Sandro Zampieri

University of Padua | UNIPD · Department of Information Engineering

In this paper, we propose control-theoretic methods as tools for the design of online optimization algorithms that are able to address dynamic, noisy, and partially uncertain time-varying quadratic objective functions. Our approach introduces two algorithms specifically tailored for scenarios where the cost function follows a stochastic linear mode...

Firing rate models are dynamical systems widely used in applied and theoretical neuroscience to describe local cortical dynamics in neuronal populations. By providing a macroscopic perspective of neuronal activity, these models are essential for investigating oscillatory phenomena, chaotic behavior, and associative memory processes. Despite their w...

The Hopfield model provides a mathematically idealized yet insightful framework for understanding the mechanisms of memory storage and retrieval in the human brain. This model has inspired four decades of extensive research on learning and retrieval dynamics, capacity estimates, and sequential transitions among memories. Notably, the role and impac...

We study stochastic pairwise interaction network systems whereby a finite population of agents, identified with the nodes of a graph, update their states in response to both individual mutations and pairwise interactions with their neighbors. The considered class of systems include the main epidemic models -such as the SIS, SIR, and SIRS models-, c...

This study challenges the traditional focus on zero-lag statistics in resting-state functional magnetic resonance imaging (rsfMRI) research. Instead, it advocates for considering time-lag interactions to unveil the directionality and asymmetries of the brain hierarchy. Effective connectivity (EC), the state matrix in dynamical causal modeling (DCM)...

The study of functional brain connectivity in resting-state functional magnetic resonance imaging (rsfMRI) data has traditionally focused on zero-lag statistics. However, recent research has emphasized the need to account for dynamic aspects due to the complex patterns of time-varying co-activations among brain regions. In this regard, the importan...

An open question in neuroscience regards the origin of the flexible and heterogeneous spatio-temporal patterns of neural correlations assessed with fMRI. Model-based approaches are commonly used to shed light on this problem with the aim to reproduce the same dynamical richness observed in the empirical recordings. In particular, dynamic causal mod...

In this paper we propose a model-based approach to the design of online optimization algorithms, with the goal of improving the tracking of the solution trajectory (trajectories) w.r.t. state-of-the-art methods. We focus first on quadratic problems with a time-varying linear term, and use digital control tools (a robust internal model principle) to...

We characterize the control energy behavior of large-scale linear network systems controlled by a single input. Specifically, we establish conditions under which two widely used control energy metrics, namely the inverse of the minimum eigenvalue and the normalized determinant of the controllability Gramian, grow exponentially fast in the system di...

In this paper we propose a model-based approach to the design of online optimization algorithms, with the goal of improving the tracking of the solution trajectory (trajectories) w.r.t. state-of-the-art methods. We focus first on quadratic problems with a time-varying linear term, and use digital control tools to propose a novel online algorithm th...

Understanding the fundamental principles and limitations of controlling complex networks is of paramount importance across natural, social, and engineering sciences. The classic notion of controllability does not capture the effort needed to control dynamical networks, and quantitative measures of controllability have been proposed to remedy this p...

In this paper, we propose a feedback control approach for solving optimal power flow (OPF) problems in power distribution networks (DNs) based on a projected gradient scheme, where the cost is given by the sum of functions of local power injections. This approach does not require detailed knowledge of the grid model and enables real-time tracking o...

The controllability of large-scale network systems has been extensively investigated in the past few years. In spite of the recent advances in this field, there are still a number of unsolved problems which are of critical importance to fully understand the practical limitations arising in the control of large-scale networks. These include the deri...

In this paper, we propose a new measure of communication performance of linear network systems, the information gain, and we show that this measure is strongly affected by the degree of non-normality of the networks adjacency matrix. Specifically, we prove that the numerical abscissa of the networks adjacency matrix, a well-known indicator of matri...

In this paper we consider the problem of determining the control energy for large scale networks. Instead of controlling all the nodes of the network, we are interested in driving the value of some outputs to the desired value, by controlling directly some of the nodes. For doing this, we exploit the concept of output controllability and of output...

In both natural and engineered systems, communication often occurs dynamically over networks ranging from highly structured grids to largely disordered graphs. To use, or comprehend the use of, networks as efficient communication media requires understanding of how they propagate and transform information in the face of noise. Here, we develop a fr...

While numerous studies have suggested that large natural, biological, social, and technological networks are fragile, convincing theories are still lacking to explain why natural evolution and human design have failed to optimize networks and avoid fragility. In this paper we provide analytical and numerical evidence that a tradeoff exists in netwo...

