arXiv subjects

Julien M. Hendrickx

Publications and source records attributed to Julien M. Hendrickx.

At least 19 recordsLinked to original sources

arXiv2026

Local Identifiability of Networks with Nonlinear Node Dynamics

We study the identifiability of nonlinear network systems with partial excitation and partial measurement when the network dynamics is linear on the edges and nonlinear on the nodes. We assume that the graph topology and the nonlinear functions at the node level are known, and we aim to identify the weight matrix of the graph. Our main result is that, for almost all static analytic nonlinearities that cross the origin, directed graphs are generically locally identifiable if and only if at least one node is excited in every source component of the condensation graph and at least one node is measured in every sink component. This holds even when all other nodes remain unexcited and unmeasured and stands in sharp contrast to most findings on network identifiability requiring measurement and/or excitation of each node. The result applies to homogeneous feed-forward and recurrent artificial neural networks and generalizes previous literature by considering a broader class of activations and architectures.

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arXiv2026

Interpolation Conditions for Instant Data Consistency with Port-Hamiltonian Structure

We develop a data-driven framework for nonlinear port-Hamiltonian (pH) systems based on interpolation conditions to characterize consistency between observed data and structured dynamical models. Specifically, we derive necessary and sufficient conditions for the existence of a pH system with a smooth (convex) Hamiltonian instantly consistent with a given dataset, without requiring explicit parametrization. We further provide a semidefinite programming formulation to verify consistency with non-degenerate interconnection and dissipation structures. Our results provide a principled approach to assess instant data consistency with physical structure and pave the way for control design directly from data.

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arXiv2026

On the Worst-Case Analysis of Cyclic Block Coordinate Descent type Algorithms

We study the worst-case behavior of Block Coordinate Descent (BCD) type algorithms for unconstrained minimization of coordinate-wise smooth convex functions. This behavior is indeed not completely understood, and the practical success of these algorithms is not fully explained by current convergence analyses. We extend the recently proposed Performance Estimation Problem (PEP) approach to convex coordinate-wise smooth functions by proposing necessary interpolation conditions. We then exploit this to obtain improved numerical upper bounds on the worst-case convergence rate of three different BCD algorithms, namely Cyclic Coordinate Descent (CCD), Alternating Minimization (AM), and a Cyclic version of the Random Accelerated Coordinate Descent introduced in Fercoq and Richtárik (2015) (CACD), substantially outperforming the best current bounds in some situations. In addition, we show the convergence of the CCD algorithm with more natural assumptions in the context of convex optimization than those typically made in the literature. Our methodology uncovers a number of phenomena, some of which can be formally established. These include a scale-invariance property of the worst case of CCD with respect to the coordinate-wise smoothness constants and a lower bound on the worst-case performance of CCD which is equal to the number of blocks times the worst-case of full gradient descent over the class of smooth convex functions. We also adapt our framework to the analysis of random BCD algorithms, and present numerical results showing that the standard acceleration scheme in Fercoq and Richtárik (2015) appears to be inefficient for deterministic algorithms.

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arXiv2026

Numerical Design of Optimized First-Order Algorithms

We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimation Problem (PEP) framework, which casts the worst-case analysis of optimization algorithms as an optimization problem itself. We benchmark our methods against existing approaches in the literature on the task of optimizing the step sizes of memoryless gradient descent (which uses only the current gradient for updates) over the class of smooth convex functions. We then apply our methods to numerically tune the step sizes of several memoryless and full (i.e., using all past gradient information for updates) fixed-step first-order algorithms, namely coordinate descent, inexact gradient descent, and cyclic gradient descent, in the context of linear convergence. In all cases, we report accelerated convergence rates compared to those of classical algorithms.

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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.

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arXiv2026

A constructive approach to strengthen algebraic descriptions of function and operator classes

It is well known that functions (resp. operators) satisfying a property~$p$ on a subset $Q\subset \mathbb{R}^d$ cannot necessarily be extended to a function (resp. operator) satisfying~$p$ on the whole of~$\mathbb{R}^d$. Given $Q \subseteq \mathbb{R}^d$, this work considers the problem of obtaining necessary and ideally sufficient conditions to be satisfied by a function (resp. operator) on $Q$, ensuring the existence of an extension of this function (resp. operator) satisfying $p$ on $\mathbb{R}^d$. More precisely, given some property $p$, we present a refinement procedure to obtain stronger necessary conditions to be imposed on $Q$. This procedure can be applied iteratively until the stronger conditions are also sufficient. We illustrate the procedure on a few examples, including the strengthening of existing descriptions for the classes of smooth functions satisfying a Łojasiewicz condition, convex blockwise smooth functions, Lipschitz monotone operators, strongly monotone cocoercive operators, and uniformly convex functions. In most cases, these strengthened descriptions can be represented, or relaxed, to semi-definite constraints, which can be used to formulate tractable optimization problems on functions (resp. operators) within those classes.

