6.1.1 GTL

• Name: Grenoble Traffic Lab
• Functional Description: The Grenoble Traffic Lab (GTL) initiative, led by the NeCS team, is a real-time traffic data Center (platform) that collects traffic road infrastructure information in real-time with minimum latency and fast sampling periods. The main elements of the GTL are: a real-time data-base, a show room, and a calibrated micro-simulator of the Grenoble South Ring. Sensed information comes from a dense wireless sensor network deployed on Grenoble South Ring, providing macroscopic traffic signals such as flows, velocities, densities, and magnetic signatures. This sensor network was set in place in collaboration with Inria spin-off Karrus-ITS, local traffic authorities (DIR-CE, CG38, La Metro), and specialized traffic research centers. In addition to real data, the project also uses simulated data, in order to validate models and to test the ramp-metering, the micro-simulator is a commercial software (developed by TSS AIMSUN ©). More details at http://necs.inrialpes.fr/pages/grenoble-traffic-lab.php
• URL: http://necs.inrialpes.fr/pages/grenoble-traffic-lab.php
• Contact: Carlos Canudas-de-Wit
• Participants: Alain Kibangou, Andres Alberto Ladino Lopez, Anton Andreev, Carlos Canudas-de-Wit, Dominik Pisarski, Enrico Lovisari, Fabio Morbidi, Federica Garin, Hassen Fourati, Iker Bellicot, Maria Laura Delle Monache, Paolo Frasca, Pascal Bellemain, Pietro Grandinetti, Remi Piotaix, Rohit Singhal, Vadim Bertrand

6.1.2 GTL-Ville

• Name: Grenoble Traffic Lab - City
• Keyword: Traffic data
• Functional Description: The GTL-Ville platform is developed within the framework of the ERC Scale-FreeBack project (http://scale-freeback.eu/). Its functions are divided into three axes: 1- Collect traffic data in real time via different sources. We are currently working with three suppliers: TomTom (company) for speed data from Floating Car Data (FCD), La Métro for counting data from existing loops and Karrus (company) to complete the counting data from La Métro via radars deployed since last fall. 2- Estimate traffic indicators with the lowest possible latency using collected data and historical data applied to models developed by PhD students of the ERC project. 3- Visualize raw data and calculated indicators via a web interface (http://gtlville.inrialpes.fr/).
• URL: http://gtlville.inrialpes.fr
• Contact: Carlos Canudas-de-Wit

7.1.1 Functional target controllability of networks: structural properties and efficient algorithms

Participants: C. Commault, J. van der Waude, P. Frasca.

This line of research, accounted for in 14, considers the problem of controlling a limited number of target nodes of a network. Equivalently, we can see this problem as controlling the target variables of a structured system, where the state variables of the system are associated to the nodes of the network. We deal with this problem from a different point of view as compared to most recent literature. Indeed, instead of considering controllability in the Kalman sense, that is, as the ability to drive the target states to a desired value, we consider the stronger requirement of driving the target variables as time functions. The latter notion is called functional target controllability. We think that restricting the controllability requirement to a limited set of important variables justifies using a more accurate notion of controllability for these variables. Remarkably, the notion of functional controllability allows formulating very simple graphical conditions for target controllability in the spirit of the structural approach to controllability. The functional approach enables us, moreover, to determine the smallest set of steering nodes that need to be actuated to ensure target controllability, where these steering nodes are constrained to belong to a given set. We show that such a smallest set can be found in polynomial time. We are also able to classify the possible actuated variables in terms of their importance with respect to the functional target controllability problem.

7.1.2 Leaderless synchronization of heterogeneous oscillators by adaptively learning the group model

Participants: S. Baldi, P. Frasca.

It is well known that a synchronizing controller can be constructed when a common reference model is available to (some of) the agents. In 11, we show that synchronization can also be achieved without any access to such reference, by letting the agents cooperatively learn a suitable common model, which we refer to as group model. We show that there exists a group model that has the same structure as the oscillators and that the agents can learn its parameters and synchronize to it, by using a combination of consensus dynamics and adaptive regulation. This learning is even possible if the agents do not know their own dynamics, by using adaptive state observers. The distinguishing feature of this approach is making the agents collectively self- organize to their natural group model, instead of making them synchronize to an external reference.

7.1.3 Network games: Protecting shared information

Participants: B. de Witte, P. Frasca, B. Overvest, J. Timmer.

A digital security breach, by which confidential information is leaked, does not only affect the agent whose system is infiltrated but is also detrimental to other agents socially connected to the infiltrated system. Although it has been argued that these externalities create incentives to underinvest in security, this presumption is challenged by the possibility of strategic adversaries that attack the least protected agents. In 15 we study a new model of security games in which agents share tokens of sensitive information in a network of contacts. The agents have the opportunity to invest in security to protect against an attack that can be either strategically or randomly targeted. We show that, in the presence of random attack, underinvestments always prevail at the Nash equilibrium in comparison with the social optimum. Instead, when the attack is strategic, either underinvestments or overinvestments are possible, depending on the network topology and on the characteristics of the process of the spreading of information. Actually, agents invest more in security than socially optimal when dependencies among agents are low (which can happen because the information network is sparsely connected or because the probability that information tokens are shared is small). These overinvestments pass on to underinvestments when information sharing is more likely (and therefore, when the risk brought by the attack is higher). In order to keep our analysis tractable, some of our results on strategic attacks make an assumption of homogeneity in the network, namely, that the network is vertex‐transitive. We complement these results with an analysis on star graphs (which are nonhomogeneous), which confirms that the essential lines of our findings can remain valid on general networks.

7.1.4 On the influence of noise in randomized consensus algorithms

Participants: R. Vizuete, P. Frasca, E. Panteley.

