# Anton V ProskurnikovPolitecnico di Torino | polito · DET - Department of Electronics and Telecommunications

Anton V Proskurnikov

Doctor of Philosophy

## About

228

Publications

38,722

Reads

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3,470

Citations

Introduction

I am an applied mathematician working in the fields of nonlinear dynamics, control theory and network science. My interests include, but are not limited to: dynamics over complex networks,
agent-based modeling in economics and sociology, distributed algorithms for multi-agent coordination, biological oscillators and modeling of biological rhythms, stability and oscillations of nonlinear systems, robust and optimal control.

Additional affiliations

February 2019 - present

September 2016 - February 2019

November 2014 - December 2018

Education

October 2010 - June 2022

**St. Petersburg State University**

Field of study

- Theoretical computer science and cybernetics

## Publications

Publications (228)

This letter introduces a new multidimensional extension of the Hegselmann-Krause (HK) opinion dynamics model, where opinion proximity is not determined by a norm or metric. Instead, each agent trusts opinions within the Minkowski sum +, where is the agent’s current opinion and is the confidence set defining acceptable deviations. During each iterat...

This work extends the recent opinion dynamics model from Cheng et al., emphasizing the role of group pressure in consensus formation. We generalize the findings to incorporate social influence algorithms with general time-varying, opinion-dependent weights and multidimensional opinions, beyond bounded confidence dynamics. We demonstrate that, with...

The Impulsive Goodwin's Oscillator (IGO) is a mathematical model of a hybrid closed-loop system. It arises by closing a special kind of continuous linear positive time-invariant system with impulsive feedback, which employs both amplitude and frequency pulse modulation. The structure of IGO precludes the existence of equilibria, and all its solutio...

Recent studies on stability and contractivity have highlighted the importance of semi-inner products, which we refer to as ``pairings'', associated with general norms. A pairing is a binary operation that relates the derivative of a curve's norm to the radius-vector of the curve and its tangent. This relationship, known as the curve norm derivative...

This paper introduces a new multidimensional extension of the Hegselmann-Krause (HK) opinion dynamics model, where opinion proximity is not determined by a norm or metric. Instead, each agent trusts opinions within the Minkowski sum $\xi+\mathcal{O}$, where $\xi$ is the agent's current opinion and $\mathcal{O}$ is the confidence set defining accept...

This paper addresses a design procedure of pulse-modulated feedback control solving a dosing problem originally defined for implementation in a manual mode. Discrete dosing, as a control strategy, is characterized by exerting control action on the plant in impulsive manner at certain time instants.Dosing applications appear primarily in chemical in...

The history of the alternating projection method for finding a common point of several convex sets in Euclidean space goes back to the well-known Kaczmarz algorithm for solving systems of linear equations, which was devised in the 1930s and later found wide applications in image processing and computed tomography. An important role in the study of...

Рассматривается обобщение модели динамики мнений с ограниченным
доверием на случай многомерных мнений. Многомерное мнение характеризует
позицию человека по теме, включающей несколько подтем, либо его отношение к
некоторому объекту или событию, описываемому набором характеристик. В отличие
от имеющихся моделей, доверительное множество агента не обяз...

Financial networks are characterized by complex structures of mutual obligations. These obligations are fulfilled entirely or in part (when defaults occur) via a mechanism called clearing, which determines a set of payments that settle the claims by respecting rules such as limited liability, absolute priority, and proportionality (pro-rated paymen...

In this paper we analyze the resilience of a network of banks to joint price fluctuations of the external assets in which they have shared exposures, and evaluate the worst-case effects of the possible default contagion. Indeed, when the prices of certain external assets either decrease or increase, all banks exposed to them experience varying degr...

At the beginning of this century, Hegselmann and Krause proposed a dynamical model for opinion formation that is referred to as the Bounded Confidence Opinion Dynamics (BCOD) model and that has since attracted a wide interest from different research communities. The model can be viewed as a dynamic network, in which each agent is endowed with a sta...

Existence of periodical solutions, i.e. cycles, in the Impulsive Goodwin's Oscillator (IGO) with the continuous part of an arbitrary order m is considered. The original IGO with a third-order continuous part is a hybrid model that portrays a chemical or biochemical system composed of three substances represented by their concentrations and arranged...

