arXiv subjects

Maria Elena Valcher

Publications and source records attributed to Maria Elena Valcher.

At least 19 recordsLinked to original sources

arXiv2026

Distributed Observer Design for Discrete-Time LTI Systems via Jordan Canonical Form

This paper addresses the problem of distributed state estimation for discrete-time linear time-invariant systems. Building on the framework proposed in Gao & Yang (2025), we exploit the Jordan canonical form of the system matrix to develop two distributed estimation schemes that ensure asymptotic convergence of local estimates to the true system state. In both approaches, each node reconstructs the components of the state that are locally detectable for it via a Luenberger observer, while employing a consensus-based mechanism to estimate the components that are not directly detectable. The first scheme relies on local observers whose dimension matches that of the original state vector; however, its applicability requires the satisfaction of a large set of inequalities. The second scheme, in contrast, can be implemented under less restrictive conditions, but results in observers of increased (augmented) order. For both methods, we derive necessary and sufficient conditions - expressed in terms of the eigenvalues of the system matrix and certain submatrices of the communication network Laplacian - that guarantee the existence of a distributed observer achieving asymptotically accurate estimation. Compared to Gao & Yang (2025), the proposed approaches offer greater flexibility in the selection of coupling gains and impose less stringent solvability conditions.

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arXiv2026

Distributed State Estimation of Discrete-Time LTI Systems via Jordan Canonical Representation

In this paper, we address the problem of distributed state estimation for a discrete-time, linear time-invariant system. Building on the framework proposed in [2], we exploit the Jordan canonical form of the system matrix to develop a distributed estimation scheme that ensures the asymptotic convergence of the local state estimates to the true system state. The proposed approach relies on the idea that each node reconstructs the components of the system state that are detectable for it through a local Luenberger observer, while employing a consensus-based strategy to estimate the undetectable components. Necessary and sufficient conditions for the existence of a distributed observer that guarantees asymptotic estimation accuracy are derived. Compared with the previous work [2], the proposed design offers greater flexibility in the selection of the coupling gains and leads to a less restrictive set of conditions for solvability.

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arXiv2026

Reference Output Tracking in Boolean Control Networks

In this paper, the problem of tracking a given reference output trajectory is investigated for the class of Boolean control networks, by resorting to their algebraic representation. First, the case of a finite-length reference trajectory is addressed, and the analysis and algorithm first proposed in [17] are extended to be able to deal with arbitrary initial conditions and to identify all possible solutions. The approach developed for the finite-length case is then adjusted to cope with periodic reference output trajectories. The results of the paper are illustrated through an example.

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arXiv2025

Data-based control of Logical Networks

In recent years, data-driven approaches have become increasingly pervasive across all areas of control engineering. However, the applications of data-based techniques to Boolean control networks (BCNs) are still very limited. In this paper we aim to fill this gap, by exploring the possibility of evaluating some basic features, i.e., reachability and equilibria, and of solving two fundamental control problems, i.e., safe control and output regulation, for a BCN, leveraging only a limited amount of data generated by the network, without knowing or identifying its model.

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arXiv2025

Data-Driven Distributed Output Synchronization of Heterogeneous Discrete-Time Multi-Agent Systems

In this paper, we assume that an autonomous exosystem generates a reference output, and we consider the problem of designing a distributed data-driven control law for a family of discrete-time heterogeneous LTI agents, connected through a directed graph, in order to synchronize the agents' outputs to the reference one. The agents of the network are split into two categories: leaders, with direct access to the exosystem output, and followers, that only receive information from their neighbors. All agents aim to achieve output synchronization by means of a state feedback that makes use of their own states as well as of an estimate of the exogenous system state, provided by an internal state observer. Such observer has a different structure for leaders and followers. Necessary and sufficient conditions for the existence of a solution are first derived in the model-based set-up and then in a data-driven context. An example illustrates both the implementation procedure and the performance of the proposed approach.

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arXiv2024

Behaviors, trajectories and data: A novel perspective on the design of unknown-input observers

The purpose of this paper is to propose a novel perspective, based on Willems' "behavior theory", on the design of an unknown-input observer for a given linear time-invariant discrete-time state-space model, with unknown disturbances affecting both the state and the output equations. The problem is first addressed assuming that the original system model is known, and later assuming that the model is unknown but historical data satisfying a certain assumption are available. In both cases, fundamental concepts in behavior theory, as the projection of a behavior, the inclusion of a behavior in another one, and the use of kernel and image representations, provide quite powerful tools to determine necessary and sufficient conditions for the existence of an unknown-input observer (UIO), as well as algorithms to design one of them, if it exists.