Randomized interactions have been extensively studied in consensus systems, with a wide range of applications including social networks, sensor networks, and clock synchronization. Even if consensus in random networks has been studied for a long time, researchers have mostly considered ideal, noiseless interactions. Instead, more realistic dynamical models should at least include noise which prevents the states of the nodes from reaching consensus. In 27, we quantify the effects of noise by a noise index, which is simply the steady-state normalized mean square error between the states of the nodes and their average, and we study this index for symmetric update matrices. In our first result, we obtain an explicit expression for it. Since this closed form involves the calculation of an $N^2$-dimensional matrix, we derive an upper bound and a lower bound that depend on the eigenvalues of relevant $N$-dimensional matrices. These results generalize well-known results about deterministic consensus with noise. Next, we refine our analysis for a specific class of random update matrices, which we refer to as Randomly Induced Discretized Laplacians (RIDL), which are generated by sampling a subset of active nodes from a underlying large graph and considering the subgraph induced by the active nodes. This way of sampling random update matrices is motivated by the study of Open Multi-Agent Systems (OMAS): that is, multi-agent systems where agents can leave and join at any time. When the update matrices are RIDLs, our bounds can be expressed as functions of the Laplacian eigenvalues of the underlying graph. Further rewriting of the bounds as functions of the graph's average effective resistance reveals that they are asymptotically tight

7.1.5 Generic controllability of networks of identical SISO dynamical nodes

Participants: C. Commault, A. Kibangou.

7.1.6 Cyber-Physical Systems: a control-theoretic approach to privacy and security

Participants: F. Garin, A. Kibangou, S. Gracy.

Cyber-physical systems are composed of many simple components (agents) with interconnections giving rise to a global complex behaviour. One line or research on security of cyber-physical systems models an attack as an unknown input being maliciously injected in the system. We study linear network systems, and we aim at characterizing input and state observability (ISO), namely the conditions under which both the whole network state and the unknown input can be reconstructed from some measured local states. We complement the classical algebraic characterizations with novel structural results, which depend only on the graph of interactions (equivalently, on the zero pattern of the system matrices). More precisely, we obtain two kinds of results: structural results, true for almost all interaction weights, and strongly structural results, true for all non-zero interaction weights. Our results in 2020 concern strongly structural ISO for time-invariant systems 17. We provide first a graphical characterization for s-structural unconstrained ISO (where the input reconstruction might happen with some unspecified delay), and subsequently, sufficient conditions and necessary conditions for s-structural ISO (where we ensure that the input at time $k-1$ can be reconstructed at time $k$). The conditions presented are in terms of existence of suitable uniquely restricted matchings in bipartite graphs associated with the structured system. In order to test these conditions, we present polynomial-time algorithms. We also discuss an equivalent reformulation of the main conditions in terms of coloring algorithms as in the literature of zero forcing sets.

7.2.1 Average state estimation of clustered large-scale network systems

Participants: M.U.B. Niazi, C. Canudas-de-Wit, A. Kibangou.

Large-scale network systems pose several challenges in terms of monitoring and control. On the one hand, they challenge the computational resources at hand, while on the other hand, the number of available sensors are often limited and not sufficient to render the network system observable. This makes the state estimation task infeasible. Nonetheless, in many applications, it suffices to know the aggregated state profiles of clusters of nodes in the network system. One such profile is the average state of each cluster in the network. In 21 we provide necessary and sufficient conditions such that the average states of the pre-specified clusters of the network system can be reconstructed and/or asymptotically estimated, which are captured by the notions of average observability and average detectability, respectively. To achieve computational tractability, average observability and average detectability of a clustered network system are defined via the projected network system, which is of tractable dimension and is obtained by aggregating the clusters. The corresponding necessary and sufficient conditions of average observability and average detectability are provided and interpreted through the underlying structure of the induced subgraphs and the induced bipartite subgraphs, which capture the intra-cluster and inter-cluster topologies of the clustered network system, respectively. Moreover, the design of an average state observer whose dimension is minimum, and equals the number of clusters in the clustered network system, is presented.

7.2.2 Aggregated temperature estimation for the thermal monitoring of large buildings

Participants: M.U.B. Niazi, C. Canudas-de-Wit, A. Kibangou.

Residential and commercial buildings play a significant part in global energy consumption and greenhouse gas emissions. For instance, in France, they are one of the largest sources of energy consumption, Levy and Belaid (2018), and amount to 23% of the national greenhouse gas emissions, Derbez et al. (2014). In mitigating the effects of global warming, therefore, one of the forefronts is to develop efficient techniques for thermal monitoring and control of the buildings. Thus, thermal monitoring is important not only to ensure the comfort of building inhabitants but also to reduce energy consumption and greenhouse gas emissions. It can be, however, a challenging task because of limited computational and sensing resources at hand. In 33 we provide an efficient technique to estimate average (or mean operative) temperatures of rooms in a building. The proposed average observer to estimate the average temperatures of rooms in real-time is of minimum order and its parameters are chosen optimally in order to minimize the asymptotic estimation error. We employ a simple on/off control policy based on the average observer to regulate the mean operative temperatures of rooms. Such an on/off policy for regulation saves around 25.32% of the energy, which means that the heaters on average remain off 25.32% of the day. Since the goal of this work is to present an optimal estimation technique, we believe that a better control technique to further minimize the energy consumption can be developed, which is deferred for the future work.

7.2.3 Estimation of the state variance in large-scale network systems

Participants: M.U.B. Niazi, C. Canudas-de-Wit, A. Kibangou.

Large-scale network systems are ubiquitous in modern engineering applications such as traffic networks, building thermal systems, and distributed sensor networks. Complete monitoring of such large-scale systems is usually not possible due to limited computational and sensing resources. Limited computational resources can make the real-time state estimation task infeasible, whereas limited number of sensors may render the system unobservable. It is reasonable, therefore, to monitor the network system by estimating the aggregated state profiles such as the state average and variance. The state variance of a network system is a nonlinear functional computed as the squared deviation of the network's state vector. Such a quantity is useful to monitor how much the states of network nodes are spread around their average mean. Estimating state variance is crucial when the full state estimation of a network system is not possible due to limited computational and sensing resources. In 32 we propose a novel methodology to estimate the state variance in a computationally efficient way. We first provide the fundamental limit of functional observers with regards to the state variance, which requires that the observer should have an order of at least the number of unmeasured nodes minus one. That is, even if the observer is of minimum order, it is equivalent to estimate all but one states of the unmeasured nodes in order to asymptotically estimate the state variance. This makes the problem trivial because it can be argued that, in large-scale systems, estimating all but one states is almost the same as estimating all the states. Thus, if we can estimate all the states, there is no need to estimate the state variance. The infeasibility of designing a nonlinear functional observer directs us towards the estimation of state variance in an approximate sense. That is, we first approximate the state variance by projecting the network system on a lower dimensional state space by clustering. The state vector of the projected system includes the states of the measured nodes and the average states of the clusters. Then, by estimating the average states of the clusters, we can estimate the approximated state variance.

