Alexander Fradkov

• Doctor of Engineering
• Head of Lab at Russian Academy of Sciences

The problem of suboptimality under bounded disturbances for the adaptive systems based on speed-graadient approach is discussed. A formulation of the estimated optimality of nonlinear nonlinearly parametrized adaptive control systems is given and sufficient conditions for the estimated optimality in a specified uncertainty class are described for a...

A version of the speed-gradient evolution models for systems obeying the maximum information entropy principle developed by H. Haken in his book of 1988 is proposed in this article. An explicit relation specifying system dynamics for general linear constraints is established. Two versions of the human brain entropy detailed balance-breaking model a...

The brain-computer interface is a complex system that allows you to control external electronic devices using brain activity. This system includes several elements – a device for reading brain activity signals, a hardware and software complex that processes and analyzes these signals, and a control object. The main challenge here is the development...

Motivated by distributed statistical learning over uncertain communication networks, we study distributed stochastic optimization by networked nodes to cooperatively minimize a sum of convex cost functions. The network is modeled by a sequence of time-varying random digraphs with each node representing a local optimizer and each edge representing a...

This issue of Cybernetics and Physics (CAP) journal contains a part of the proceedings of the 11th International Conference on Physics and Control (PhysCon 2024) held on Sept. 9-12, 2024 at Kadir Has University in Istanbul. Brief information about PhysCon 2024 as well as the abstracts of the plenary talks and of the papers published in this issue o...

A new scientific field is introduced and discussed, named cybernetical neuroscience, which studies mathematical models adopted in computational neuroscience by methods of cybernetics -- the science of control and communication in a living organism, machine and society. It also considers the practical application of the results obtained when studyin...

This paper investigates the formation of vibration fields in a mechatronic setup driven by dual induction motors, relying on the controlled synchronization of unbalanced rotors. The proposed algorithm enables precise control over rotor speeds and phase shifts. Experimental results from a multi-resonance vibration laboratory setup demonstrate this a...

This paper delves into the challenge of controlling the multiple synchronizations in mechatronic vibration machines featuring a duo of unbalanced rotors. Its primary aim is to not only attain specific rotation speeds but also to ensure the desired phase shift between these rotors. To tackle this issue, the paper employs a control law integrating cr...

In this paper, we propose a method for identifying the parameters of the multispecies Lotka-Volterra model based on sampled data. The conditions (nonhyperplanarity, recurrence) under which the “Stripe” algorithm achieves the identification goals are found. The relation between nonhyperplanar recurrent trajectories and the persistent excitation cond...

This paper considers one of the problems that arise in the developing of the ergatic brain-computer interfaces. This technology allows a person to control various mechatronic systems through the "power of thought", i.e. based on the registration of electrical activity of the brain. The problem is the complexity and poor knowledge of the brain. To d...

The milestones of the history of the scientific school on cybernetics (the School), established in 1959 by outstanding scientist V.A. Yakubovich at Leningrad State University (LSU), are presented. The connections of the School with other Russian and foreign scientific schools in related fields are outlined.

The paper is devoted to the parameter identification problem for two-neuron FitzHugh-Nagumo models under condition when only one variable, namely, the membrane potential, is measured. Another practical assumption is that both variable derivatives cannot be measured. Finally, it is assumed that the sensor measuring the membrane potential is imprecis...

The paper is devoted to the problem of parameter identification of two FitzHugh-Nagumo neuron models. The FitzHugh-Nagumo model is a simplification of the Hodgkin-Huxley model and it is very valuable for using on practice thanks to its simplicity. However, within an experiment only one variable of the FitzHugh-Nagumo model, the membrane potential,...

In the paper, a brief history of life and work of celebrated Russian mathematician Lev Meerovich Bregman (the author of Bregman divergence and Bregman method) is exposed. The list of Bregman’s main publications is given.

In the paper, a brief history of life and work of the celebrated Russian mathematician Boris Teodorovich Polyak is exposed. The list of Polyak’s main publications is given.

An approach to control of invariant sets of quasi-polynomial nonlinear systems in the presence and absence of bounded uncertainty (disturbances) in the model is proposed. The control strategy is based on introduction of an invariant functional for uncontrolled system and posing the control task as achieving the desired value of the invariant functi...

