arXiv subjects

Giovanni Russo

Publications and source records attributed to Giovanni Russo.

At least 73 records · Page 4Linked to original sources

arXiv2023

Euclidean Contractivity of Neural Networks with Symmetric Weights

This paper investigates stability conditions of continuous-time Hopfield and firing-rate neural networks by leveraging contraction theory. First, we present a number of useful general algebraic results on matrix polytopes and products of symmetric matrices. Then, we give sufficient conditions for strong and weak Euclidean contractivity, i.e., contractivity with respect to the $\ell_2$ norm, of both models with symmetric weights and (possibly) non-smooth activation functions. Our contraction analysis leads to contraction rates which are log-optimal in almost all symmetric synaptic matrices. Finally, we use our results to propose a firing-rate neural network model to solve a quadratic optimization problem with box constraints.

math.OC↗

arXiv2023

Reconstructing higher-order interactions in coupled dynamical systems

Higher-order interactions play a key role for the stability and function of a complex system. However, how to identify them is still an open problem. Here, we propose a method to fully reconstruct the structural connectivity of a system of coupled dynamical units, identifying both pairwise and higher-order interactions from the system time evolution. Our method works for any dynamics, and allows the reconstruction of both hypergraphs and simplicial complexes, either undirected or directed, unweighted or weighted. With two concrete applications, we show how the method can help understanding the ecosystemic complexity of bacterial systems, or the microscopic mechanisms of interaction underlying coupled chaotic oscillators.

physics.soc-ph↗

arXiv2023

On the design of multiplex control to reject disturbances in nonlinear network systems affected by heterogeneous delays

We consider the problem of designing control protocols for nonlinear network systems affected by heterogeneous, time-varying delays and disturbances. For these networks, the goal is to reject polynomial disturbances affecting the agents and to guarantee the fulfilment of some desired network behaviour. To satisfy these requirements, we propose an integral control design implemented via a multiplex architecture. We give sufficient conditions for the desired disturbance rejection and stability properties by leveraging tools from contraction theory. We illustrate the effectiveness of the results via a numerical example that involves the control of a multi-terminal high-voltage DC grid.

math.OC↗

arXiv2023

Discrete fully probabilistic design: towards a control pipeline for the synthesis of policies from examples

We present the principled design of a control pipeline for the synthesis of policies from examples data. The pipeline, based on a discretized design which we term as discrete fully probabilistic design, expounds an algorithm recently introduced in Gagliardi and Russo (2021) to synthesize policies from examples for constrained, stochastic and nonlinear systems. Contrary to other approaches, the pipeline we present: (i) does not need the constraints to be fulfilled in the possibly noisy example data; (ii) enables control synthesis even when the data are collected from an example system that is different from the one under control. The design is benchmarked numerically on an example that involves controlling an inverted pendulum with actuation constraints starting from data collected from a physically different pendulum that does not satisfy the system-specific actuation constraints. We also make our fully documented code openly available.

eess.SY↗

arXiv2023

Probabilistic design of optimal sequential decision-making algorithms in learning and control

This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that combines a problem formulation and a set of resolution methods. The formulation consists of an infinite-dimensional optimization problem. The methods come from approaches to search optimal solutions in the space of probability functions. Through the lenses of this overarching framework we revisit popular learning and control algorithms, showing that these naturally arise from suitable variations on the formulation mixed with different resolution methods. A running example, for which we make the code available, complements the survey. Finally, a number of challenges arising from the survey are also outlined.

math.OC↗

arXiv2022

GKM actions on cohomogeneity one manifolds

We consider compact manifolds $M$ with a cohomogeneity one action of a compact Lie group $G$ such that the orbit space $M/G$ is a closed interval. For $T$ a maximal torus of $G$, we find necessary and sufficient conditions on the group diagram of $M$ such that the $T$-action on $M$ is of GKM type, and describe its GKM graph. The general results are illustrated on explicit examples.

