arXiv subjects

Renato Vizuete

Publications and source records attributed to Renato Vizuete.

15 recordsLinked to original sources

arXiv2026

Identification of Nonlinear Acyclic Networks in Continuous Time from Nonzero Initial Conditions and Full Excitations

This paper addresses the identifiability and identification of nonlinear acyclic networks in continuous time when the dynamics are located on the edges and all the nodes are excited. First, we establish necessary and sufficient conditions for network identifiability. We show that it is necessary and sufficient to measure all the sinks to identify any tree in continuous time when the functions associated with the dynamics are analytic and satisfy $f(0)=0$, which is analogous to the discrete-time case. We then extend the result to general directed acyclic graphs (DAGs), showing that it is necessary and sufficient to measure all sinks when the dynamics are not linear (a condition that can be relaxed for trees). Next, based on these identifiability results and under the assumption of known dictionary functions, we introduce a method for the identification of trees that exploits higher order derivatives and nonzero initial conditions. Finally, we propose a method to identify multiple parallel paths of the same length between two nodes, which allows us to identify any DAG when combined with the algorithm for the identification of trees. Several examples are added to illustrate the results.

math.OC↗

arXiv2026

Path-Based Conditions for the Identifiability of Non-additive Nonlinear Networks with Full Measurements

We analyze the identifiability of nonlinear networks with non necessarily additive node dynamics, where the influence of in-neighbors is represented by a multivariate nonlinear function that cannot necessarily be separated into individual edge functions. We consider the full measurement case (all the nodes are measured) and we introduce the notion of generic identifiability. Based on a generic nonlinear matrix associated with an unfolded digraph constructed from the network, we characterize the space of functions that satisfies the generic property. For directed acyclic graphs (DAGs) composed of analytic functions, we derive a sufficient condition for identifiability based on vertex-disjoint paths from excited nodes to the in-neighbors of each node in the network. Furthermore, for the class of polynomial functions, by using well-known results on algebraic varieties, we prove that the identifiability is impossible if the vertex-disjoint path condition is not satisfied. Finally, we show that this identifiability condition is not necessary for the additive nonlinear model, where the node function can be decomposed into a sum of edge-wise nonlinearities.

math.OC↗

arXiv2026

Nonlinear Network Identifiability with Full Excitations

We derive conditions for the identifiability of nonlinear networks characterized by additive dynamics at the level of the edges when all the nodes are excited. In contrast to linear systems, we show that the measurement of all sinks is necessary and sufficient for the identifiability of directed acyclic graphs, under the assumption that dynamics are described by twice continuously differentiable functions without constant terms (i.e., $f(0)=0$). But if constant terms are present, then the identifiability is impossible as soon as one node has more than one in-neighbor. In the case of general digraphs that may contain cycles, we consider additively separable functions for the analysis of the identifiability, and we show that the measurement of one node of all the sinks of the condensation digraph is necessary and sufficient. Several examples are added to illustrate the results.

math.OC↗

arXiv2025

Consensus on Open Multi-Agent Systems Over Graphs Sampled from Graphons

We show how graphons can be used to model and analyze open multi-agent systems, which are multi-agent systems subject to arrivals and departures, in the specific case of linear consensus. First, we analyze the case of replacements, where under the assumption of a deterministic interval between two replacements, we derive an upper bound for the disagreement in expectation. Then, we study the case of arrivals and departures, where we define a process for the evolution of the number of agents that guarantees a minimum and a maximum number of agents. Next, we derive an upper bound for the disagreement in expectation, and we establish a link with the spectrum of the expected graph used to generate the graph topologies. Finally, for stochastic block model (SBM) graphons, we prove that the computation of the spectrum of the expected graph can be performed based on a matrix whose dimension depends only on the graphon and it is independent of the number of agents.

eess.SY↗

arXiv2024

Nonlinear identifiability of directed acyclic graphs with partial excitation and measurement