Critical questions in dynamical neuroscience and machine learning are related to the study of continuous-time neural networks and their stability, robustness, and computational efficiency. These properties can be simultaneously established via a contraction analysis. This paper develops a comprehensive non-Euclidean contraction theory for continuou...

Control systems that arise in phase synchronization problems are featured by infinite sets of stable and unstable equilibria, caused by presence of periodic nonlinearities. For this reason, such systems are often called “pendulum-like”. Their dynamics are thus featured by multi-stability and cannot be examined by classical methods that have been de...

This paper proposes a novel dynamical model for determining clearing payments in financial networks. We extend the classical Eisenberg-Noe model of financial contagion to multiple time periods, allowing financial operations to continue after initial pseudo defaults, thus permitting nodes to possibly recover and eventually fulfill their liabilities....

We consider a decentralized convex unconstrained optimization problem, where the cost function can be decomposed into a sum of strongly convex and smooth functions, associated with individual agents, interacting over a static or time-varying network. Our main concern is the convergence rate of first-order optimization algorithms as a function of th...

In the Impulsive Goodwin's oscillator (IGO), a continuous positive linear time-invariant (LTI) plant is controlled by an amplitude-and frequency-modulated feedback into an oscillating solution. Self-sustained oscillations in the IGO model have been extensively used to portray periodic rhythms in endocrine systems, whereas the potential of the conce...

Consensus among autonomous agents is a key problem in multi-agent control. In this paper, we consider averaging consensus policies over time-varying graphs in presence of unknown but bounded communication delays. It is known that consensus is established (no matter how large the delays are) if the graph is periodically, or
uniformly
quasi-strongl...

We consider a decentralized convex unconstrained optimization problem, where the cost function can be decomposed into a sum of strongly convex and smooth functions, associated with individual agents, interacting over a static or time-varying network. Our main concern is the convergence rate of first-order optimization algorithms as a function of th...

The takeoff point for this paper is the voluminous body of literature addressing recursive betting games with expected logarithmic growth of wealth being the performance criterion. Whereas almost all existing papers involve use of linear feedback, the use of nonlinear control is conspicuously absent. This is epitomized by the large subset of this l...

The impulsive Goodwin's oscillator (IGO) is a hybrid model composed of a third-order continuous linear part and a pulse-modulated feedback. This paper introduces a design problem of the IGO to admit a desired periodic solution. The dynamics of the continuous states represent the plant to be controlled, whereas the parameters of the impulsive feedba...

While monotone operator theory is traditionally studied on Hilbert spaces, many interesting problems in data science and machine learning arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as diagonally-weighted $\ell_1$ or $\ell_\infty$ norms. This paper provides a natural generalization of monotone operator...

The takeoff point for this paper is the voluminous body of literature addressing recursive betting games with expected logarithmic growth of wealth being the performance criterion. Whereas almost all existing papers involve use of linear feedback, the use of nonlinear control is conspicuously absent. This is epitomized by the large subset of this l...

Existence of periodical solutions, i.e. cycles, in the Impulsive Goodwin's Oscillator (IGO) with the continuous part of an arbitrary order m is considered. The original IGO with a third-order continuous part is a hybrid model that portrays a chemical or biochemical system composed of three substances represented by their concentrations and arranged...

Consider discrete-time linear distributed averaging dynamics, whereby a finite number of agents in a network start with uncorrelated and unbiased noisy measurements of a common state of the world modeled as a scalar parameter, and iteratively update their estimates following a non-Bayesian learning rule. Specifically, let every agent update her est...

Maneuvers of human-operated and autonomous marine vessels in the safety zone of drilling rigs, wind farms and other installations present a risk of collision. This article proposes an algorithmic toolkit that ensures maneuver safety, taking into account the restrictions imposed by ship dynamics. The algorithms can be used for anomaly detection, dec...

In this paper we examine stability of Lur’e-type systems arising as a feedback superpositions of infinite-dimensional linear blocks, described by integrodifferential Volterra equations, and periodic nonlinearities. Such systems have multiple equilibria, so traditional methods of stability investigation, defined for systems with single equilibrium a...

The celebrated S-Lemma was originally proposed to ensure the existence of a quadratic Lyapunov function in the Lur'e problem of absolute stability. A quadratic Lyapunov function is, however, nothing else than a squared Euclidean norm on the state space (that is, a norm induced by an inner product). A natural question arises as to whether squared no...

