmed, P. Riedinger, and S. Pierfederici. Distributed cooperative control for dc microgrids. In International Conference on NETwork Games, Control and Optimisation, Corsica, France, 2021.