We analyze the identifiability of directed acyclic graphs in the case of partial excitation and measurement. We consider an additive model where the nonlinear functions located in the edges depend only on a past input, and we analyze the identifiability problem in the class of pure nonlinear functions satisfying $f(0)=0$. We show that any identification pattern (set of measured nodes and set of excited nodes) requires the excitation of sources, measurement of sinks and the excitation or measurement of the other nodes. Then, we show that a directed acyclic graph (DAG) is identifiable with a given identification pattern if and only if it is identifiable with the measurement of all the nodes. Next, we analyze the case of trees where we prove that any identification pattern guarantees the identifiability of the network. Finally, by introducing the notion of a generic nonlinear network matrix, we provide sufficient conditions for the identifiability of DAGs based on the notion of vertex-disjoint paths.

math.OC↗

arXiv2024

Corrections to and improvements on results from "The Laplacian spectrum of large graphs sampled from graphons"

In this note we correct the proof of Proposition 4 in our paper "The Laplacian Spectrum of Large Graphs Sampled from Graphons" (arXiv:2004.09177) and we improve several results therein. To this end, we prove a new concentration lemma about degrees and Laplacian eigenvalues. This lemma allows us to improve several bounds and to dispense from assuming that the graphon is bounded away from zero in several results. This extension leads, in particular, to correct the proof of Proposition 4. Additionally, we extend Proposition 4 to graphs that are sampled from graphons by using deterministic latent variables.

math.OC↗

arXiv2024

SIS epidemics on open networks: A replacement-based approximation

In this paper we analyze continuous-time SIS epidemics subject to arrivals and departures of agents, by using an approximated process based on replacements. In defining the SIS dynamics in an open network, we consider a stochastic setting in which arrivals and departures take place according to Poisson processes with similar rates, and the new value of the infection probability of an arriving agent is drawn from a continuous distribution. Since the system size changes with time, we define an approximated process, in which replacements take place instead of arrivals and departures, and we focus on the evolution of an aggregate measure of the level of infection. So long as the reproduction number is less than one, the long-term behavior of this function measures the impact of the changes of the set of agents in the epidemic. We derive upper bounds for the expectation and variance of this function and we include a numerical example to show that the approximated process is close to the original SIS process.

eess.SY↗

arXiv2023

Random Coordinate Descent for Resource Allocation in Open Multi-Agent Systems

We propose a method for analyzing the distributed random coordinate descent algorithm for solving separable resource allocation problems in the context of an open multiagent system, where agents can be replaced during the process. In particular, we characterize the evolution of the distance to the minimizer in expectation by following a time-varying optimization approach which builds on two components. First, we establish the linear convergence of the algorithm in closed systems, in terms of the estimate towards the minimizer, for general graphs and appropriate step-size. Second, we estimate the change of the optimal solution after a replacement, in order to evaluate its effect on the distance between the current estimate and the minimizer. From these two elements, we derive stability conditions in open systems and establish the linear convergence of the algorithm towards a steady-state expected error. Our results enable to characterize the trade-off between speed of convergence and robustness to agent replacements, under the assumptions that local functions are smooth, strongly convex, and have their minimizers located in a given ball. The approach proposed in this paper can moreover be extended to other algorithms guaranteeing linear convergence in closed system.

cs.MA↗

arXiv2023

Nonlinear network identifiability: The static case

We analyze the problem of network identifiability with nonlinear functions associated with the edges. We consider a static model for the output of each node and by assuming a perfect identification of the function associated with the measurement of a node, we provide conditions for the identifiability of the edges in a specific class of functions. First, we analyze the identifiability conditions in the class of all nonlinear functions and show that even for a path graph, it is necessary to measure all the nodes except by the source. Then, we consider analytic functions satisfying $f(0)=0$ and we provide conditions for the identifiability of paths and trees. Finally, by restricting the problem to a smaller class of functions where none of the functions is linear, we derive conditions for the identifiability of directed acyclic graphs. Some examples are presented to illustrate the results.