7.2.4 Average state estimation in presence of outliers

Participants: U. Pratap, C. Canudas-de-Wit, F. Garin.

In recent years, there has been a lot of interest in the problem of estimation in network control systems due to its vast area of application such as power networks, communication networks, and traffic networks to name a few. In particular, in some networks, instead of reconstructing the entire states, some aggregation of the unmeasured states are estimated using a few available measurements obtained from the dedicated sensors placed at some positions. One of the options is to estimate the average of the unmeasured states. This approach is very beneficial in terms of reducing the complexity. However, if there is an outlier among the unmeasured states, which is so different from the other states that it affects the average value significantly, the average value so estimated may not lead to the true average value. Instead, one might look for an average value that excludes the outlier. In 35, we propose a methodology to detect the outlier and to estimate the average state excluding the outlier (trimmed-average). At first, a design of a scalar and tunable observer has been given along with the condition under which a bank of these observers can be designed to estimate the average of the unmeasured states while excluding an element at every possible position. In the proposed method, we deploy a bank of these observers, and then compare the estimates so obtained using a dissimilarity criterion in order to measure how far are the estimates from each other. Then by finding the estimates with largest distance from all the other estimates, we detect the outlier and the average estimate without the outlier.

7.2.5 Subgraph detection for average detectability of LTI systems

Participants: N. Martin, C. Canudas-de-Wit, P. Frasca.

Observation and detection of networked systems aim to reconstruct the evolution of the system based on the measurement of few nodes. In large-scale networks, reconstructing the exact state of each node becomes more complex and in practice it is often superfluous. Reconstructing an aggregated version of the system is often sufficient. In the light of this observation, paper 20 considers the notion of average detectability: A system is said to be average detectable if it is possible to reconstruct the average of the subset of its unmeasured nodes. We show here that for a particular type of system, that is negative uniform networks, the average detectability property is reached when the subgraph induced by the unmeasured nodes is regular. Thus, we study the detection of such regular induced subgraph and we propose an algorithm to complete this task. We introduce also the relaxed notion of quasi-regularity ensuring an approximate reconstruction of the average. This paper presents algorithms to detect regular induced subgraphs (RIS) and quasi-regular induced subgraph (q-RIS). We propose an extension to detect multiple quasi-regular induced subgraphs (mq-RIS) in order to reconstruct the average of several subgraphs of the system. Finally we apply our method to the evolution of an epidemic spreading over a simulated contact network over the largest cities in France based on a SIS model.

7.2.6 Shape-based nonlinear model reduction for 1D conservation laws

Participants: D. Nikitin, C. Canudas-de-Wit, P. Frasca.

The problems of controlling high-dimensional systems appear naturally in many areas, including urban traffic, flow dynamics, chemical processes, heating processes, etc. Mathematical models of such systems can be described in various ways, for example, partial differential equations, conservation laws, or networks. However, regardless of the way it is modelled, the problem of controlling the state of the entire system is usually highly complex. It is often preferable to control not the entire state of the system, but some aggregated characteristics. In 34 we present a novel method for model reduction of one-dimensional conservation law to the dynamics of the parameters describing the approximate shape of the solution. Depending on the parametrization, each parameter has a well-defined physical meaning. Thus, the dynamics of the system turns into the dynamics of the shape parameters, and this new ODE system can be used for the estimation and control purposes. The model reduction is performed by minimizing the divergence of flows between the original and reduced systems, and we show that this is equivalent to the minimization of the Wasserstein distance derivative. The method is then tested on the heat equation and on the LWR (Lighthill-Whitham-Richards) model for vehicle traffic.

7.2.7 Continuation Method for Large-Scale Modeling and Control: from ODEs to PDE

Participants: D. Nikitin, C. Canudas-de-Wit, P. Frasca.

Most of the systems we encounter in real life consist of such a large number of particles that the direct analysis of their interaction is impossible. In such cases, simplified models are used that aggregate the behavior of a set of particles and replace them with a continuous representation. In 42 we present a continuation method which transforms spatially distributed ODE systems into continuous PDE. We show that this continuation can be performed both for linear and nonlinear systems, including multidimensional, space-and time-varying systems. When applied to a large-scale network, the continuation provides a PDE describing evolution of continuous state approximation that respects the spatial structure of the original ODE. Our method is illustrated by multiple examples including transport equations, Kuramoto equations and heat diffusion equations. As a main example, we perform the continuation of a Newtonian system of interacting particles and obtain the Euler equations for compressible fluids, thereby providing an original alternative solution to Hilbert's 6th problem. Finally, we leverage our derivation of the Euler equations to control multiagent systems, designing a nonlinear control algorithm based on the continuous approximation to stabilize a robotic formation along the desired trajectory, performing a maneuver of passing through a window. The control is derived on a level of a PDE representation and then it is discretized to be implemented on every agent.

7.2.8 Graphon-based sensitivity analysis of SIS epidemics

Participants: R. Vizuete, P. Frasca, F. Garin.