In our recent article [1] published in this journal we provide quantitative evidence to show that there are warnings and caveats in the way Gu and collaborators [2] define controllability of brain networks and measure the contribution of each of its nodes. The comment by Pasqualetti et al. [3] confirms the need to go beyond the methodology and appr...

In our recent article (Tu et al., Warnings and caveats in brain controllability, arXiv:1705.08261) we provided quantitative evidence to show that there are warnings and caveats in the way Gu and collaborators (Gu et al. Controllability of structural brain networks. Nature communications 6 (2015): 8414) define brain controllability. The comment by P...

We consider the problem of regulating the voltage profile of a power distribution grid by controlling the reactive power injection of distributed microgenerators. We define a very general class of purely local feedback controllers in which reactive power injection is adjusted based on the local voltage measurements. This class includes most of the...

In both natural and engineered systems, communication often occurs dynamically over networks ranging from highly structured grids to largely disordered graphs. To use, or comprehend the use of, networks as efficient communication media requires understanding of how they propagate and transform information in the face of noise. Here, we develop an i...

Reliable information processing is a hallmark of many physical and biological networked systems. In this paper, we propose a novel framework for modelling information transmission within a linear dynamical network. Information propagation is modelled by means of a digital communication protocol that takes into account the realistic phenomenon of in...

2018 AACC. Mathematical theories and empirical evidence suggest that several complex natural and man-made systems are fragile: as their size increases, arbitrarily small and localized alterations of the system parameters may trigger system-wide failures. Examples are abundant, from perturbation of the population densities leading to extinction of s...

In this work we challenge the main conclusions of Gu et al work (Controllability of structural brain networks. Nature communications 6, 8414, doi:10.1038/ncomms9414, 2015) on brain controllability. Using the same methods and analyses on four datasets we find that the minimum set of nodes to control brain networks is always larger than one. We also...

In this work we review a class of deterministic nonlinear models for the propagation of infectious diseases over contact networks with strongly-connected topologies. We consider network models for susceptible-infected (SI), susceptible-infected-susceptible (SIS), and susceptible-infected-recovered (SIR) settings. In each setting, we provide a compr...

In this work we review a class of deterministic nonlinear models for the propagation of infectious diseases over contact networks with strongly-connected topologies. We consider network models for susceptible-infected (SI), susceptible-infected-susceptible (SIS), and susceptible-infected-recovered (SIR) settings. In each setting, we provide a compr...

A broad family of randomized clock synchronization protocols based on a second order consensus algorithm is proposed. Under mild conditions on the graph connectivity, it is proved that the parameters of the algorithm can always be tuned in such a way that the clock synchronization is achieved in the probabilistic mean - square sense. This family of...

In recent years complex networks have gained increasing attention in different fields of science and engineering. The problem of controlling these networks is an interesting and challenging problem to investigate. In this paper we look at the controllability problem focusing on the energy needed for the control. Precisely not only we want to analyz...

In recent years complex networks have gained increasing attention in different fields of science and engineering. The problem of controlling these networks is an interesting and challenging problem to investigate. In this paper we look at the controllability problem focusing on the energy needed for the control. Precisely not only we want to analyz...

In this work we present a new algorithm to solve the average-consensus problem. The main goal of this algorithm is to obtain exact convergence despite the existence of quantized communication channels between the agents. Starting from the Zoom-in Zoom-out strategy already presented in [5], we introduce the equations describing the behaviour of the...

This paper studies the controllability degree of complex networks as a function of the network weights and the location and number of control nodes. We quantify the controllability degree of a network with the worst-case control energy to drive the network to an arbitrary configuration. We show that isotropic networks are difficult to control, as t...

We consider the problem of minimizing the power generation cost by exploiting the distributed renewable energy sources (DRES) located in the power distribution network. The proposed strategy requires that the intelligent agents, located at the microgenerator buses, measure their voltage and then adjust the amount of injected power, according to a f...

This paper studies the problem of controlling complex networks, i.e., the joint problem of selecting a set of control nodes and of designing a control input to steer a network to a target state. For this problem, 1) we propose a metric to quantify the difficulty of the control problem as a function of the required control energy, 2) we derive bound...

This paper focuses on reactive power flow and voltage stability in electrical grids. We provide novel analytical understanding of the solutions to the classic nonlinear polynomial equations describing the decoupled reactive power flow. As of today, solutions to these equations can be found only via numerical methods. Yet an analytical understanding...

We consider the problem of deriving an explicit approximate solution of the nonlinear power equations that describe a power distribution network. We give sufficient conditions for the existence of a practical solution to the power flow equations, and we propose an approximation that is linear in the active and reactive power demands and generations...