math.DG↗

arXiv2022

CRAWLING: a Crowdsourcing Algorithm on Wheels for Smart Parking

We present the principled design of CRAWLING: a CRowdsourcing Algorirthm on WheeLs for smart parkING. CRAWLING is an in-car service for the routing of connected cars. Specifically, cars equipped with our service are able to {\em crowdsource} data from third-parties, including other cars, pedestrians, smart sensors and social media, in order to fulfill a given routing task. CRAWLING relies on a solid control-theoretical formulation and the routes it computes are the solution of an optimal control problem where cars maximize a reward capturing environmental conditions while tracking some desired behavior. A key feature of our service is that it allows to consider stochastic behaviors, while taking into account streams of heterogeneous data. We propose a stand-alone, general-purpose, implementation of CRAWLING and we show its effectiveness on a set of scenarios aimed at illustrating all the key features of our service. Simulations show that, when cars are equipped with CRAWLING, the service effectively orchestrates the vehicles, making them able to react online to road conditions, minimizing their cost functions. The code implementing our service and to replicate the numerical results is made openly available.

math.OC↗

arXiv2022

CT-DQN: Control-Tutored Deep Reinforcement Learning

One of the major challenges in Deep Reinforcement Learning for control is the need for extensive training to learn the policy. Motivated by this, we present the design of the Control-Tutored Deep Q-Networks (CT-DQN) algorithm, a Deep Reinforcement Learning algorithm that leverages a control tutor, i.e., an exogenous control law, to reduce learning time. The tutor can be designed using an approximate model of the system, without any assumption about the knowledge of the system's dynamics. There is no expectation that it will be able to achieve the control objective if used stand-alone. During learning, the tutor occasionally suggests an action, thus partially guiding exploration. We validate our approach on three scenarios from OpenAI Gym: the inverted pendulum, lunar lander, and car racing. We demonstrate that CT-DQN is able to achieve better or equivalent data efficiency with respect to the classic function approximation solutions.

cs.LG↗

arXiv2022

Comparison of two aspects of a PDE model for biological network formation

We compare the solutions of two systems of partial differential equations (PDE), seen as two different interpretations of the same model that describes formation of complex biological networks. Both approaches take into account the time evolution of the medium flowing through the network, and we compute the solution of an elliptic-parabolic PDE system for the conductivity vector $m$, the conductivity tensor $\mathbb{C}$ and the pressure $p$. We use finite differences schemes in a uniform Cartesian grid in the spatially two-dimensional setting to solve the two systems, where the parabolic equation is solved by a semi-implicit scheme in time. Since the conductivity vector and tensor appear also in the Poisson equation for the pressure $p$, the elliptic equation depends implicitly on time. For this reason we compute the solution of three linear systems in the case of the conductivity vector $m\in\mathbb{R}^2$, and four linear systems in the case of the symmetric conductivity tensor $\mathbb{C}\in\mathbb{R}^{2\times 2}$, at each time step. To accelerate the simulations, we make use of the Alternating Direction Implicit (ADI) method. The role of the parameters is important for obtaining detailed solutions. We provide numerous tests with various values of the parameters involved, to see the differences in the solutions of the two systems.

math.NA↗

arXiv2022

Implicit and semi-implicit well-balanced finite-volume methods for systems of balance laws

The aim of this work is to design implicit and semi-implicit high-order well-balanced finite-volume numerical methods for 1D systems of balance laws. The strategy introduced by two of the authors in a previous paper for explicit schemes based on the application of a well-balanced reconstruction operator has been applied. The well-balanced property is preserved when quadrature formulas are used to approximate the averages and the integral of the source term in the cells. Concerning the time evolution, this technique is combined with a time discretization method of type RK-IMEX or RK-implicit. The methodology will be applied to several systems of balance laws.