Traditionally, researchers have used concepts of Graph Theory for the analysis of networks, where a complete knowledge of the network graph is required for most applications. One of the most important dynamics over networks is a Susceptible-Infected-Susceptible (SIS) epidemic which describes a disease that can infect agents irrespective of whether they were infected earlier. Even if the analysis and control of epidemics are well studied topics, the applicability of the theoretical results is often limited by restrictive assumptions that require complete knowledge of the dynamical laws of the nodes, of their states, and of the structure of the network. One of the most promising tools to address these problems are graph functions, also called graphons, which are limits of sequences of dense graphs. In 26 we focus on the deterministic SIS epidemic model, interpreted as a meta-population model, where the state of each node is the fraction of infected individuals in a sub-population and we model the network as a graphon. We consider special cases of graphons corresponding to stochastic block models, which are used to model the community structures that are frequent in real social networks such that each node can be considered as a small population, like a village or a neighborhood, and each block as a region or city. The inclusion of additive noise is also frequently used to include un-modeled phenomena and features in epidemics models. In network dynamics, the properties of robustness to noise can often be expressed through the spectral properties of the network. Therefore, we look at the spectral properties of graphons to evaluate the robustness properties of large networks described by graphons. We leverage the properties of piecewise Lipschitz graphons with finite rank (that encompass stochastic block models) for the stability and sensitivity analysis of SIS epidemics over large networks and show that the spectral properties of the graphon allow to approximately evaluate stability and robustness to noise.

7.3.1 Adaptive cruise control systems: stability and parameter estimation

Participants: M. L. Delle Monache, Y. Wang, G Gunter, M. Nice, D Gloudemans, R. Stern, S. McQuade, R. Bhadani, M. Bunting, R. Lysecky, B. Seibold, J. Sprinkle, B. Piccoli, D. Work.

Subsequently, in 19 the string stability of seven 2018 model year ACC equipped vehicles that are widely available in the US market is assessed. Seven distinct vehicle models from two different vehicle makes are analyzed using data collected from more than 1,200 miles of driving in car-following experiments with ACC engaged by the follower vehicle. The resulting dataset is used to identify the parameters of a linear second order delay differential equation model that approximates the behavior of the black box ACC systems. The string stability of the data-fitted model associated with each vehicle is assessed, and the main finding is that all seven vehicle models have string unstable ACC systems. For one commonly available vehicle model that offers ACC as a standard feature on all trim levels, we validate the string stability finding with a multi-vehicle platoon experiment in which all vehicles are the same year, make, and model. In this test, an initial disturbance of 6 mph is amplified to a 25 mph disturbance, at which point the last vehicle in the platoon is observed to disengage the ACC. The data collected in the driving experiments is made available, representing the largest publicly available comparative driving dataset on ACC equipped vehicles.

7.3.2 Control using autonomous vehicles: string stability approach

Participants: V. Giammarino, S. Baldi, P. Frasca, M. L. Delle Monache.

7.3.3 Control using autonomous vehicles: a pde-ode model approach

Participants: T. Liard, R. Stern, M. L. Delle Monache.

7.3.4 Three phase fundamental diagram from three dimensional traffic data

Participants: M. L. Delle Monache, K. Chi, Y. Chen, P. Goatin, K. Han, J.-M. Qiu, B. Piccoli.

7.3.5 Variable Speed Limits Control in an Urban Road Network to Reduce Environmental Impact of Traffic

Participants: B. Othman, G. De Nunzio, D. Di Domenico, C. Canudas-de-Wit.

7.3.6 Boundary Control Design for Traffic with Nonlinear Dynamics

Participants: L. Tumash, C. Canudas-de-Wit, M.L. Delle Monache.

7.3.7 Equilibrium Manifolds in 2D Fluid Traffic Models

Participants: L. Tumash, C. Canudas-de-Wit, M.L. Delle Monache.

7.3.8 Topology-based control design for congested areas in urban networks

Participants: L. Tumash, C. Canudas-de-Wit, M.L. Delle Monache.

7.3.9 Average density detectability in traffic networks using virtual road divisions

Participants: M. Rodriguez-Vega, C. Canudas-de-Wit, H. Fourati.

Accurate traffic state estimation is important in modern intelligent transportation systems, as they provide traffic operators with the necessary information to take decisions about control strategies, network design, and design traffic policies. As the size of the network increases, the state estimation for every road becomes computationally expensive. In some applications, the individual states might not be necessary, and an average state might be sufficient. In 36, we deal with the problem of the average density estimation of a large scale traffic network. Our main contribution is the proposal of a reduced-order open-loop observer for the average density of a region. This observer is shown to converge for a virtual representation of the network where each road is divided into a specific number of cells. The proposed observer is tested using simulations of the real case of the Grenoble traffic network.

7.4.1 Junk news bubbles: modelling the rise and fall of attention in online arenas

Participants: M. Castaldo, T. Venturini, P. Frasca, F. Gargiulo.

In this article 12, we present a type of media disorder which we call ‘junk news bubbles’ and which derives from the effort invested by online platforms and their users to identify and circulate contents with rising popularity. Such emphasis on trending matters, we claim, can have two detrimental effects on public debates: first, it shortens the amount of time available to discuss each matter and second, it increases the ephemeral concentration of media attention. We provide a formal description of the dynamic of junk news bubbles, through a mathematical exploration of the famous ‘public arenas model’ developed by Hilgartner and Bosk in 1988. Our objective is to describe the dynamics of the junk news bubbles as precisely as possible to facilitate its further investigation with empirical data.

7.4.2 A dynamic game of opinion dynamics in social networks: Accord and discord as Nash equilibria

Participants: M.U.B. Niazi, A.B. Özgüler.

Most of the models of opinion dynamics in the literature focus on the consensus formation between social agents in a network as an emergent phenomenon. However, disagreements and situations of conflict are also quite common in real life. Thus, several models have also been proposed to explain the emergence of conflict or discord in a social network in terms of polarization of agents into multiple groups. Nonetheless, such an emergence of discord remains to be explained when the social agents are strategic in nature. In 22 we present a non-cooperative dynamic game model of opinion dynamics with open-loop information structure. In this game, the agents’ motives are shaped by their expectations of the nature of others’ opinions as well as how susceptible they are to get influenced by others, how stubborn they are, and how quick they are willing to change their opinions on a set of issues in a prescribed time interval. These motives are independently formed by all agents. The existence of a Nash equilibrium in the network means that a collective behavior emerges out of local interaction rules and these individual motives. We prove that a unique Nash equilibrium may exist in the game under quite different circumstances. It may exist not only if there is a harmony of perceptions among the agents of the network, but also when agents have different views about the correlation among issues. The first leads to an accord in the network usually expressed as a partial consensus, and the second to a discord in the form of oscillating opinions. In the case of an accord, the harmony in the network may be in the form of similarity in pairwise conceptions about the issues but may also be an agreement on the status of a “leader” in the network. A Nash equilibrium may fail to exist only if the network is in a state of discord.

