arXiv subjects

Giacomo Innocenti

Publications and source records attributed to Giacomo Innocenti.

15 recordsLinked to original sources

arXiv2026

Mixed Potential Approach to Convergence of Nonlinear RLC Circuits with Memristors

The paper considers a large class of nonlinear circuits, termed RLCM, containing all four basic circuit elements, i.e., resistors, inductors, capacitors and memristors. A companion paper [1] has introduced a mixed potential for RLCM circuits generalizing that found by Brayton and Moser for circuits without memristors. In this paper, systematic Lyapunov-like results on convergence of RLCM circuits are proved by means of the mixed potential. These hold under the basic assumption that an RLCM circuit has a complete set of variables in the flux-charge domain and they require, roughly speaking, that there is a balance, which is quantitatively estimated, between capacitors and inductors. The convergence results are robust with respect to circuit parameter variations and they include cases where the memristor circuits possess multiple stable equilibrium points, which is of importance for instance to implement content addressable memories (CAMs). The results extend to circuits possessing all four basic circuit elements previous results that pertain to circuits without memristors or memristor circuits without inductors. The main proofs are conducted by using the flux-charge analysis method (FCAM) to analyze RLCM circuits in the flux-charge domain.

eess.SY↗

arXiv2026

Mixed potential for nonlinear RLC circuits with memristors

In two seminal articles published in 1964, Brayton and Moser introduced the concept of a mixed potential as a fundamental theoretic tool to describe and analyze a class RLC of nonlinear circuits containing resistors, capacitors and inductors. In this paper, it is shown for the first time that a mixed potential can be introduced for a class RLCM of RLC circuits containing also memristors. This is possible provided a memristor circuit is analyzed not in the traditional voltage-current domain but rather in the flux-charge domain. The flux-charge analysis method (FCAM) plays a crucial role in the extension, in particular, a key step is an equivalence principle established via FCAM between an RLCM circuit in the flux-charge domain and a nonlinear RLC circuit in the voltage-current domain. Several examples are discussed where the mixed potential is explicitly found. These include basic circuits with memristors, such as Chua's circuit with a memristor and also large-scale memristor arrays with a neural architecture. This paper is mainly devoted to the introduction of a mixed potential for memristor circuits and the study of its main theoretic properties, as the possibility to write the circuit state equations in the flux-charge domain in an effective and compact form via the mixed potential. In a companion paper [1], the mixed potential is used to obtain in a systematic way Lyapunov-like results on convergence of RLCM circuits. Those results will extend existing results on convergence that do not cover the important case where there is the simultaneous presence of capacitors and inductors in a memristor circuit.

eess.SY↗

arXiv2025

Convergent Weight and Activation Dynamics in Memristor Neural Networks

Convergence of dynamic feedback neural networks (NNs), as the Cohen-Grossberg, Hopfield and cellular NNs, has been for a long time a workhorse of NN theory. Indeed, convergence in the presence of multiple stable equilibrium points (EPs) is crucial to implement content addressable memories and solve several other signal processing tasks in real time. There are two typical ways to use a convergent NN, i.e.: a) let the activations evolve while maintaining fixed weights and inputs (activation dynamics) or b) adapt the weights while maintaining fixed activations (weight dynamics). As remarked in a seminal paper by Hirsch, there is another interesting possibility, i.e., let the neuron interconnection weights evolve while simultaneously running the activation dynamics (weight-activation dynamics). The weight-activation dynamics is of importance also because it is more plausible than the other two types for modeling neural systems. The paper breaks new ground by analyzing for the first time in a systematic way the convergence properties of the weight-activation dynamics for a class of memristor feedback dynamic NNs. The main result is that, under suitable assumptions on the structure of the memristor interconnections, the solutions (weights and activations) converge to an EP, except at most for a set of initial conditions with zero measure. The result includes the most important case where the NN has multiple stable EPs.

eess.SY↗

arXiv2024

A small-gain criterion for 2-contraction of large scale interconnected systems

Despite modular conditions to guarantee stability for large-scale systems have been widely studied, few methods are available to tackle the case of networks with multiple equilibria. This paper introduces small-gain like sufficient conditions for 2-contraction of large-scale interconnected systems on the basis of a family of upper-bounds to the $L_2$ gains that arise from the gains computed on individual channels of the second additive variational equation. Such a condition guarantee the 2-additive compound of the system's Jacobian to be exponentially contractive, thus implying convergence towards equilibria of the system's solutions. The gains are obtained by solving suitable Linear Matrix Inequalities. Three interconnected Thomas' systems are considered in order to illustrate the application of the theory and the degree of conservatism.