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arXiv2024

A data-driven approach to UIO-based fault diagnosis

In this paper we propose a data-driven approach to the design of a residual generator, based on a dead-beat unknown-input observer, for linear time-invariant discrete-time state-space models, whose state equation is affected both by disturbances and by actuator faults. We first review the modelbased conditions for the existence of such a residual generator, and then prove that under suitable assumptions on the collected historical data, we are both able to determine if the problem is solvable and to identify the matrices of a possible residual generator. We propose an algorithm that, based only on the collected data (and not on the system description), is able to perform both tasks. An illustrating example and some remarks on limitations and possible extensions of the current results conclude the paper.

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arXiv2024

Data-Driven Reduced-Order Unknown-Input Observers

In this paper we propose a data-driven approach to the design of reduced-order unknown-input observers (rUIOs). We first recall the model-based solution, by assuming a problem set-up slightly different from those traditionally adopted in the literature, in order to be able to easily adapt it to the data-driven scenario. Necessary and sufficient conditions for the existence of a reduced-order unknown-input observer, whose matrices can be derived from a sufficiently rich set of collected historical data, are first derived and then proved to be equivalent to the ones obtained in the model-based framework. Finally, a numerical example is presented, to validate the effectiveness of the proposed scheme.

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arXiv2024

Distributed Data-driven Unknown-input Observers for State Estimation

Unknown inputs related to, e.g., sensor aging, modeling errors, or device bias, represent a major concern in wireless sensor networks, as they degrade the state estimation performance. To improve the performance, unknown-input observers (UIOs) have been proposed. Most of the results available to design UIOs are based on explicit system models, which can be difficult or impossible to obtain in real-world applications. Data-driven techniques, on the other hand, have become a viable alternative for the design and analysis of unknown systems using only data. In this context, a novel data-driven distributed unknown-input observer (D-DUIO) for unknown continuous-time linear time-invariant (LTI) systems is developed, which requires solely some data collected offline, without any prior knowledge of the system matrices. In the paper, first, a model-based approach to the design of a DUIO is presented. A sufficient condition for the existence of such a DUIO is recalled, and a new one is proposed, that is prone to a data-driven adaption. Moving to a data-driven approach, it is shown that under suitable assumptions on the input/output/state data collected from the continuous-time system, it is possible to both claim the existence of a D-DUIO and to derive its matrices in terms of the matrices of pre-collected data. Finally, the efficacy of the D-DUIO is illustrated by means of numerical examples.

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arXiv2023

On the equivalence of model-based and data-driven approaches to the design of unknown-input observers

In this paper we investigate a data-driven approach to the design of an unknown-input observer (UIO). Specifically, we provide necessary and sufficient conditions for the existence of an unknown-input observer for a discrete-time linear time-invariant (LTI) system, designed based only on some available data, obtained on a finite time window. We also prove that, under weak assumptions on the collected data, the solvability conditions derived by means of the data-driven approach are in fact equivalent to those obtained through the model-based one. In other words, the data-driven conditions do not impose further constraints with respect to the classic model-based ones, expressed in terms of the original system matrices.

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arXiv2023

On an extension of the Friedkin-Johnsen model: The effects of a homophily-based influence matrix

In this paper we propose an extended version of the Friedkin-Johnsen (FJ) model that accounts for the effects of homophily mechanisms on the agents' mutual appraisals. The proposed model consists of two difference equations. The first one describes the opinions' evolution, namely how agents modify their opinions taking into account both their personal beliefs and the influences of other agents, as in the standard FJ model. Meanwhile, the second equation models how the influence matrix involved in the opinion formation process updates according to a homophily mechanism, by allowing both positive and negative appraisals. We show that the proposed time-varying version of the classical FJ model always asymptotically converges to a constant solution. Moreover, in the case of a single discussion topic, the asymptotic behavior of the system is derived in closed form.

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arXiv2022

Dual Seminorms, Ergodic Coefficients and Semicontraction Theory

Dynamical systems that are contracting on a subspace are said to be semicontracting. Semicontraction theory is a useful tool in the study of consensus algorithms and dynamical flow systems such as Markov chains. To develop a comprehensive theory of semicontracting systems, we investigate seminorms on vector spaces and define two canonical notions: projection and distance semi-norms. We show that the well-known lp ergodic coefficients are induced matrix seminorms and play a central role in stability problems. In particular, we formulate a duality theorem that explains why the Markov-Dobrushin coefficient is the rate of contraction for both averaging and conservation flows in discrete time. Moreover, we obtain parallel results for induced matrix log seminorms. Finally, we propose comprehensive theorems for strong semicontractivity of linear and non-linear time-varying dynamical systems with invariance and conservation properties both in discrete and continuous time.