7.4.3 Opinion Dynamics with Topological Gossiping: Asynchronous Updates under Limited Attention

Participants: W.S. Rossi, P. Frasca.

7.5.1 Modeling and control of COVID-19 epidemic through testing policies

Participants: M.U.B. Niazi, A. Kibangou, C. Canudas-de-Wit, D. Nikitin, L. Tumash, P.-A. Bliman.

The COVID-19 epidemic started in Wuhan, China, at the end of 2019, was declared to be a pandemic by the World Health Organization (WHO) on March 11, 2020. The pandemic shook the economy of the whole world with a significant reduction of exports, a decline in tourism, mass unemployment, and business closures. Governments and health authorities worldwide have responded by implementing non-pharmaceutical intervention (NPI) policies that include travel restrictions, lockdown strategies, social distancing measures, workplace hazard controls, closing down of schools and workplaces, curfew strategies, and cancellation of public events. On March 16, 2020, the Director General of WHO, Dr. T. A. Ghebreyesus, gave a simple message to all countries, “Test, test, test." Following the recommendation of the WHO director, with different levels of setups, many governments increased their testing capacities. Testing for the infected cases is one of the most important mechanisms to control an epidemic. It enables to isolate the detected infected individuals, thereby limiting the disease transmission to the susceptible population. However, despite the significance of testing policies, the recent literature on the subject lacks a control-theoretic perspective. In 41 an epidemic model that incorporates the testing rate as a control input is presented. The proposed model differentiates the undetected infected from the detected infected cases, who are assumed to be removed from the disease spreading process in the population. First, the model is estimated and validated for COVID-19 data in France. Then, two testing policies are proposed, the so-called best-effort strategy for testing (BEST) and constant optimal strategy for testing (COST). The BEST policy is a suppression strategy that provides a lower bound on the testing rate such that the epidemic switches from a spreading to a non-spreading state. The COST policy is a mitigation strategy that provides an optimal value of testing rate that minimizes the peak value of the infected population when the total stockpile of tests is limited. Both testing policies are evaluated by predicting the number of active intensive care unit (ICU) cases and the cumulative number of deaths due to COVID-19. We found that the BEST policy could have reduced the peak of number of ICU cases and the cumulative number of deaths by 34.71% and 74.45%, respectively. On the other hand, the COST policy could have reduced the peak of number of ICU cases and the cumulative number of deaths by 11.12% and 37.52%, respectively.

7.5.2 Analyzing essential traffic impact extracted during COVID-19 lockdown in a developing country

Participants: T. Moyo, A. Kibangou, W. Musakwa.

7.5.3 The rhythms of the night: increase in online night activity and emotional resilience during the spring 2020 Covid-19 lockdown

Participants: M. Castaldo, T. Venturini, P. Frasca, F. Gargiulo.

The lockdown orders established in multiple countries in response to the Covid-19 pandemic are arguably one of the most widespread and deepest shock experienced by societies in recent years. Studying their impact trough the lens of social media offers an unprecedented opportunity to understand the susceptibility and the resilience of human activity patterns to large-scale exogenous shocks. In 44 we firstly investigate the changes that this upheaval has caused in online activity in terms of time spent online, themes and emotion shared on the platforms, and rhythms of content consumption. Secondly, we examine the resilience of certain platform characteristics, such as the daily rhythms of emotion expression. In order to do so, two independent datasets about the French cyberspace ave been considered: a fine-grained temporal record of almost 100 thousand YouTube videos and a collection of 8 million Tweets between February 17 and April 14, 2020. In both datasets we observe a reshaping of the circadian rhythms with an increase of night activity during the lockdown. The analysis of the videos and tweets published during lockdown shows a general decrease in emotional contents and a shift from themes like work and money to themes like death and safety. However, the daily patterns of emotions remain mostly unchanged, thereby suggesting that emotional cycles are resilient to exogenous shocks.

7.6.1 Magnetic field gradient and magnetometers network for velocity estimation in indoor navigation

We proposed an advanced solution to improve the inertial velocity estimation of a rigid body, for indoor navigation, through implementing a magnetic field gradient-based Extended Kalman Filter (EKF) 29. The proposed estimation scheme considers a set of data from a triad of inertial sensors (accelerometer and gyroscope), as well as a determined arrangement of magnetometers array. The inputs for the estimation scheme are the spatial derivatives of the magnetic field, from the magnetometers array, and the attitude, from the inertial sensors. As shown in the literature, there is a strong relation between the velocity and the measured magnetic field gradient. However, the latter usually suffers from high noises. Then, the novelty of the proposed EKF is to develop a specific equation to describe the dynamics of the magnetic field gradient. This contribution helps to filter, first, the magnetic field and its gradient and second, to better estimate the inertial velocity. Some numerical simulations that are based on an open source database show the targeted improvements. This approach is extended to position estimation in the case of a foot-mounted application and the results are very promising.

7.6.2 Magnetic gradient-based EKF and LSTM learning model for velocity estimation under a network of magnetometers

We present a novel method to improve the inertial velocity estimation of a mobile body, for indoor navigation, using solely raw data from a triad of inertial sensors (accelerometer and gyroscope), as well as a determined arrangement of magnetometers array 40. The key idea of the method is the use of deep neural networks to dynamically tune the measurement covariance matrix of an Extended Kalman Filter (EKF). To do so, a Long Short-Term Memory (LSTM) model is derived to determine a pseudo measurement of inertial velocity of the target under investigation. This measurement is used afterwords to dynamically adapt the measurement noise parameters of a magnetic field gradient-based EKF. As it was shown in the literature, there is a strong relation between inertial velocity and magnetic field gradient, which is highlighted with the proposed approach in this work. Its performance is tested on the Openshoe dataset, and the obtained results compete with the INS/ZUPT approach, that unlike the proposed solution, can only be applied on foot-mounted applications and is not adequate to all walking paces.

