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), 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), Mohamed Maghenem (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:

[C23] 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:

[C23] 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.

[C28] 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.

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.

[C15] L. Zaccarian. Lyapunov-based reset control. In Symposium on Nonlinear Control Systems(NOLCOS), pages 272–273, Vienna, Austria, September 2019.

[C26] 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.

[C34] 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.

[J8] L. G. Moreira, J. M. Gomes da Silva Jr, S. Tarbouriech, and A. Seuret. Observer-based event-triggered control for systems with slope-restricted nonlinearities. International Journal of Robustand Nonlinear Control, to appear, 2020.

[C9] 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.

[C12] 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.

[C16] 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, Nice, France, 2019.

[C17] 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, Jeju Island, South Korea, 2019.

[C19] 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, Jeju Island, South Korea, 2019.

[C20] 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, Nice, France, 2019.

[C27] 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.

[J10] R. Merco, F. Ferrante, and P. Pisu. A hybrid controller for dos-resilient string-stable vehicle platoons. IEEE Transactions On Intelligent Transportation Systems, to appear, 2020.

[C3] 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), 2020.

[C10] 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.

[C22] 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, Jeju Island, South Korea, 2019.

[C24] 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, Nice, France, 2019.

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:Giacomo Casadei (adj-france), Antonio Loria (L2S), Antoine Girard (L2S), Irinel-Constantin Morărescu (CRAN), Christophe Prieur (Gipsa), Simone Mariano (CRAN), Riccardo Bertollo (adj-europe), 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), Mohamed Maghenem (Gipsa).

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:

[J4] 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.

[J13] 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.

[C21] 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.

[C31] 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.

[C35] V. Andrieu and S. Tarbouriech. LMI conditions for contraction and synchronization. In Symposium on Nonlinear Control Systems (NOLCOS), Vienna, Austria, September 2019.

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:

[C19] 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, Jeju Island, South Korea, 2019.

[C27] 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.

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.

[C6] A. Rodrguez, 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.

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.

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

Output feedback stabilization

The purpose of this task is to develop output feedback stabilization strategies for hybrid singularly perturbed multi-agent systems, which is still largely unexplored in the literature.

We propose an emergent dynamics based tool to approximate the synchronized behavior in large networks of interconnected linear systems with switching interconnection topologies and 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 practically synchronized, and its’ synchronized behavior can be approximated by a reduced order switching system independent of the control gains. To develop such reduced order system we use the singular perturbation theory, the time-scale separation techniques and
system analysis for interconnection gains tending to infinity.
The results are ensured for strongly connected networks under fairly mild assumptions by introducing a minimum dwell-time between two consecutive switches.

Lyapunov Methods for networks

It is well known that for consensus of systems interconnected under a general directed graph topology a necessary and sufficient condition for consensus is existence of at least one rooted spanning tree. In this paper we present an original statement of linear algebra that serves to characterize the spanning-tree condition for directed graphs in terms of a Lyapunov equation involving the graph’s Laplacian. Our results apply to the case of systems described by simple first and second order integrators. As a result, we provide strict Lyapunov functions that ensure, via direct constructive proof, global exponential stability of the consensus manifold.

Relevant References:

[C8] 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.

Cluster control

Many of the existing networks have a modular structure that is characterized by the presence of 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 three time scales systems, where the intermediate level is added to describe the dynamics of the clusters. Under suitable conditions, 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.

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: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), Mohamed Maghenem (Gipsa).

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

Microgrids

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 is 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:

[C1] 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.

[C2] 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.

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.

[C7] 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.

[C33] 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.

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.

[C34] 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.

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:

[J5] 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.

[J14] 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.

[J15] 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.

[J31] 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.

[C11] 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.

[C13] 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.