math.NA↗

arXiv2022

Scalability in nonlinear network systems affected by delays and disturbances

This paper is concerned with the study of scalability in nonlinear heterogeneous networks affected by communication delays and disturbances. After formalizing the notion of scalability, we give two sufficient conditions to assess this property. Our results can be used to study leader-follower and leaderless networks and also allow to consider the case when the desired configuration of the system changes over time. We show how our conditions can be turned into design guidelines to guarantee scalability and illustrate their effectiveness via numerical examples.

eess.SY↗

arXiv2022

A finite-difference ghost-point multigrid method for multi-scale modelling of sorption kinetics of a surfactant past an oscillating bubble

We propose a method for the numerical solution of a multiscale model describing sorption kinetics of a surfactant around an oscillating bubble. The evolution of the particles is governed by a convection-diffusion equation for the surfactant concentration $c$, with suitable boundary condition on the bubble surface, which models the action of the short range attractive-repulsive potential acting on them when they get sufficiently close to the surface \cite{multiscale_mod}. In the domain occupied by the fluid, the particles are transported by the fluid motion generated by the bubble oscillations. The method adopted to solve the equation for $c$ is based on a finite-difference scheme on a uniform Cartesian grid and implemented in 2D and 3D axisymmetric domains. We use a level-set function to define the region occupied by the bubble, while the boundary conditions are discretized by a ghost-point technique to guarantee second order accuracy at the curved boundary. The sparse linear system is finally solved with a geometric multigrid technique designed \textit{ad-hoc\/} for this specific problem. Several accuracy tests are provided to prove second order accuracy in space and time. The fluid dynamics generated by the oscillating bubble is governed by the Stokes equation solved with a second order accurate method based on a monolithic approach, where the momentum and continuity equations are solved simultaneously. Since the amplitude of the bubble oscillations are very small, a simplified model is presented where the computational bubble is actually steady and its oscillations are represented purely with time-dependent boundary conditions. A numerical comparison with the moving domain model confirms that this simplification is perfectly reasonable for the class of problems investigated in this paper.

math.NA↗

arXiv2022

On the design of scalable networks rejecting first order disturbances

This paper is concerned with the problem of designing distributed control protocols for network systems affected by delays and disturbances consisting of a first-order polynomial component and a residual signal. Specifically, we propose the use of a multiplex architecture to design distributed control protocols to reject polynomial disturbances up to ramps and guarantee a scalability property that prohibits the amplification of residual disturbances. For this architecture, we give a sufficient condition on the control protocols to guarantee scalability and ramps rejection. The effectiveness of the result, which can be used to study networks of nonlinearly coupled nonlinear agents, is illustrated via a robot formation control problem.

eess.SY↗

arXiv2022

External control of a genetic toggle switch via Reinforcement Learning

We investigate the problem of using a learning-based strategy to stabilize a synthetic toggle switch via an external control approach. To overcome the data efficiency problem that would render the algorithm unfeasible for practical use in synthetic biology, we adopt a sim-to-real paradigm where the policy is learnt via training on a simplified model of the toggle switch and it is then subsequently exploited to control a more realistic model of the switch parameterized from in-vivo experiments. Our in-silico experiments confirm the viability of the approach suggesting its potential use for in-vivo control implementations.

eess.SY↗

arXiv2022

A smart electric bike for smart cities

This is a Masters Thesis completed at University College Dublin, Ireland in 2017 which involved augmenting an off-the-shelf electric bike with sensors to enable new services to be delivered to cyclists in cities. The application of primary interest was to control the cyclist's ventilation rate based on the concentration of local air pollutants. Detailed modelling and system design is presented for our Cyberphysical system which consisted of a modified BTwin e-bike, Cycle Analyst sensors, the cyclist themselves, a Bluetooth connected smartphone and our algorithms. Control algorithms to regulate the proportion of power the cyclist provided as a proxy for their ventilation rate were proposed and validated in a basic way, which were later proven significantly further in Further Work (see IEEE Transactions on Intelligent Transportation Systems paper: https://ieeexplore.ieee.org/abstract/document/8357977). The basic idea was to provide more electrical assistance to cyclists in areas of high air pollution to reduce the cyclist ventilation rate and thereby the amount of air pollutants inhaled. This presents an interesting control challenge due to the human-in-the-loop characteristics and the potential for impactful real life applications. A background literature review is provided on energy as it relates to cycling and some other applications are also discussed. A link to a video which demonstrates the system is provided, and also to a blog published by IBM Research about the system.