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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.

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arXiv2026

Preserving Topology Privacy of Network Systems by Feedback: Conditions and Distributed Design

This paper develops a feedback-based method to preserve the topology privacy of consensus protocols in network systems. The key idea is to intentionally violate topology identifiability conditions, thereby preventing unique or accurate recovery of the true topology from available observations, while preserving the intended consensus behavior. This problem is challenging because the feedback magnitude directly reflects the privacy level of edges, while it is strongly coupled with the consensus convergence and constrained by local communications at each node. To begin with, we derive the feedback conditions of both partial and full observation cases, where the topology unsolvability from observation data is characterized in the former, and the solution space that enforces topology inaccuracy from data is constructed in the latter. Then, we propose a novel distributed topology modification design under limited privacy budgets, and establish the performance guarantees through a controllable tradeoff between the consensus deviation and the topology privacy. Finally, we develop a low-complexity heuristic algorithm to achieve optimal privacy preservation on existing edges. Comparative simulations validate the effectiveness and outperformance of the proposed preservation design.

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arXiv2026

Data Poisoning Attacks Can Systematically Destabilize Data-Driven Control Synthesis

Data-driven control has emerged as a powerful paradigm for synthesizing controllers directly from data, bypassing explicit model identification. However, this reliance on data introduces new and largely unexplored vulnerabilities. In this paper, we show that an attacker can systematically poison the data used for control synthesis, causing any linear state-feedback controller synthesized by the planner to destabilize the physical system. Concerningly, we show that the attacker can achieve this objective without knowledge of the system model or the controller synthesis procedure. To this end, we develop a recursive data-poisoning mechanism that generates falsified state trajectories, inducing a precise geometric shift in the apparent system dynamics. More broadly, our results establish that data-driven control pipelines can be deterministically destabilized by model-agnostic attacks operating solely at the data level. Numerical simulations corroborate these findings for both noise-free and noisy data.

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arXiv2026

On the Convergence of an Opinion-Action Coevolution Model with Bounded Confidence

This paper presents a theoretical convergence analysis for an opinion-action coevolution model that integrates the opinion updating rule of the Hegselmann-Krause model with a utility-based decision-making mechanism. The model is reformulated into an augmented state-space representation, where the state matrix induces a time-varying social interaction digraph. The convergence analysis is grounded on two existing theoretical findings that establish convergence for the Hegselmann-Krause type of models and containment control systems with multiple stationary leaders, respectively. Results indicate that, if the structure of the interaction digraph stabilizes within finite time, the model either converges to consensus, where all agents' opinions and actions reach an identical state, or exhibits clustering, where some opinion nodes act as stationary leaders while the remaining nodes approach the convex hull formed by the leaders. Numerical simulations are then provided to validate the theoretical results.

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arXiv2026

2-D Directed Formation Control Based on Bipolar Coordinates

This work proposes a novel 2-D formation control scheme for acyclic triangulated directed graphs (a class of minimally acyclic persistent graphs) based on bipolar coordinates with (almost) global convergence to the desired shape. Prescribed performance control is employed to devise a decentralized control law that avoids singularities and introduces robustness against external disturbances while ensuring predefined transient and steady-state performance for the closed-loop system. Furthermore, it is shown that the proposed formation control scheme can handle formation maneuvering, scaling, and orientation specifications simultaneously. Additionally, the proposed control law is implementable in agents' arbitrarily oriented local coordinate frames using only low-cost onboard vision sensors, which are favorable for practical applications. Finally, a formation maneuvering simulation study verifies the proposed approach.

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arXiv2026

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

We propose a method to identify nonlinear acyclic networks in continuous time when the dynamics are located on the edges and all the nodes are excited. 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. For general directed acyclic graphs (DAGs), we show that it is necessary and sufficient to measure all sinks, assuming that the dynamics are not linear (a condition that can be relaxed for trees). Then, based on the measurement of higher order derivatives and nonzero initial conditions, we introduce a method for the identification of trees, which allows us to recover the nonlinear functions located in the edges of the network under the assumption of dictionary functions. Finally, we propose a method to identify multiple parallel paths of the same length between two nodes, which allow us to identify any DAG when combined with the algorithm for the identification of trees. Several examples are added to illustrate the results.

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arXiv2026

Computer-aided analyses of stochastic first-order methods, via interpolation conditions for stochastic optimization

This work proposes a framework, embedded within the Performance Estimation framework (PEP), for obtaining worst-case performance guarantees on stochastic first-order methods. Given a first-order method, a function class, and a noise model with prescribed expectation and variance properties, we present a semidefinite program (SDP), whose size grows linearly with $N$, the number of iterations analyzed, and whose solution yields a convergence guarantee on the problem. The framework accommodates a wide range of stochastic settings, with finite or infinite support, including the unstructured noise model with bounded variance, finite-sum optimization, and block-coordinate methods, in a unified manner, as guarantees apply to any setting consistent with the noise model, i.e., its expectation and variance. It covers both non-variance-reduced and variance-reduced methods. Using the framework, we analyze the stochastic gradient method under several noise models, and illustrate how the resulting numerical and analytical convergence rates connect with existing results. In particular, we provide improved convergence rates on the unstructured noise model with bounded variance and in the block-coordinate setting.

