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Elisa Continelli

Publications and source records attributed to Elisa Continelli.

12 recordsLinked to original sources
arXiv2026

Asymptotic consensus and flocking under decaying persistent excitation on rooted digraphs

In this paper, we investigate first- and second-order alignment models with non-universal interaction, time delays and possible communication failures, extending the results in [17] to interaction digraphs that are only assumed to be rooted and to a weaker Persistence Excitation Condition. In particular, we allow the amount of interaction over time intervals of fixed length to decay polynomially in time. For the first-order Hegselmann-Krause type model, we prove asymptotic convergence to consensus under a suitable condition relating the decay exponent of the communication weights to the maximal distance from the root. For the second-order Cucker-Smale model, we establish asymptotic flocking under an additional assumption on the decay of the influence function. These results show that collective behavior can still emerge under progressively weakening communication and without requiring strong connectivity of the interaction graph.

math.OC↗
arXiv2026

Consensus and flocking with transmission and reaction delays

We investigate consensus formation and flocking behavior in multi-agent systems subject to two distinct types of delays: a transmission delay accounting for information exchange between agents, and a reaction delay representing the processing time before agents adjust their states. For a simplified linear two-agent system, we provide explicit insight into how these delays affect asymptotic stability. We then derive sufficient conditions for asymptotic consensus and flocking in the general multi-agent setting with a nonlinear, globally positive influence function. These conditions require the delays to be sufficiently small relatively to the initial data and the decay rate of the influence function. The analysis is based on a Lyapunov functional approach combined with a Halanay-type inequality. Our results establish rigorous conditions under which collective behavior emerges in delayed multi-agent systems where both communication and reaction lags are non-negligible, with applications to biological, social, and engineered systems.

math.DS↗
arXiv2025

Uniqueness of solutions to MFG systems with large discount

We prove that solutions to a class of Mean Field Game systems with discount are unique provided that the discount factor is large enough, and the Lagrangian term is (proportionally) small enough. This identifies an asymptotic uniqueness regime that falls outside the usual ones involving monotonicity.

math.AP↗
arXiv2025

A note on the Cucker-Smale model with time delay and communication failures

In this paper, we deal with a Cucker-Smale model with time-dependent time delay and communication failures. Namely, we investigate the situation in which the agents involved in a flocking process can possibly suspend the exchange of information among themselves at some times. Under a so-called Persistence Excitation Condition, we establish the exponential flocking for the considered model. The exponential decay estimates on the velocity diameters we obtain are independent of the number of agents, which is convenient especially when the number of agents becomes too large. Exponential decay estimates with decay rate depending on the number of agents appear instead in the case of pair-dependent time delays and non-universal interaction, i.e. not all the agents are able to exchange information among themselves. In this paper, we rather consider a universal interaction and the time delay functions do not depend on the pair of agents. The analysis is then extended to a model with distributed time delay, namely the time delay is not pointwise but the agents are influenced by the information received from the other components of the system in a certain time interval.

math.OC↗
arXiv2024

First and second-order Cucker-Smale models with non-universal interaction, time delay and communication failures

In this paper, we deal with first and second-order alignment models with non-universal interaction, time delay and possible lack of connection between the agents. More precisely, we analyze the situation in which the system's agents do not transmit information to all the other agents and also agents that are linked to each other can suspend their interaction at certain times. Moreover, we take into account of possible time lags in the interactions. To deal with the considered "non-universal" connection, a graph topology over the structure of the model has to be considered. Under a so-called Persistence Excitation Condition, we establish the exponential convergence to consensus for both models whenever the digraph that describes the interaction between the agents is strongly connected.

math.OC↗
arXiv2024

Energy decay for semilinear evolution equations with memory and time-dependent time delay feedback

In this paper, we study well-posedness and exponential stability for semilinear second order evolution equations with memory and time-varying delay feedback. The time delay function is assumed to be continuous and bounded. Under a suitable assumption on the delay feedback, we are able to prove that solutions corresponding to small initial data are globally defined and satisfy an exponential decay estimate.

math.AP↗
arXiv2024

Exponential decay of solutions to linear evolution equations with time-dependent time delay

In this note, we analyze an abstract evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. We assume that the operator corresponding to the nondelayed part of the model generates an exponentially stable semigroup. Under an appropriate assumption on the delay feedback, we prove the well-posedness and an exponential stability estimate for our model. Applications of our abstract results to concrete models are also illustrated.

math.OC↗
arXiv2023

Hegselmann-Krause and Cucker-Smale type models with attractive-repulsive interaction

In this paper, we analyze a Hegselmann-Krause opinion formation model and a Cucker-Smale flocking model with attractive-repulsive interaction. To be precise, we investigate the situation in which the individuals involved in an opinion formation or a flocking process attract each other in certain time intervals and repeal each other in other ones. Under quite general assumptions, we prove the convergence to consensus for the Hegselmann-Krause model and the exhibition of asymptotic flocking for the Cucker-Smale model in presence of positive-negative interaction. With some additional conditions, we are able to improve the convergence to consensus for the solutions of the Hegselmann-Krause model, namely we establish an exponential convergence to consensus result.

math.OC↗
arXiv2023

Convergence to consensus results for Hegselmann-Krause type models with attractive-lacking interaction

In this paper, we analyze a Hegselmann-Krause opinion formation model with attractive-lacking interaction. More precisely, we investigate the situation in which the individuals involved in an opinion formation process interact among themselves but can eventually suspend the exchange of information among each other at some times. Under quite general assumptions, we prove the exponential convergence to consensus for the Hegselmann-Krause model in presence of possible lack of interaction. We then extend the analysis to an analogous model in presence of time delays.

math.OC↗
arXiv2023

Semiconcavity for the minimum time problem in presence of time delay effects

In this paper, we deal with a minimum time problem in presence of a time delay $\tau.$ The value function of the considered optimal control problem is no longer defined in a subset of $\mathbb{R}^{n}$, as it happens in the undelayed case, but its domain is a subset of the Banach space $C([-\tau,0];\mathbb{R}^{n})$. For the undelayed minimum time problem, it is known that the value function associated with it is semiconcave in a subset of the reachable set and is a viscosity solution of a suitable Hamilton-Jacobi-Belmann equation. The Hamilton-Jacobi theory for optimal control problems involving time delays has been developed by several authors. Here, we are rather interested in investigating the regularity properties of the minimum time functional. Extending classical arguments, we are able to prove that the minimum time functional is semiconcave in a suitable subset of the reachable set.

math.OC↗
arXiv2022

Consensus for the Hegselmann-Krause model with time variable time delays

In this paper, we analyze a Hegselmann-Krause opinion formation model with time-variable time delay and prove that, if the influence function is always positive, then there is exponential convergence to consensus without requiring any smallness assumptions on the time delay function. The analysis is then extended to a model with distributed time delay.

math.OC↗