math.OC↗

arXiv2023

On Lyapunov functions for open Hegselmann-Krause dynamics

In this paper, we provide a formulation of an open Hegselmann-Krause (HK) dynamics where agents can join and leave the system during the interactions. We consider a stochastic framework where the time instants corresponding to arrivals and departures are determined by homogeneous Poisson processes. Then, we provide a survey of Lyapunov functions based on global and local disagreement, whose asymptotic behavior can be used to measure the impact of arrivals and departures. After proving analytical results on these Lyapunov functions in the open system, we illustrate them through numerical simulations in two scenarios characterized by a different number of expected agents.

eess.SY↗

arXiv2022

Resource allocation in open multi-agent systems: an online optimization analysis

The resource allocation problem consists of the optimal distribution of a budget between agents in a group. We consider such a problem in the context of open systems, where agents can be replaced at some time instances. These replacements lead to variations in both the budget and the total cost function that hinder the overall network's performance. For a simple setting, we analyze the performance of the Random Coordinate Descent algorithm (RCD) using tools similar to those commonly used in online optimization. In particular, we study the accumulated errors that compare solutions issued from the RCD algorithm and the optimal solution or the non-collaborating selfish strategy and we derive some bounds in expectation for these accumulated errors.

cs.MA↗

arXiv2021

Random coordinate descent algorithm for open multi-agent systems with complete topology and homogeneous agents

We study the convergence in expectation of the Random Coordinate Descent algorithm (RCD) for solving optimal resource allocations problems in open multi-agent systems, i.e., multi-agent systems that are subject to arrivals and departures of agents. Assuming all local functions are strongly-convex and smooth, and their minimizers lie in a given ball, we analyse the evolution of the distance to the minimizer in expectation when the system is occasionally subject to replacements in addition to the usual iterations of the RCD algorithm. We focus on complete graphs where all agents interact with each other with the same probability, and provide conditions to guarantee convergence in open system. Finally, a discussion around the tightness of our results is provided.

cs.MA↗

arXiv2020

The Laplacian Spectrum of Large Graphs Sampled from Graphons

This paper studies the Laplacian spectrum and the average effective resistance of (large) graphs that are sampled from graphons. Broadly speaking, our main finding is that the Laplacian eigenvalues of a large dense graph can be effectively approximated by using the degree function of the corresponding graphon. More specifically, we show how to approximate the distribution of the Laplacian eigenvalues and the average effective resistance (Kirchhoff index) of the graph. For all cases, we provide explicit bounds on the approximation errors and derive the asymptotic rates at which the errors go to zero when the number of nodes goes to infinity. Our main results are proved under the conditions that the graphon is piecewise Lipschitz and bounded away from zero.

math.PR↗

arXiv2020

On the Influence of Noise in Randomized Consensus Algorithms

In this paper we study the influence of additive noise in randomized consensus algorithms. Assuming that the update matrices are symmetric, we derive a closed form expression for the mean square error induced by the noise, together with upper and lower bounds that are simpler to evaluate. Motivated by the study of Open Multi-Agent Systems, we concentrate on Randomly Induced Discretized Laplacians, a family of update matrices that are generated by sampling subgraphs of a large undirected graph. For these matrices, we express the bounds by using the eigenvalues of the Laplacian matrix of the underlying graph or the graph's average effective resistance, thereby proving their tightness. Finally, we derive expressions for the bounds on some examples of graphs and numerically evaluate them.

eess.SY↗

arXiv2020

Graphon-based sensitivity analysis of SIS epidemics

In this work, we use the spectral properties of graphons to study stability and sensitivity to noise of deterministic SIS epidemics over large networks. We consider the presence of additive noise in a linearized SIS model and we derive a noise index to quantify the deviation from the disease-free state due to noise. For finite networks, we show that the index depends on the adjacency eigenvalues of its graph. We then assume that the graph is a random sample from a piecewise Lipschitz graphon with finite rank and, using the eigenvalues of the associated graphon operator, we find an approximation of the index that is tight when the network size goes to infinity. A numerical example is included to illustrate the results.

eess.SY↗