Pietro DeLellis

Marco Coraggio, Pietro DeLellis, Mario di Bernardo

Complex networks are a successful framework to describe collective behaviour in many applications, but a notable gap remains in the current literature, that of proving asymptotic convergence in networks of piecewise-smooth systems. Indeed, a wide variety of physical systems display discontinuous dynamics that change abruptly, including dry friction mechanical oscillators, electrical power converters, and biological neurons. In this paper, we study how to enforce global asymptotic state-synchronization in these networks. Specifically, we propose the addition of a distributed discontinuous coupling action to the commonly used diffusive coupling protocol. Moreover, we provide analytical estimates of the thresholds on the coupling gains required for convergence, and highlight the importance of a new connectivity measure, which we named minimum density. The theoretical results are illustrated by a set of representative examples.

Pietro DeLellis, Franco Garofalo, Francesco Lo Iudice

The paradigmatic formation control problem of steering a multi-agent system towards a balanced circular formation has been the subject of extensive studies in the control engineering community. Indeed, this is due to the fact that it shares several features with relevant applications such as distributed environmental monitoring or fence-patrolling. However, these applications may also present some relevant differences from the ideal setting such as the curve on which the formation must be achieved not being a circle, or the measurements being neither ideal nor as a continuous information flow. In this work, we attempt to fill this gap between theory and applications by considering the problem of steering a multi-agent system towards a balanced formation on a generic closed curve and under very restrictive assumptions on the information flow amongst the agents. We tackle this problem through an estimation and control strategy that borrows tools from interval analysis to guarantee the robustness that is required in the considered scenario.

Eleonora Vitanza, Pietro DeLellis, Chiara Mocenni et al.

This study integrates causal inference, graph analysis, temporal complexity measures, and machine learning to examine whether individual symptom trajectories can reveal meaningful diagnostic patterns. Testing on a longitudinal dataset of N=45 individuals affected by General Anxiety Disorder (GAD) and/or Major Depressive Disorder (MDD) derived from Fisher et al. 2017, we propose a novel pipeline for the analysis of the temporal dynamics of psychopathological symptoms. First, we employ the PCMCI+ algorithm with nonparametric independence test to determine the causal network of nonlinear dependencies between symptoms in individuals with different mental disorders. We found that the PCMCI+ effectively highlights the individual peculiarities of each symptom network, which could be leveraged towards personalized therapies. At the same time, aggregating the networks by diagnosis sheds light to disorder-specific causal mechanisms, in agreement with previous psychopathological literature. Then, we enrich the dataset by computing complexity-based measures (e.g. entropy, fractal dimension, recurrence) from the symptom time series, and feed it to a suitably selected machine learning algorithm to aid the diagnosis of each individual. The new dataset yields 91% accuracy in the classification of the symptom dynamics, proving to be an effective diagnostic support tool. Overall, these findings highlight how integrating causal modeling and temporal complexity can enhance diagnostic differentiation, offering a principled, data-driven foundation for both personalized assessment in clinical psychology and structural advances in psychological research.