arXiv subjects

Alberto Tesi

Publications and source records attributed to Alberto Tesi.

7 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.

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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.

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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.

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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.

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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.

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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.

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