9.1.1 Inria associate team not involved in an IIL

9.1.2 Participation in other international programs

9.3.1 FP7 & H2020 Projects

9.3.2 Collaborations in European programs, except FP7 and H2020

10.1.1 Scientific events: organisation

10.1.2 Scientific events: selection

10.1.3 Journal

10.1.4 Invited talks

M. L. Delle Monache gave the following invited talks during 2020:

• Modeling for mixed autonomy traffic: a control-based approach, Workshop on large scale autonomy: connectivity and mobility networks, IPAM (UCLA), USA, November 2020
• Coupled PDE-ODE systems: applications to traffic flow modeling, estimation and control, 42nd workshop of research center for complex systems and network sciences, Southeastearn university, China, September 2020
• Coupled PDE-ODE systems: applications to traffic flow modeling, estimation and control, Journée de l'équipe EMS, Université d'Orléans, France, February 2020

A. Kibangou gave a talk at GDR MACS for COVID Initiative on July 7, 2020.

M. U. B. Niazi gave the following invited talk

• Modeling and Control of COVID-19 Epidemic through Testing Policies, the International e-Seminar on Control and Systems Theory, TU Kaiserslautern, Germany, November 2020.

P. Frasca gave the following invited talks during 2020:

• “Traffic Flow on a Ring with a Single Autonomous Vehicle: An Interconnected Stability Perspective”, Southeast University, Nanjing, China, September 4, 2020
• “The closed loop between opinion formation and personalised recommendations”, Peking University, Beijing, China, July 21, 2020

10.1.5 Leadership within the scientific community

Team members participate to the following technical committees of IEEE Control Systems Society and of the International Federation of Automatic Control:

• IEEE-CSS Technical Committee “Networks and Communications Systems” (P. Frasca and F. Garin);
• IFAC Technical Committee 1.5 on Networked Systems (P. Frasca and C. Canudas de Wit);
• IFAC Technical Committee 2.5 on Robust Control (P. Frasca);
• IFAC Technical Committee 9.2 on Human Impact of Automation (P. Frasca);
• IFAC Technical Committee 7.1 Automotive Control (C. Canudas de Wit);
• IFAC Technical Committee 7.4 Transportation systems (C. Canudas de Wit).

P. Frasca is a member of the steering committee of the GdR MACS (body coordinating national activities in Automatic Control in France), 2019–2023, and C. Canudas de Wit is member of the board of SAGIP (Société d'Automatique, de Génie Industriel et de Productique).

10.1.6 Scientific expertise

F. Garin was a member of the recruiting committee for researchers at Inria Grenoble–Rhône-Alpes.

10.1.7 Research administration

F. Garin is `responsable du pôle automatique et diagnostic’ at GIPSA-lab, since Jan 2020 and `Présidente du CES (Comité des Emplois Scientifiques) du Centre Inria Grenoble–Rhône-Alpes’, since July 2019. She is also `co-responsable de l'axe CPS (Cyber-Physical Systems)' of Persyval2, since Nov. 2019.

C. Canudas de Wit is a member of the COST-Inria-RA (Conseil d’Orientation Scientifique et Technologique, Inria Rhône-Alpes), since 2017, and an elected member of the `Commission d'Évaluation Inria' since 2020.

M.L. Delle Monache is member of two local committees at Inria Grenoble Rhône-Alpes: Commission de développement technologique (research engineers) and Comité des Études Doctorales (PhD grants CORDI-S).

H. Fourati is an elected member of CNU61 (Conseil National des Universités, Génie informatique, Automatique et Traitement du Signal).

A. Kibangou is an elected member of "Conseil du pôle MSTIC" at Univ. Grenoble Alpes.

10.2.1 Teaching

• Master: F. Garin, Distributed Algorithms and Network Systems, 13.5h, M2, Univ. Grenoble Alpes, France.
• Licence: H. Fourati, Mathématiques, 30h, L2, IUT1 (GEII1), Univ. Grenoble Alpes, France.
• Licence: H. Fourati, Informatique Industrielle, 111h, L1, IUT 1 (GEII), Univ. Grenoble Alpes, France.
• Licence: H. Fourati, Réseaux locaux industriels, 34h, L2, IUT1 (GEII), Univ. Grenoble Alpes, France.
• Licence: H. Fourati, Automatique, 39h, L3, UFR physique, Univ. Grenoble Alpes, France.
• Licence: H. Fourati, Automatique continue et discrete, 27h, L2, IUT1 (GEII), Univ. Grenoble Alpes, France.
• Master: H. Fourati, Perception and states estimation for mobile robotics, 14h, M2, Grenoble-INP ENSE3.
• Licence: A. Kibangou, Automatique, 75h, L2, IUT1(GEII), Univ. Grenoble Alpes, France.
• Licence: A. Kibangou, Mathématiques, 44h, L2, IUT1 (GEII), Univ. Grenoble Alpes, France.
• Licence: A. Kibangou, Mathématiques, 126h, L1, IUT1 (GEII), Univ. Grenoble Alpes, France.
• Master: A. Kibangou, Automatique-Préparation à l'aggrégation, 6h, M2, Ministère de l'education nationale-Académie de Grenoble, France.