We consider the problem of exploiting the microgenerators connected to the power distribution network to provide distributed reactive power compensation for power losses minimization and voltage support. The proposed strategy relies on the fact that all the intelligent agents, located at the microgenerator buses, can measure their voltage, communic...

We consider the problem of optimal reactive power compensation for the minimization of power distribution losses in a smart microgrid. We first propose an approximate model for the power distribution network, which allows us to cast the problem into the class of convex quadratic, linearly constrained, optimization problems. We then consider the spe...

This paper studies the problem of controlling complex networks, that is, the joint problem of selecting a set of control nodes and of designing a control input to steer the network to a target state. For this problem (i) we propose a metric to quantify the difficulty of the control problem as a function of the required control energy, (ii) we deriv...

We consider the problem of exploiting the microgenerators dispersed in the power distribution network in order to provide distributed reactive power compensation for power losses minimization and voltage regulation. In the proposed strategy, microgenerators are smart agents that can measure their phasorial voltage, share these data with the other a...

We consider the problem of exploiting the microgenerators dispersed in the power distribution network in order to provide distributed reactive power compensation for power losses minimization and voltage support. The proposed strategy requires that all the intelligent agents, located at the microgenerator buses, measure their voltage and share thes...

We consider the problem of exploiting the microgenerators dispersed in the power distribution network in order to provide distributed reactive power compensation for power losses minimization. The proposed strategy requires that all the intelligent agents, located at the microgenerator buses, measure their voltage and share these data with the othe...

We consider the problem of exploiting the microgenerators connected to the low voltage or medium voltage grid in order to provide distributed reactive power compensation in the power distribution network, solving the optimal reactive power flow problem for the minimization of power distribution losses subject to voltage constraints. The proposed st...

In this paper a randomized linear protocol for time synchronization of clocks in a multi-agent scenario is considered. Clocks are allowed to have different offsets and different rates, and they communicate through an asymmetric broadcast protocol. The contribution of this paper is twofold. It is first shown that, under very mild conditions on the c...

We consider the problem of dynamic reactive power compensation in power distribution networks populated by a large number of microgeneration devices. We model the power losses minimization problem in the case of stochastic, time-varying reactive power demands. For this control problem, we propose a randomized iterative optimization algorithm, and w...

This paper deals with the problem of the angular calibration for a network of cameras, namely the problem of estimating a common orientation reference frame. In the proposed set–up each camera obtains noisy measurements of its relative orientation with respect to some other cameras. The set of measurements can be described by a graph having the cam...

The average consensus algorithm is a distributed procedure which allows a network of agents to agree on the average of a set of initial values. The computation occurs through local exchange of information only, namely the information exchange takes place only between agents which are neighbors with respect to a graph representing the system communi...

Recently, multi-agent systems have become a central study topic in many different disciplines including biology, engineering, physics, and social science. This has led to the emergence of large and constantly growing interdisciplinary research field, known as network science. The analysis of the mathematical models describing such systems has achie...

Average-consensus algorithms allow one to compute the average of some agents' data in a distributed way, and they are used as a basic building block in many algorithms for distributed estimation, load balancing, formation, and distributed control. Traditional analysis of such algorithms studies, for a given communication graph, the convergence rate...

The performance of the linear consensus algorithm is studied by using a Linear Quadratic (LQ) cost. The objective is to understand how the communication topology inuences this algorithm. This is achieved by exploiting an analogy between Markov Chains and electrical resistive networks. Indeed, this permits to uncover the relation between the LQ perf...

We consider the problem of optimal reactive power compensation for the minimization of power distribution losses in a smart microgrid. We first propose an approximate model for the power distribution network, which allows us to cast the problem into the class of convex quadratic, linearly constrained, optimization problems. We also show how this mo...

In this paper a distributed clock synchronization algorithm is proposed. The algorithm requires asymmetric gossip communications between the nodes of the network, and is based on an PI-like consensus protocol where the proportional part compensates the different clock speeds while the integral part eliminates the different clock offsets. Convergenc...

In the analysis of a recently proposed distributed estimation algorithm based on the Kalman filtering and on gossip iterations, we needed to apply a new inequality which is valid for i.i.d. matrix valued random processes. This inequality can be useful in the analysis of the convergence rate of general jump Markov linear systems.In this paper, we pr...

We considered the problem of minimizing reactive power flows in a smart microgrid. First we modeled this problem as a linearly constrained quadratic optimization, in which the decision variables are the amount of reactive power that compensators inject into the network. Then, we designed a distributed algorithm in which agents are clustered into ov...

