arXiv subjects

Marco Tulio Angulo

Publications and source records attributed to Marco Tulio Angulo.

9 recordsLinked to original sources

arXiv2026

Who Pays for a Connected Public Good?

Connectivity can turn separate contributions into a public good that benefits participants and nonparticipants alike. Yet only participants pay for it, and each can avoid her charge by withdrawing while enjoying whatever public output survives. How do network connections constrain who can or must pay, and how large a cost can the group bear? We study a participation game in which public output equals the size of the largest connected group of active players, whose members divide a fixed operating cost. The output a participant destroys by withdrawing is her withdrawal responsibility and bounds her payment. These bounds determine the group's cost-bearing capacity and, whenever the group can be kept active, which participants must pay. We prove that among connected networks with at least five players, the path uniquely maximizes the cost-bearing capacity of a group, yet minimizes the expected surviving output after a uniformly selected participant withdraws. As the group grows, the ratio of maximal capacity to gross social benefit under full participation converges to one quarter. Fragility can therefore strengthen voluntary finance, but even the most financeable network cannot close the gap between the value it creates and what its participants will pay to sustain it.

cs.GT↗

arXiv2023

An arbitrary-order predefined-time exact differentiator for signals with exponential growth bound

There is a growing interest in differentiation algorithms that converge in fixed time with a predefined Upper Bound on the Settling Time (UBST). However, existing differentiation algorithms are limited to signals having an $n$-th order Lipschitz derivative. Here, we introduce a general methodology based on time-varying gains to circumvent this limitation, allowing us to design $n$-th order differentiators with a predefined UBST for the broader class of signals whose $(n+1)$-th derivative is bounded by a function with bounded logarithmic derivative. Unlike existing methods whose time-varying gain tends to infinity, our approach yields a time-varying gain that remains bounded at convergence time. We show how this last property maintains exact convergence using bounded gains when considering a compact set of initial conditions and improves the algorithm's performance to measurement noise.

math.OC↗

arXiv2022

Designing predefined-time differentiators with bounded time-varying gains

There is an increasing interest in designing differentiators, which converge exactly before a prespecified time regardless of the initial conditions, i.e., which are fixed-time convergent with a predefined Upper Bound of their Settling Time (UBST), due to their ability to solve estimation and control problems with time constraints. However, for the class of signals with a known bound of their $(n+1)$-th time derivative, the existing design methodologies yield a very conservative UBST, or result in gains that tend to infinity at the convergence time. Here, we introduce a new methodology based on time-varying gains to design arbitrary-order exact differentiators with a predefined UBST. This UBST is a priori set as one parameter of the algorithm. Our approach guarantees that the UBST can be set arbitrarily tight, and we also provide sufficient conditions to obtain exact convergence while maintaining bounded time-varying gains. Additionally, we provide necessary and sufficient conditions such that our approach yields error dynamics with a uniformly Lyapunov stable equilibrium. Our results show how time-varying gains offer a general and flexible methodology to design algorithms with a predefined UBST.

math.OC↗

arXiv2020

A methodology for designing fixed-time stable systems with a predefined upper-bound in their settling time

Algorithms having uniform convergence with respect to their initial condition (i.e., with fixed-time stability) are receiving increasing attention for solving control and observer design problems under time constraints. However, we still lack a general methodology to design these algorithms for high-order perturbed systems when we additionally need to impose a user-defined upper-bound on their settling time, especially for systems with perturbations. Here, we fill this gap by introducing a methodology to redesign a class of asymptotically, finite- and fixed-time stable systems into non-autonomous fixed-time stable systems with a user-defined upper-bound on their settling time. Our methodology redesigns a system by adding time-varying gains. However, contrary to existing methods where the time-varying gains tend to infinity as the origin is reached, we provide sufficient conditions to maintain bounded gains. We illustrate our methodology by building fixed-time online differentiators with user-defined upper-bound on their settling time and bounded gains.

math.OC↗

arXiv2018

Structural accessibility and structural observability of nonlinear networked systems

The classical notions of structural controllability and structural observability are receiving increasing attention in Network Science, since they provide a mathematical basis to answer how the network structure of a dynamic system affects its controllability and observability properties. However, these two notions are formulated assuming systems with linear dynamics, which significantly limit their applicability. To overcome this limitation, here we introduce and fully characterize the notions "structural accessibility" and "structural observability" for systems with nonlinear dynamics. We show how nonlinearities make easier the problem of controlling and observing networked systems, reducing the number of variables that are necessary to directly control and directly measure. Our results contribute to understanding better the role that the network structure and nonlinearities play in our ability to control and observe complex dynamic systems.

eess.SY↗

arXiv2016

Sensitivity of Complex Networks

The sensitivity (i.e. dynamic response) of complex networked systems has not been well understood, making difficult to predict whether new macroscopic dynamic behavior will emerge even if we know exactly how individual nodes behave and how they are coupled. Here we build a framework to quantify the sensitivity of complex networked system of coupled dynamic units. We characterize necessary and sufficient conditions for the emergence of new macroscopic dynamic behavior in the thermodynamic limit. We prove that these conditions are satisfied only for architectures with power-law degree distributions. Surprisingly, we find that highly connected nodes (i.e. hubs) only dominate the sensitivity of the network up to certain critical frequency.

eess.SY↗

arXiv2016

Qualitative stability of nonlinear networked systems

In many large systems, such as those encountered in biology or economics, the dynamics are nonlinear and are only known very coarsely. It is often the case, however, that the signs (excitation or inhibition) of individual interactions are known. This paper extends to nonlinear systems the classical criteria of linear sign stability introduced in the 70's, yielding simple sufficient conditions to determine stability using only the sign patterns of the interactions.

eess.SY↗

arXiv2015

Fundamental limitations of network reconstruction

Network reconstruction is the first step towards understanding, diagnosing and controlling the dynamics of complex networked systems. It allows us to infer properties of the interaction matrix, which characterizes how nodes in a system directly interact with each other. Despite a decade of extensive studies, network reconstruction remains an outstanding challenge. The fundamental limitations governing which properties of the interaction matrix (e.g., adjacency pattern, sign pattern and degree sequence) can be inferred from given temporal data of individual nodes remain unknown. Here we rigorously derive necessary conditions to reconstruct any property of the interaction matrix. These conditions characterize how uncertain can we be about the coupling functions that characterize the interactions between nodes, and how informative does the measured temporal data need to be; rendering two classes of fundamental limitations of network reconstruction. Counterintuitively, we find that reconstructing any property of the interaction matrix is generically as difficult as reconstructing the interaction matrix itself, requiring equally informative temporal data. Revealing these fundamental limitations shed light on the design of better network reconstruction algorithms, which offer practical improvements over existing methods.

eess.SY↗

arXiv2014

Network motifs emerge from interconnections that favor stability

Network motifs are overrepresented interconnection patterns found in real-world networks. What functional advantages may they offer for building complex systems? We show that most network motifs emerge from interconnections patterns that best exploit the intrinsic stability characteristics of individual nodes. This feature is observed at different scales in a network, from nodes to modules, suggesting an efficient mechanism to stably build complex systems.

eess.SY↗