10.2.2 Supervision

• PhD: Nicolas Martin, Network partitioning algorithms with scale-free objective, Univ. Grenoble Alpes, Feb. 2020, co-advised by C. Canudas de Wit and P. Frasca.
• PhD: Stéphane Mollier, Two-dimensional macroscopic models for large scale traffic networks, Univ. Grenoble Alpes, Feb. 2020, co-advised by C. Canudas de Wit, M. L. Delle Monache and B. Seibold.
• PhD in progress: Tarso Kraemer Sarzi Sartori, Mitigation des effets du rayonnement cosmique dans les algorithmes d'estimation d'attitude de systèmes de navigation inertielle, from Oct. 2020, co-advised by R. Possamai Bastos and H. Fourati.
• PhD in progress: Nigina Toktassynova, Simulation and research of industrial flow control systems of the enterprise based on MES systems, from Sep. 2016, co-advised by B. Suleimenov and H. Fourati.
• PhD in progress: Martin Rodriguez-Vega, Traffic density, traveling time and vehicle emission estimation in large-scale traffic networks, from Oct. 2017, co-advised by C. Canudas de Wit and H. Fourati.
• PhD in progress: Muhammad Umar B. Niazi, State-state estimation design and optimal sensor placement algorithms for large-scale evolutionary dynamical networks, from Dec. 2017, co-advised by C. Canudas de Wit and A. Kibangou.
• PhD in progress: Thembani Moyo, Origin and destination modeling and estimation for smart mobility, from May 2018, co-advised by A. Kibangou and W. Musakwa (Univ. of Johannesburg).
• PhD in progress: Denis Nikitin, Scalable large-scale control of network aggregates, from Sept. 2018, co-advised by C. Canudas de Wit and P. Frasca.
• PhD in progress: Liudmila Tumash, Traffic control in large-scale urban networks, from Sept. 2018, co-advised by C. Canudas de Wit and M. L. Delle Monache.
• PhD in progress: Bassel Othman, Dynamic optimization of road traffic in a large-scale urban network from Oct. 2018, co-advised by C. Canudas de Wit and G. De Nunzio.
• PhD in progress: Makia Zmitri, Estimating the attitude by IMU, magnetic and vision measures: an automatic control approach, from Oct. 2018, co-advised by H. Fourati and C. Prieur.
• PhD in progress: Ujjwal Pratap, Resilient control in scale-free networks, from Feb. 2019, co-advised by C. Canudas-de-Wit, F. Garin, and H. Sandberg (KTH Stockholm).
• PhD in progress: Renato Vizuete, Open Multi-Agent Systems, from Sept. 2019, co-advised with Elena Panteley
• PhD in progress: Maria Castaldo, Disorders of online media, from Nov. 2019, co-advised with Tommaso Venturini (Centre Internet et Société, CNRS)
• PhD in progress: Nomfundo Cele, Perception of Quality of Service on public transportation in developing countries, from November 2020, co-advised by A. Kibangou and W. Musakwa (Univ. of Johannesburg).

10.2.3 Juries

• P. Frasca was external referee for the Ph.D. defense of Francesco Sasso, University of Salento, Lecce, Italy (Ph.D. advisors: Giuseppe Notarstefano and Angelo Coluccia), 2020

10.3.1 Articles and contents

Article on “Le Journal du CNRS” on online behaviors during COVID-19 lock-down, 2020

International journals

• 11 articleSimoneS. Baldi and PaoloP. Frasca. Leaderless synchronization of heterogeneous oscillators by adaptively learning the group modelIEEE Transactions on Automatic Control6512020, 412-418
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• 12 article MariaM. Castaldo, TommasoT. Venturini, PaoloP. Frasca and FlorianaF. Gargiulo. Junk News Bubbles: Modelling the Rise and Fall of Attention in Online Arenas New Media and Society 2021
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• 13 articleChristianC. Commault and AlainA. Kibangou. Generic controllability of networks with identical SISO dynamical nodesIEEE Transactions on Control of Network Systems72February 2020, 855-865
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• 14 articleChristianC. Commault, JacbJ. Van der Woude and PaoloP. Frasca. Functional target controllability of networks: structural properties and efficient algorithmsIEEE Transactions on Network Science and Engineering732020, 1521-1530
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• 15 articleBramB. De Witte, PaoloP. Frasca, BastiaanB. Overvest and JudithJ. Timmer. Protecting shared information in networks: a network security game with strategic attacksInternational Journal of Robust and Nonlinear Control3011July 2020, 4255-4277
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• 16 article Maria LauraM. Delle Monache, KarenK. Chi, YongY. Chen, PaolaP. Goatin, KeK. Han, Jing-MeiJ.-M. Qiu and BenedettoB. Piccoli. A three-phase fundamental diagram from three-dimensional traffic data Axioms 10 1 2021
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• 17 articleFedericaF. Garin, SebinS. Gracy and AlainA. Kibangou. Strong Structural Input and State Observability of Linear Time-Invariant Systems: Graphical Conditions and AlgorithmsEuropean Journal of Control58March 2021, 27-42
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• 18 articleVittorioV. Giammarino, SimoneS. Baldi, PaoloP. Frasca and Maria LauraM. Delle Monache. Traffic Flow on a Ring With a Single Autonomous Vehicle: An Interconnected Stability PerspectiveIEEE Transactions on Intelligent Transportation Systems2021, 1-11
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• 19 articleGeorgeG. Gunter, DerekD. Gloudemans, Raphael E.R. Stern, Sean TS. McQuade, RahulR. Bhadani, MattM. Bunting, Maria LauraM. Delle Monache, RomanR. Lysecky, BenjaminB. Seibold, JonathanJ. Sprinkle, BenedettoB. Piccoli and Daniel B.D. Work. Are commercially implemented adaptive cruise control systems string stable?IEEE Transactions on Intelligent Transportation Systems2021, 1-12
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• 20 articleNicolasN. Martin, PaoloP. Frasca and CarlosC. Canudas de Wit. Subgraph detection for average detectability of LTI systemsIEEE Transactions on Network Science and Engineering2020, 1-12
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• 21 articleMuhammad Umar B.M. Niazi, CarlosC. Canudas de Wit and AlainA. Kibangou. Average State Estimation in Large-scale Clustered Network SystemsIEEE Transactions on Control of Network Systems74December 2020, 1736 - 1745
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• 22 articleMuhammad Umar B.M. Niazi and Arif BülentA. Özgüler. A Differential Game Model of Opinion Dynamics: Accord and Discord as Nash EquilibriaDynamic Games and Applications111March 2021, 137–160
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• 23 articleWilbert SamuelW. Rossi and PaoloP. Frasca. Opinion Dynamics with Topological Gossiping: Asynchronous Updates under Limited AttentionIEEE Control Systems Letters43July 2020, 566-571
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• 24 articleNiginaN. Toktassynova, HassenH. Fourati and BatyrbekB. Suleimenov. Application of grey system theory to phosphorite sinter process: From modeling to controlAsian Journal of Control31April 2020, 13-22
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• 25 articleNiginaN. Toktassynova, HassenH. Fourati and BatyrbekB. Suleimenov. Modelling and Control Structure of a Phosphorite Sinter Process with Grey System TheoryThe Journal of Grey System322October 2020, 150-166
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• 26 articleRenatoR. Vizuete, PaoloP. Frasca and FedericaF. Garin. Graphon-based sensitivity analysis of SIS epidemicsIEEE Control Systems Letters43July 2020, 542 - 547
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• 27 articleRenatoR. Vizuete, PaoloP. Frasca and ElenaE. Panteley. On the influence of noise in randomized consensus algorithmsIEEE Control Systems Letters532021, 1025-1030
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• 28 articleYanbingY. Wang, GeorgeG. Gunter, MattM. Nice, Maria LauraM. Delle Monache and Daniel BD. Work. Online parameter estimation methods for adaptive cruise control systemsIEEE Transactions on Intelligent Vehicles2021, 1-1
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• 29 articleMakiaM. Zmitri, HassenH. Fourati and ChristopheC. Prieur. Magnetic Field Gradient-Based EKF for Velocity Estimation in Indoor NavigationSensors2020October 2020, 5726
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International peer-reviewed conferences