eess.SY↗

arXiv2024

Embedding classic chaotic maps in simple discrete-time memristor circuits

In the last few years the literature has witnessed a remarkable surge of interest for chaotic maps implemented by discrete-time (DT) memristor circuits. This paper investigates on the reasons underlying this type of chaotic behavior. To this end, the papers considers the map implemented by the simplest memristor circuit given by a capacitor and an ideal flux-controlled memristor or an inductor and an ideal charge-controlled memristor. In particular, the manuscript uses the DT flux-charge analysis method (FCAM) introduced in a recent paper to ensure that the first integrals and foliation in invariant manifolds of continuous-time (CT) memristor circuits are preserved exactly in the discretization for any step size. DT-FCAM yields a two-dimensional map in the voltage-current domain (VCD) and a manifold-dependent one-dimensional map in the flux-charge domain (FCD), i.e., a one-dimensional map on each invariant manifold. One main result is that, for suitable choices of the circuit parameters and memristor nonlinearities, both DT circuits can exactly embed two classic chaotic maps, i.e., the logistic map and the tent map. Moreover, due to the property of extreme multistability, the DT circuits can simultaneously embed in the manifolds all the dynamics displayed by varying one parameter in the logistic and tent map. The paper then considers a DT memristor Murali-Lakshmanan-Chua circuit and its dual. Via DT-FCAM these circuits implement a three-dimensional map in the VCD and a two-dimensional map on each invariant manifold in the FCD. It is shown that both circuits can simultaneously embed in the manifolds all the dynamics displayed by two other classic chaotic maps, i.e., the Henon map and the Lozi map, when varying one parameter in such maps. In essence, these results provide an explanation of why it is not surprising to observe complex dynamics even in simple DT memristor circuits.

nlin.CD↗

arXiv2023

Physical Implementation of a Tunable Memristor-based Chua's Circuit

Nonlinearity is a central feature in demanding computing applications that aim to deal with tasks such as optimization or classification. Furthermore, the consensus is that nonlinearity should not be only exploited at the algorithm level, but also at the physical level by finding devices that incorporate desired nonlinear features to physically implement energy, area and/or time efficient computing applications. Chaotic oscillators are one type of system powered by nonlinearity, which can be used for computing purposes. In this work we present a physical implementation of a tunable Chua's circuit in which the nonlinear part is based on a nonvolatile memristive device. Device characterization and circuit analysis serve as guidelines to design the circuit and results prove the possibility to tune the circuit oscillatory response by electrically programming the device.

cs.ET↗

arXiv2023

A small-gain theorem for 2-contraction of nonlinear interconnected systems

This paper introduces small-gain sufficient conditions for $2$-contraction of feedback interconnected systems, on the basis of individual gains of suitable subsystems arising from a modular decomposition of the second additive compound equation. The condition applies even to cases when individual subsystems might fail to be contractive (due to the extra margin of contraction afforded by the second additive compound matrix). Examples of application are provided to illustrate the theory and show its degree of conservatism and scope of applicability.

eess.SY↗

arXiv2021

Collective canard explosions of globally-coupled rotators with adaptive coupling

Canards, special trajectories that follow invariant repelling slow manifolds for long time intervals, have been frequently observed in slow-fast systems of either biological, chemical and physical nature. Here, collective canard explosions are demonstrated in a population of globally-coupled phase-rotators subject to adaptive coupling. In particular, we consider a bimodal Kuramoto model displaying coexistence of asynchronous and partially synchronized dynamics subject to a linear global feedback. A detailed geometric singular perturbation analysis of the associated mean-field model allows us to explain the emergence of collective canards in terms of the stability properties of the one-dimensional critical manifold, near which the slow macroscopic dynamics takes place. We finally show how collective canards and related manifolds gradually emerge in the globally-coupled system for increasing system sizes, in spite of the trivial dynamics of the uncoupled rotators.

nlin.AO↗

arXiv2019

Resilience for stochastic systems interacting via a quasi-degenerate network

A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear lattice, noise gets amplified via a self-consistent process which we trace back to the degenerate spectrum of the embedding support. The same phenomenon holds when the system is bound to explore a quasi degenerate network. In this case, the eigenvalues of the Laplacian operator, which governs species diffusion, accumulate over a limited portion of the complex plane. The larger the network, the more pronounced the amplification. Beyond a critical network size, a system deemed deterministically stable, hence resilient, may turn unstable, yielding seemingly regular patterns in the concentration amount. Non-normality and quasi-degenerate networks may therefore amplify the inherent stochasticity, and so contribute to altering the perception of resilience, as quantified via conventional deterministic methods.