cs.MA↗

arXiv2022

Anomalous sorption kinetics of self-interacting particles by a spherical trap

In this paper we propose a computational framework for the investigation of the correlated motion between positive and negative ions exposed to the attraction of a bubble surface that mimics the (oscillating) cell membrane. The correlated diffusion of surfactants is described by a Poisson-Nernst-Planck (PNP) system, in which the drift term is given by the gradient of a potential which includes both the effect of the bubble and the Coulomb interaction between the carriers. The latter term is obtained from the solution of a self-consistent Poisson equation. For very short Debye lengths one can adopt the so called Quasi-Neutral limit which drastically simplifies the system, thus allowing for much faster numerical simulations. The paper has four main objectives. The first one is to present a PNP model that describes ion charges in presence of a trap. The second one is to provide benchmark tests for the validation of simplified multiscale models under current development [1]. The third one is to explore the relevance of the term describing the interaction among the apolar tails of the anions. The last one is to quantitatively explore the validity of the Quasi-Neutral limit by comparison with detailed numerical simulation for smaller and smaller Debye lengths. In order to reach these goals, we propose a simple and efficient Alternate Direction Implicit method for the numerical solution of the non-linear PNP system, which guarantees second order accuracy both in space and time, without requiring solution of nonlinear equation at each time step. New semi-implicit scheme for a simplified PNP system near quasi neutrality is also proposed.

physics.comp-ph↗

arXiv2022

On a probabilistic approach to synthesize control policies from example datasets

This paper is concerned with the design of control policies from example datasets. The case considered is when just a black box description of the system to be controlled is available and the system is affected by actuation constraints. These constraints are not necessarily fulfilled by the (possibly, noisy) example data and the system under control is not necessarily the same as the one from which these data are collected. In this context, we introduce a number of theoretical results to compute a control policy from example datasets that: (i) makes the behavior of the closed-loop system similar to the one illustrated in the data; (ii) guarantees compliance with the constraints. We recast the control problem as a finite-horizon optimal control problem and give an explicit expression for its optimal solution. Moreover, we turn our findings into an algorithmic procedure. The procedure gives a systematic tool to compute the policy. The effectiveness of our approach is illustrated via a numerical example, where we use real data collected from test drives to synthesize a control policy for the merging of a car on a highway.

math.OC↗

arXiv2021

High Order Semi-implicit WENO Schemes for All Mach Full Euler System of Gas Dynamics

In this paper, we propose a new high order semi-implicit scheme for the all Mach full Euler equations of gas dynamics. Material waves are treated explicitly, while acoustic waves are treated implicitly, thus avoiding severe CFL restrictions for low Mach flows. High order accuracy in time is obtained by semi-implicit temporal integrator based on the IMEX Runge-Kutta (IMEX-RK) framework. High order in space is achieved by finite difference WENO schemes with characteristic-wise reconstructions adapted to the semi-implicit IMEX-RK time discretization. Type A IMEX schemes are constructed to handle not well-prepared initial conditions. Besides, these schemes are proven to be asymptotic preserving and asymptotically accurate as the Mach number vanishes for well-prepared initial conditions. Divergence-free property of the time-discrete schemes is proved. The proposed scheme can also well capture discontinuous solutions in the compressible regime, especially for two dimensional Riemann problems. Numerical tests in one and two space dimensions will illustrate the effectiveness of the proposed schemes.

math.NA↗