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arXiv2022

Multi-dimensional extensions of the Hegselmann-Krause model

In this paper, we consider two multi-dimensional Hagselmann-Krause (HK) models for opinion dynamics. The two models describe how individuals adjust their opinions on multiple topics, based on the influence of their peers. The models differ in the criterion according to which individuals decide whom they want to be influenced from. In the average-based model, individuals compare their average opinions on the various topics with those of the other individuals and interact only with those individuals whose average opinions lie within a confidence interval. For this model, we provide an alternative proof for the contractivity of the range of opinions and show that the agents' opinions reach consensus/clustering if and only if their average opinions do so. In the uniform affinity model agents compare their opinions on every single topic and influence each other only if, topic-wise, such opinions do not differ more than a given tolerance. We identify conditions under which the uniform affinity model enjoys the order-preservation property topic-wise and we prove that the global range of opinions (and hence the range of opinions on every single topic) are nonincreasing.

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arXiv2022

Modeling the Cooperative Process of Learning a Task

In this paper, we propose a mathematical model for a Transactive Memory System (TMS) involved in the cooperative process of learning a task. The model is based on an intertwined dynamics involving both the individuals level of expertise and the interaction network among the cooperators. The model shows that if all the agents are non-stubborn, then all of them are able to acquire the competence of the most expert members of the group, asymptotically reaching their level of proficiency. Conversely, when dealing with all stubborn agents, the capability to pass on the task depends on the connectedness properties of the interaction graph.

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arXiv2022

On the Herdability of Linear Time-Invariant Systems with Special Topological Structures

In this paper, we investigate the herdability property, namely the capability of a system to be driven towards the (interior of the) positive orthant, for linear time-invariant state-space models. Herdability of certain matrix pairs (A,B), where A is the adjacency matrix of a multi-agent network, and B is a selection matrix that singles out a subset of the agents (the "network leaders"), is explored. The cases when the graph associated with A, G(A), is directed and clustering balanced (in particular, structurally balanced), or it has a tree topology and there is a single leader, are investigated.

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arXiv2022

A Bandwagon Bias Based Model for Opinion Dynamics: Intertwining between Homophily and Influence Mechanisms

Recently a model for the interplay between homophily-based appraisal dynamics and influence-based opinion dynamics has been proposed. The model explores for the first time how the opinions of a group of agents on a certain number of issues/topics is influenced by the agents' mutual appraisal and, conversely, the agents' mutual appraisal is updated based on the agents' opinions on the various issues, according to a homophily model. In this paper we show that a simplified (and, in some situations, more feasible) version of the model, that accounts only for the signs of the agents' appraisals rather than for their numerical values, provides an equally accurate and effective model of the opinion dynamics in small networks. The equilibria reached by this model correspond, almost surely, to situations in which the agents' network is complete and structurally balanced. On the other hand, we ensure that such equlibria can always be reached in a finite number of steps, and, differently from the original model, we rule out other types of equilibria that correspond to disconnected social networks.

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arXiv2021

Algebraic and Graph-Theoretic Conditions for the Herdability of Linear Time-Invariant Systems

In this paper we investigate a relaxed concept of controllability, known in the literature as herdability, namely the capability of a system to be driven towards the(interior of the) positive orthant. Specifically, we investigate herdability for linear time-invariant systems, both from an algebraic perspective and based on the graph representing the systems interactions. In addition, we focus on linear state-space models corresponding to matrix pairs (A;B) in which the matrix B is a selection matrix that determines the leaders in the network, and we show that the weights that followers give to the leaders do not affect the herdability of the system. We then focus on the herdability problem for systems with a single leader in which interactions are symmetric and the network topology is acyclic, in which case an algorithm for the leader selection is provided. In this context, under some additional conditions on the mutual distances, necessary and sufficient conditions for the herdability of the overall system are given.

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arXiv2021

Tripartite and Sign Consensus for Clustering Balanced Social Networks

In this paper, we address two forms of consensus for multi-agent systems with undirected, signed, weighted, and connected communication graphs, under the assumption that the agents can be partitioned into three clusters, representing the decision classes on a given specific topic, for instance, the in favour, abstained and opponent agents. We will show that under some assumptions on the cooperative/antagonistic relationships among the agents, simple modifications of DeGroot's algorithm allow to achieve tripartite consensus(if the opinions of agents belonging to the same class all converge to the same decision) or sign consensus (if the opinions of the agents in the three clusters converge to positive, zero and negative values, respectively).

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