In this paper, we consider the problem of simultane- ously classifying sensor types and estimating hidden parameters in a network of sensors subject to gossip-like communication. More precisely, we consider a network of noisy sensors which measure a common scalar unknown parameter. We assume that a fraction of the nodes is subject to the same (but...

Ranking a set of numbers plays a key role in many application areas such as signal processing, statistics, computer science and so on. Distributed algorithms for ranking have been proposed in the computer science literature first for tree networks. Extension to general networks has been performed by constructing a spanning tree, which can be done i...

This is a Deliverable Report for the FeedNetBack project (www.feednetback.eu). It describes the research performed within Work Package 3, Task 3.1 (Control Subject to Transmission Constraints, no Transmission Errors), in the first 35 months of the project. It targets the issue of control subject to transmission constraints with no transmission erro...

This is a Deliverable Report for the FeedNetBack project (www.feednetback.eu). This report, divided into 4 chapters, we report the final advances on WP2 and in particular on the task 3.2, "Communication network design". Chapter one introduces the developed arguments and presents parts of the literature review. Chapter two is devoted to network topo...

In this technical note, we present a novel synchronization protocol to synchronize a network of controlled discrete-time double integrators which are nonidentical, with unknown model parameters and subject to additive measurement and process noise. This framework is motivated by the typical problem of synchronizing a network of clocks whose speeds...

We study the well known linear consensus algorithm by means of a LQ-type performance cost. We want to understand how the communication topology influences this algorithm. In order to do this, we recall the analogy between Markov Chains and electrical resistive networks. By exploiting this analogy, we are able to rewrite the performance cost as the...

In this paper a distributed algorithm for clock synchronization is proposed. This algorithm is based on an extension of the consensus algorithm able to synchronize a family of double integrators. Since the various clocks may have different drifts, the algorithm needs to be designed so that it can work also in case of heterogeneous double integrator...

A rendezvous problem for a team of autonomous vehicles that is com-municating through quantized channels is considered. Communication topologies and feedback control law are presented that solves the rendezvous problem in the sense that a meeting point for the vehicles is practically stabilized. In particular, it is shown that uniform quantizers ca...

In this work we consider the problem of simultaneously classifying sensor types and estimating hidden parameters in a network of sensors subject to gossip-like communication limitations. In particular, we consider a network of scalar noisy sensors which measure a common unknown parameter. We assume that a fraction of the nodes is subject to the sam...

We consider a distributed system of N agents, on which we define a quadratic optimization problem subject to a linear equality constraint. We assume that the nodes can estimate the gradient of the cost function by measuring the steady state response of the system. Even if the cost function cannot be decoupled into individual terms for the agents, a...

We study the well–known linear consensus algorithm by means of a LQ-type performance cost. We want to understand how the communication topology influences this algorithm. In order to do this, we recall the analogy between Markov Chains and electrical resistive networks. By exploiting this analogy, we are able to rewrite the performance cost as the...

This paper considers the average consensus problem on a network of digital links, and proposes a set of algorithms based on pairwise ''gossip'' communications and updates. We study the convergence properties of such algorithms with the goal of answering two design questions, arising from the literature: whether the agents should encode their commun...

Trust management, broadly intended as the ability to maintain belief relationship among entities, is recognized as a fundamental security challenge for autonomous and self-organizing networks. In this work, we focus on the evaluation process of trust evidence in distributed networks, where no pre-established infrastructure can be assumed. After cas...

In this paper we consider the problem of estimating a random process from noisy measurements, collected by a sensor network. We analyze a distributed two-stage algorithm. The first stage is a Kalman-like estimate update, in which each agent makes use only of its own measurements. During the second phase agents communicate with their neighbors to im...

This work presents a contribution to the solution of the average agreement problem on a network with quantized links. Starting from the well-known linear diffusion algorithm, we propose a simple and effective adaptation which is able to preserve the average of states and to drive the system near to the consensus value, when a uniform quantization i...

Abstract—When,consensus,algorithms,are used in very large networks, spreading information across the whole graph requires a long time. Hence, traditional convergence analysis, studying the essential spectral radius of the transition matrix, predicts very poor performance. However, in estimation problems, it is clear that a growing,number,of measure...

Average-consensus algorithms allow to compute the average of some agents' data in a distributed way, and they are used as a basic building block in algorithms for distributed estimation, load balancing, formation and distributed control. Traditional analysis of linear average-consensus algorithms studies, for a given communication graph, the conver...

This paper presents an algorithm which solves exponentially fast the average consensus problem on strongly connected network of digital links. The algorithm is based on an efficient zooming-in/zooming-out quantization scheme.