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

Anton V Proskurnikov

Doctor of Philosophy

## About

199

Publications

30,485

Reads

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2,591

Citations

Citations since 2017

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 (199)

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...

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...

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...

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...

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...

Many multi-agent control algorithms and dynamic agent-based models arising in natural and social sciences are based on
the principle of iterative averaging. Each agent is associated to a value of interest, which may represent, for instance, the opinion of an individual in a social group, the velocity vector of a mobile robot in a
flock, or the mea...

Many multi-agent control algorithms and dynamic agent-based models arising in natural and social sciences are based on the principle of iterative averaging. Each agent is associated to a value of interest, which may represent, for instance, the opinion of an individual in a social group, the velocity vector of a mobile robot in a flock, or the meas...

We investigate the problem of practical robust output regulation: keeping the state of an uncertain dynamical system uniformly bounded while the system output eventually resides within a prescribed ball centered at a desired target. We consider uncertain systems that are possibly nonlinear and the uncertainty of the linear part is modeled element-w...

The method of nonlocal reduction has been proposed by G.A. Leonov in the 1980s for stability analysis of nonlinear feedback systems. The method combines the comparison principle with Lyapunov techniques. A feedback system is investigated via its reduction to a simpler "compar-ison" system, whose dynamics can be studied efficiently. The trajectories...

Whereas classical control theory provides many methods for designing continuous-time feedback controllers, nowadays control algorithms are implemented on digital platforms and have to be designed in sampled time. Approaches to sampled-time control design are based on either discretization of the plant enabling discrete-time controller synthesis, or...

We introduce the concept of Bounded Input Dissipativity (BID) for the characterization from an energy perspective of linearized models of nonlinear circuit blocks. Such linearized models are commonly employed in the design of large systems to approximate circuit blocks that operate in the neighborhood of some well-defined and asymptotically stable...

Roll damping is an important problem of ship motion control since excessive roll motion may cause motion sickness of human occupants and damage fragile cargo. Actuators used for roll damping (fins, rudders and thrusters) inevitably create a rotating yaw moment, interfering thus with the vessel's autopilot (heading control system). To reach and main...

A constructive tool of nonlinear control systems design, the method of Control Lyapunov Functions (CLF) has found numerous applications in stabilization problems for continuoustime, discrete-time and hybrid systems. In this paper, we address the fundamental question: given a CLF, corresponding to the continuous-time controller with some predefined...

The classical field of Social Network Analysis (SNA) considers societies and social groups as networks, assembled of social actors (individuals, groups or organizations) and relationships among them, or social ties. From the systems and control perspective, a social network may be considered as a complex dynamical system where an actor's attitudes,...

Balance theory has advanced with interdisciplinary contributions from social science, physical science, engineering, and mathematics. The common focus of attention is social networks in which every individual has either a positive or negative, cognitive or emotional, appraisal of every other individual. The current frontier of work on balance theor...

In this paper, we consider the mean-field model of noisy bounded confidence opinion dynamics under exogenous influence of static radical opinions. The long-term behavior of the model is analyzed by providing a sufficient condition for exponential convergence of the dynamics to stationary state. The stationary state is also characterized by a global...

The impulsive Goodwin oscillator (IGO) is nowadays an established mathematical model of pulsatile regulation that is suitable for e.g. capturing non-basal regulation of testosterone, cortisol, and growth hormone. The model consists of a continuous linear time-invariant block closed by a nonlinear pulse-modulated feedback. The hybrid closed-loop dyn...

The classical field of social network analysis (SNA) considers societies and social groups as networks, assembled of social actors (individuals, groups or organizations) and relationships among them, or social ties. From the systems and control perspective, a social network may be considered as a complex dynamical system where an actor’s attitudes,...

n this paper, we examine dynamics of multidimensional control systems obtained as feedback interconnections of stable linear blocks and periodic nonlinearities. The simplest of such systems is the model of mathematical pendulum (with viscous friction), so we call such systems pendulum-like. Other examples include, but are not limited to, coupled vi...

The paper is concerned with the rate at which a discrete-time, deterministic, and possibly large network of nonlinear systems generates information, and so with the minimum rate of data transfer under which the addressee can maintain the level of awareness about the current state of the network. While being aimed at development of tractable techniq...

Lur'e-type systems with periodic nonlinearities arise in many physical and engineering applications, from the simplest model of a pendulum to large-scale networks of power generators or biological oscillators. Periodic nonlinearities often cause the existence of multiple stable and unstable equilibria, which can lead to presence of "hidden attracto...

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 1040s. 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...

Periodic phenomena and oscillations are fundamental characteristics of the dynamics of living systems at all levels of organization, from a single cell to complex organisms. In spite of the recent progress in understanding biological oscillators and clocks, most of the aspects of their control, observation, and identification still remain nearly un...

In this article, we study the nonlinear Fokker-Planck (FP) equation that arises as a mean-field (macroscopic, Eulerian) 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 co...

In this paper, systems of nonlinear integro-differential Volterra equations are examined that can be represented as feedback interconnections of linear time-invariant block and periodic nonlinearities. The interest in such systems is motivated by their numerous applications in mechanical, electrical and communication engineering; examples include,...

Whereas development of mathematical models describing the endocrine system as a whole remains a challenging problem, visible progress has been demonstrated in modeling its subsystems, or axes. Models of hormonal axes portray only the most essential interactions between the hormones and can be described by low-order
systems of differential equations...

Optimal decisions on the distribution of finite resources are explicitly structured by mathematical models that specify relevant variables, constraints, and objectives. Here we report analysis and evidence that implicit mathematical structures are also involved in group decision-making on resource allocation distributions under conditions of uncert...