cond-mat.dis-nn↗

arXiv2018

Reactive explorers to unravel network topology

A procedure is developed and tested to recover the distribution of connectivity of an a priori unknown network, by sampling the dynamics of an ensemble made of reactive walkers. The relative weight between reaction and relocation is gauged by a scalar control parameter, which can be adjusted at will. Different equilibria are attained by the system, following the externally imposed modulation, and reflecting the interplay between reaction and diffusion terms. The information gathered on the observation node is used to predict the stationary density as displayed by the system, via a direct implementation of the celebrated Heterogeneous Mean Field (HMF) approximation. This knowledge translates into a linear problem which can be solved to return the entries of the sought distribution. A variant of the model is then considered which consists in assuming a localized source where the reactive constituents are injected, at a rate that can be adjusted as a stepwise function of time. The linear problem obtained when operating in this setting allows one to recover a fair estimate of the underlying system size. Numerical experiments are carried so as to challenge the predictive ability of the theory.

physics.soc-ph↗

arXiv2018

Complex dynamics in a vehicle platoon with nonlinear drag and ACC controllers

In this paper a novel platoon model is presented. Nonlinear aerodynamic effects, such as the wake generated by the preceding vehicle, are considered, and their influence in the set up of a Adaptive Cruise Controller (ACC) is investigated. To this aim, bifurcation analysis tools are exploited in combination with an embedding technique independent from the vehicles number. The results highlight the importance of a proper configuration for the ACC in order to guarantee the platoon convergence to the desired motion.

nlin.AO↗

arXiv2018

Non normal amplification of stochastic quasi-cycles

Stochastic quasi-cycles for a two species model of the excitatory-inhibitory type, arranged on a triangular loop, are studied. By increasing the strength of the inter-nodes coupling, one moves the system towards the Hopf bifurcation and the amplitude of the stochastic oscillations are consequently magnified. When the system is instead constrained to evolve on specific manifolds, selected so as to return a constant rate of deterministic damping for the perturbations, the observed amplification correlates with the degree of non normal reactivity, here quantified by the numerical abscissa. The thermodynamics of the reactive loop is also investigated and the degree of inherent reactivity shown to facilitate the out-of-equilibrium exploration of the available phase space.

cond-mat.stat-mech↗

arXiv2011

A frequency approach to topological identification and graphical modeling

This works explores and illustrates recent results developed by the author in field of dynamical network analysis. The considered approach is blind, i.e., no a priori assumptions on the interconnected systems are available. Moreover, the perspective is that of a simple "observer" who can perform no kind of test on the network in order to study the related response, that is no action or forcing input aimed to reveal particular responses of the system can be performed. In such a scenario a frequency based method of investigation is developed to obtain useful insights on the network. The information thus derived can be fruitfully exploited to build acyclic graphical models, which can be seen as extension of Bayesian Networks or Markov Chains. Moreover, it is shown that the topology of polytree linear networks can be exactly identified via the same mathematical tools. In this respect, it is worth observing that important real systems, such as all the transportation networks, fit this class.

eess.SY↗

arXiv2009

Abstraction and control techniques for non-stationary scheduling problems

The paper faces the problem of scheduling from a new perspective, trying to bridge the gap between classical heuristic approaches and system identification and control strategies. To this aim, a complete mathematical formulation of a general scheduling process is derived, beginning from very broad assumptions. This allows a greater freedom of manipulation and guarantee the resolution of the identification (and control) techniques. Both an adaptive and a switching strategies are presented in relation to the performances of a simple Round Robin algorithm.

nlin.AO↗

arXiv2008

Coherence-based multivariate analysis of high frequency stock market values

The paper tackles the problem of deriving a topological structure among stock prices from high frequency historical values. Similar studies using low frequency data have already provided valuable insights. However, in those cases data need to be collected for a longer period and then they have to be detrended. An effective technique based on averaging a metric function on short subperiods of the observation horizon is suggested. Since a standard correlation-based metric is not capable of catching dependencies at different time instants, it is not expected to perform the best when dealing with high frequency data. Hence, the choice of a more suitable metric is discussed. In particular, a coherence-based metric is proposed, for it is able to detect any possible linear relation between two times series, even at different time instants. The averaging technique is employed to analyze a set of 100 high volume stocks of the New York Stock Exchange, observed during March 2008.

q-fin.ST↗