Consider discrete-time linear distributed averaging dynamics, whereby agents in a network start with uncorrelated and unbiased noisy measurements of a common underlying parameter (state of the world) and iteratively update their estimates following a non-Bayesian rule. Specifically, let every agent update her estimate to a convex combination of her...

We investigate the problem of practical output regulation , i.e., to design a controller that brings the system output in the vicinity of a desired target value while keeping the other variables bounded. We consider uncertain systems that are possibly nonlin-ear and the uncertainty of their linear parts is modeled element-wise through a parametric...

The current global financial system forms a highly interconnected network where a default in one of its nodes can propagate to many other nodes, causing a catastrophic avalanche effect. In this paper we consider the problem of reducing the financial contagion by introducing some targeted interventions that can mitigate the cascaded failure effects....

We provide a novel transcription of monotone operator theory to the non-Euclidean finite-dimensional spaces $\ell_1$ and $\ell_{\infty}$. We first establish properties of mappings which are monotone with respect to the non-Euclidean norms $\ell_1$ or $\ell_{\infty}$. In analogy with their Euclidean counterparts, mappings which are monotone with res...

This paper proposes a novel dynamical model for determining clearing payments in financial networks. We extend the classical Eisenberg-Noe model of financial contagion to multiple time periods, allowing financial operations to continue after possible initial pseudo defaults, thus permitting nodes to recover and eventually fulfil their liabilities....

The current global financial system forms a highly interconnected network where a default in one of its nodes can propagate to many other nodes, causing a catastrophic avalanche effect. In this letter we consider the problem of reducing the financial contagion by introducing some targeted interventions that can mitigate the cascaded failure effects...

This is my habilitation ("Doctor of Science") thesis, summarizing my most cited works on first-order, (or averaging) algorithms of multi-agent consensus, convergence of associated averaging inequalities, and applications to models of opinion dynamics. I started this journey in 2010 and it took me almost 12 years, but I promised to finish it to myse...

Modern financial networks are characterized by complex structures of mutual obligations. Such interconnections may propagate and amplify individual defaults, leading in some cases to financial disaster. For this reason, mathematical models for the study and control of systemic risk have attracted considerable research attention in recent years. One...

The recent progress of measurement devices and algorithms of inertial navigation opens up the perspective of deep integration between inertial navigation systems (INS) and dynamic positioning (DP) systems. In the literature, novel mathematical algorithms for INS-guided sensor fusion and sensor fault isolation have recently been proposed, aimed prim...

We consider a problem of self-synchronization in a system of vibro-exciters (rotors) installed on a common oscillating platform. This problem was studied by I.I. Blekhman and later by L. Sperling. Extending their approach, we derive the equations for a system of n rotors and show that, separating the slow and fast motions, the “slow” dynamics of th...

In this paper, we consider a delayed counterpart of the mathematical pendulum model that is termed sunflower equation and originally was proposed to describe a helical motion (circumnutation) of the apex of the sunflower plant. The “culprits” of this motion are, on one hand, the gravity and, on the other hand, the hormonal processes within the plan...

Critical questions in neuroscience and machine learning can be addressed by establishing strong stability, robustness, entrainment, and computational efficiency properties of neural network models. The usefulness of such strong properties motivates the development of a comprehensive contractivity theory for neural networks. This paper makes two set...

Slides of the conference presentation.

The recent progress of measurement devices and algorithms of inertial navigation opens up the perspective of deep integration between inertial navigation systems (INS) and dynamic positioning (DP) systems. In the literature, novel mathematical algorithms for INS-guided sensor fusion and sensor fault isolation have recently been proposed, aimed prim...

Towards a unified system theory of opinion formation and social influence Processes of information diffusion over social networks (for example, opinions spread and 2 beliefs formation) are attracting substantial interest to various disciplines ranging from behavioral sciences to mathematics and engineering. Since the opinions and behaviors of each...

This paper proposes a black-box behavioral modeling framework for analog circuit blocks operating under small-signal conditions around non-stationary operating points. Such variations may be induced either by changes in the loading conditions or by event-driven updates of the operating point for system performance optimization, e.g., to reduce powe...

muscles that affect a liquid flow [5]. Naturally, the muscles are neurally controlled and, in this case, act as actuators. A. Pulsatile endocrine regulation The endocrine system of an organism is constituted by glands communicating through hormone molecules as messengers [6]. Hormones are chemical blood-borne substances produced by the glands and r...