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arXiv2025

Modeling, Analysis, and Control of Continuous-Time Weighted-Median Opinion Dynamics

Simple yet predictive mathematical models are essential for mechanistic understanding of opinion evolution in social groups. The weighted-median mechanism has recently been proposed as a well-founded alternative to conventional DeGroot-type opinion dynamics. However, the original weighted-median model excludes compromise behavior, as individuals directly adopt their neighbors' opinions without forming intermediate values. In this paper, we introduce a parsimonious continuous-time extension of the weighted-median model by incorporating individual inertia, allowing opinions to move gradually toward the neighbors' weighted median. Empirical evidence shows that this model outperforms both the original weighted-median and DeGroot models with inertia in predicting opinion shifts. We provide a complete theoretical analysis of the proposed dynamics: the equilibria are characterized and shown to be Lyapunov stable; global convergence is established via the Bony-Brezis method, yielding necessary and sufficient conditions for consensus from arbitrary initial states. In addition, we derive a graph-theoretic condition for persistent disagreement and a necessary and sufficient condition for steering the system to any prescribed consensus value through constant external inputs to a subset of individuals. These results reveal how a social group's resilience to external manipulation fundamentally depends on its internal network structure.

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arXiv2025

On the Convex Interpolation for Linear Operators

The worst-case performance of an optimization method on a problem class can be analyzed using a finite description of the problem class, known as interpolation conditions. In this work, we study interpolation conditions for linear operators given scalar products between discrete inputs and outputs. First, we show that if only convex constraints on the scalar products of inputs and outputs are allowed,it is only possible to characterize classes of linear operators or symmetric linear operator whose all singular values or eigenvalues belong to some subset of R. Then, we propose new interpolation conditions for linear operators with minimal and maximal singular values and linear operators whose eigenvalues or singular values belong to unions of subsets. Finally, we illustrate the new interpolation conditions through the analysis of the Gradient and Chambolle-Pock methods. It allows to obtain new numerical worst-case guarantees on these methods.

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arXiv2025

Interpolation Conditions for Data Consistency and Prediction in Noisy Linear Systems

We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all trajectories consistent with the measured data and these prior bounds in a purely data-driven manner. This characterization enables data-consistency verification, inference, and one-step ahead prediction, which can be leveraged for safety verification and cost minimization. Ultimately, this work represents a preliminary step toward exploiting interpolation conditions in data-driven control, offering a systematic way to characterize trajectories consistent with a dynamical system within a given class and enabling their use in control design.

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arXiv2025

Exploiting Agent Symmetries for Performance Analysis of Distributed Optimization Methods

We show that, in many settings, the worst-case performance of a distributed optimization algorithm is independent of the number of agents in the system, and can thus be computed in the fundamental case with just two agents. This result relies on a novel approach that systematically exploits symmetries in worst-case performance computation, framed as Semidefinite Programming (SDP) via the Performance Estimation Problem (PEP) framework. Harnessing agent symmetries in the PEP yields compact problems whose size is independent of the number of agents in the system. When all agents are equivalent in the problem, we establish the explicit conditions under which the resulting worst-case performance is independent of the number of agents and is therefore equivalent to the basic case with two agents. Our compact PEP formulation also allows the consideration of multiple equivalence classes of agents, and its size only depends on the number of equivalence classes. This enables practical and automated performance analysis of distributed algorithms in numerous complex and realistic settings, such as the analysis of the worst agent performance. We leverage this new tool to analyze the performance of the EXTRA algorithm in advanced settings and its scalability with the number of agents, providing a tighter analysis and deeper understanding of the algorithm performance.

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arXiv2025

A constraint-based approach to function interpolation, with application to performance estimation for weakly convex optimisation

We consider the problem of obtaining interpolation constraints for function classes, i.e., necessary and sufficient constraints that a set of points, function values and (sub)gradients must satisfy to ensure the existence of a global function of the class considered, consistent with this set. The derivation of such constraints is crucial, e.g., in the performance analysis of optimization methods, since obtaining a priori tight performance guarantees requires using a tight description of function classes of interest. We propose an approach that allows setting aside all analytic properties of the function class to work only at an algebraic level, and to obtain counterexamples when a condition characterizing a function class cannot serve as an interpolation constraint. As an illustration, we provide interpolation constraints for the class of weakly convex functions with bounded subgradients, and rely on these constraints to outperform state-of-the-art bounds on the performance of the subgradient method on this class.

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