• 30 inproceedingsThibaultT. Liard, RaphaelR. Stern and Maria LauraM. Delle Monache. Optimal driving strategies for traffic control with autonomous vehiclesIFAC 2020 - 21st IFAC World Congress 2020Berlin (virtual), Germanyhttps://www.ifac2020.org/July 2020, 1-8
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• 31 inproceedingsThembaniT. Moyo, AlainA. Kibangou and WalterW. Musakwa. Exploring the Potential of Traffic Index Data to Analyze Essential Traffic Impact in Developing CitiesISPRS 2020 - XXIV ISPRS Congress International Society for Photogrammetry and Remote SensingXLIII-B4-2020Nice (online), France2020, 137-141
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• 32 inproceedingsMuhammad Umar B.M. Niazi, CarlosC. Canudas de Wit and AlainA. Kibangou. State Variance Estimation in Large-Scale Network SystemsCDC 2020 - 59th IEEE Conference on Decision and ControlJeju Island (virtual), South Koreahttps://cdc2020.ieeecss.org/December 2020, 1-6
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• 33 inproceedingsMuhammad Umar B.M. Niazi, CarlosC. Canudas de Wit and AlainA. Kibangou. Thermal Monitoring of Buildings by Aggregated Temperature EstimationIFAC 2020 - 21st IFAC World Congress 2020Berlin (virtual), Germanyhttps://www.ifac2020.org/July 2020, 1-6
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• 34 inproceedingsDenisD. Nikitin, CarlosC. Canudas de Wit and PaoloP. Frasca. Shape-Based Nonlinear Model Reduction for 1D Conservation LawsIFAC 2020 - 21st IFAC World Congress 2020Berlin (virtual), Germanyhttps://www.ifac2020.org/July 2020, 1-6
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• 35 inproceedings UjjwalU. Pratap, CarlosC. Canudas de Wit and FedericaF. Garin. Average state estimation in presence of outliers CDC 2020 - 59th IEEE Conference on Decision and Control Jeju Island (virtual), South Korea https://cdc2020.ieeecss.org/ December 2020
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• 36 inproceedings MartinM. Rodriguez-Vega, CarlosC. Canudas de Wit and HassenH. Fourati. Average density detectability in traffic networks using virtual road divisions IFAC 2020 - 21st IFAC World Congress 2020 Berlin (virtual), Germany https://www.ifac2020.org/ July 2020
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• 37 inproceedingsLiudmilaL. Tumash, CarlosC. Canudas de Wit and Maria LauraM. Delle Monache. Equilibrium Manifolds in 2D Fluid Traffic ModelsIFAC 2020 - 21st IFAC World Congress 2020Berlin (virtual), Germanyhttps://www.ifac2020.org/July 2020, 1-6
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• 38 inproceedingsLiudmilaL. Tumash, CarlosC. Canudas de Wit and Maria LauraM. Delle Monache. Topology-based control design for congested areas in urban networksIEEE23rd International Conference on Intelligent Transportation Systems (ITSC)Rhodos (Virtual), Greecehttps://www.ieee-itsc2020.org/September 2020, 1-6
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Conferences without proceedings

• 39 inproceedingsBasselB. Othman, GiovanniG. De Nunzio, Domenico DiD. Domenico and CarlosC. Canudas de Wit. Variable speed limits control in an urban road network to reduce environmental impact of trafficACC 2020 - American Control Conference (ACC 2020)Denver (online), United Stateshttps://acc2020.a2c2.org/July 2020, 1-6
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• 40 inproceedingsMakiaM. Zmitri, HassenH. Fourati and ChristopheC. Prieur. Inertial Velocity Estimation for Indoor Navigation Through Magnetic Gradient-based EKF and LSTM Learning ModelIROS 2020 - IEEE/RSJ International Conference on Intelligent Robots and SystemsLas Vegas, United Stateshttps://www.iros2020.org/October 2020, 1-6
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Reports & preprints

• 41 misc Muhammad Umar B.M. Niazi, AlainA. Kibangou, CarlosC. Canudas de Wit, DenisD. Nikitin, LiudmilaL. Tumash and Pierre-AlexandreP.-A. Bliman. Modeling and Control of COVID-19 Epidemic through Testing Policies November 2020
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• 42 misc DenisD. Nikitin, CarlosC. Canudas de Wit and PaoloP. Frasca. A Continuation Method for Large-Scale Modeling and Control: from ODEs to PDE, a Round Trip February 2021
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• 43 misc LiudmilaL. Tumash, CarlosC. Canudas de Wit and Maria LauraM. Delle Monache. Boundary Control Design for Traffic with Nonlinear Dynamics October 2020
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