Structural balance is a classic property of signed graphs satisfying Heider's seminal axioms. Mathematical sociologists have studied balance theory since its inception in the 1940s. Recent research has focused on the development of dynamic models explaining the emergence of structural balance. In this paper, we introduce a novel class of parsimonio...

In this paper, we study a distributed parameter estimation problem in a large-scale network of communication sensors. The goal of the sensors is to find a global estimate of an unknown parameter minimizing, which minimizes some aggregate cost function. Each sensor can communicated to a few “neighbors”, furthermore, the communication channels have l...

Implicit neural networks, a.k.a., deep equilibrium networks, are a class of implicit-depth learning models where function evaluation is performed by solving a fixed point equation. They generalize classic feedforward models and are equivalent to infinite-depth weight-tied feedforward networks. While implicit models show improved accuracy and signif...

Consensus of autonomous agents is a benchmark problem in multi-agent control. In this paper, we consider continuous-time averaging consensus policies (or Laplacian flows) and their discrete-time counterparts over time-varying graphs in presence of unknown but bounded communication delays. It is known that consensus is established (no matter how lar...

The literature on attitudes toward objects includes seminal research on threat appraisals indicating that individuals locate an object in a multidimensional threat appraisal space defined by the object's perceived degree of being good or bad, weak or strong, and passive or active. We advance this research in three ways. First, we generalize the inf...

The paper is devoted to asymptotic behavior of synchronization systems, i.e. Lur’e–type systems with periodic nonlinearities and infinite sets of equilibrum. This class of systems can not be efficiently investigated by standard Lyapunov functions. That is why for synchronization systems several new methods have been elaborated in the framework of L...

Modern financial networks are characterized by complex structures of mutual obligations. Such interconnections may propagate and amplificate individual defaults, leading in some cases to financial disaster. For this reason, mathematical models for the study and control of systemic risk (the risk of severe instabilities on the system as a whole, due...

In this article, we study the nonlinear Fokker- Planck (FP) equation that arises as a mean-field (macroscopic) approximation of bounded confidence opinion dynamics, where opinions are influenced by environmental noises and opinions of radicals (stubborn individuals). The distribution of radical opinions serves as an infinite-dimensional exogenous i...

We propose a model of Markovian quantity flows on connected networks that relaxes several properties of the standard compartmental Markov process. The motivation of our generalization are social science applications of the standard model that do not comport with its steady state predictions. The proposed generalization relaxes the predictions that...

Consensus of autonomous agents is a benchmark problem in cooperative control. In this paper, we consider standard continuous-time averaging consensus policies (or Laplacian flows) over time-varying graphs and focus on robustness of consensus against communication delays. Such a robustness has been proved under the assumption of uniform quasi-strong...

Interpersonal influence estimation from empirical data is a central challenge in the study of social structures and dynamics. Opinion dynamics theory is a young interdisciplinary science that studies opinion formation in social networks and has a huge potential in applications, such as marketing, advertisement and recommendations. The term social i...

We consider a dynamic network of sensors that cooperate to estimate parameters of multiple targets. Each sensor can observe parameters of a few targets, reconstructing the trajectories of the remaining targets via interactions with “neighbouring” sensors. The multi-target tracking has to be provided in the face of uncertainties, which include unkno...

A new bidirectional decentralized control algorithm for vehicle platoons is proposed, which guarantees absence of collisions between the vehicles. The algorithm exploits an elegant parallel between vehicles platoon and chains of interconnected mass-spring-damper systems and the idea of barrier certificates. Stability and robustness properties of th...

Dynamics and control of processes over social networks, such as the evolution of opinions, social influence and interpersonal appraisals, diffusion of information and misinformation, emergence and dissociation of communities, are now attracting significant attention from the broad research community that works on systems, control, identification an...

Starting from pioneering works by Lur’e, Popov and Zames, global stability theory for nonlinear control systems has been primarily focused on systems with only one equilibrium. Global stability criteria for other kinds of attractors (such as e.g. infinite sets of equilibria) are not well studied and typically require special tools, primarily based...