With the digitalization of mechatronic systems in the conditions of a shortage of available bandwidth of digital communication channels, the problem of ensuring the transfer of information between various components of the system can arise. This problem can be especially challenging in the observation and control of spatially distributed objects du...

Increasing the productivity of technological operations is a current task of modern science. The introduction of modern industrial equipment control systems is associated with the digitalization and computerization of enterprises. Vibration technology is one of the common types of industrial equipment used for screening, crushing, vibratory movemen...

In the article the history of cybernetics and artificial intelligence in the world and, particularly in the USSR is outlined starting from the 1940s-1950s. The rapid development of these areas in the 1960s is described in more detail. Special attention is paid to the results of Leningrad (St. Petersburg) researchers, particularly to the work of Vla...

In the paper, a simple discrete dynamical model for the dynamics of two antagonistic parties (opponents) under iterated sanctions and counter-sanctions is proposed. The model is inspired by the Osipov-Lanchester model for combats. Simple stability criteria are derived both for the full information case and for the stochastic uncertainty case. A cyb...

We develop and analyze a new method for manipulation of energy in a quantum harmonic oscillator using coherent, e.g., electromagnetic, field and incoherent control. Coherent control is typically implemented by shaped laser pulse or tailored electromagnetic field. Incoherent control is implemented by engineered environment, whose mean number of exci...

The paper studies robustness with respect to time-sampling of the energy regulation for one-dimensional sine-Gordon system. Such a problem is a new to control of invariants for hyperbolic partial differential equations (PDEs). In the absence of analytic results, the problem is studied numerically. The properties of four sampled-data algorithms are...

In the paper a simple discrete dynamical model for dynamics of two antagonistic agents (opponents) under iterated sanctions and counter-sanctions is proposed. The model is inspired with Osipov-Lanchester model for combats. Simple stability criteria are derived both for the full information case and for stochastic uncertainty case. The results provi...

Prehistory and history of the Cybernetics and Physics journal are outlined on occasion of its ten years jubilee. Recent trends in the scope of the journal are discussed.

The obituary of Professor Arkadii Gelig, who passed away on October 6, 2021. The English translation is provided as linked data.

The paper is devoted to development of the speed-gradient method in the IPME RAS in 1986–2021 and its applications to the problems of mechanical engineering.KeywordsSpeed gradientMechanical engineeringNonlinear dynamicsControlAdaptationIdentificationEnergyOscillations

In the paper, a new adaptive model of a neuron based on the Hindmarsh–Rose third-order model of a single neuron is proposed. The learning algorithm for adaptive identification of the neuron parameters is proposed and analyzed both theoretically and by computer simulation. The proposed algorithm is based on the Lyapunov functions approach and reduce...

The paper is devoted to the problem of controlling the rotation speed of unbalanced rotors of a vibration machine. The solution to this problem is important for vibration technologies, such as transportation and mixing of bulk media. Since the characteristics of the rotor drives can vary in the wide range depending on the mode (operating rotation s...

In this paper the implementation of the speed-gradient single or multiple synchronization control algorithm with learning for a two-rotor vibration setup is considered. The main contribution of the paper is demonstration of possibility of neural network control of vibration setups under uncertainty. We propose the structure of the learning control...

In the paper, the adaptive synchronization problem is studied for a class of time-varying nonlinear systems. The only assumption imposed is the boundedness of the rate of change of the controlled system parameters, while the initial uncertainty can be quite large. The adaptation algorithms in the discrete-time form are derived based on adaptive con...

The paper is devoted to application of Bregman divergence to nonlinear adaptive control. Using Bregman divergence instead of quadratic function leads to a new class of Lyapunov functions in adaptive control that can be called Lyapunov-Bregman functions. An extended control algorithms design scheme is proposed and the properties of the designed cont...

In the paper the adaptive synchronization problem is studied for a class of time-varying non-linear systems. A number of approaches to the control of such systems are based on the construction of an internal model of parameter variations. In this paper, the only assumption imposed is the boundedness of the rate of change of the controlled system pa...

The problem of the equidistant deployment of mobile agents on a line segment is studied. It is assumed that agent dynamics are modeled by linear second-order models. Two types of control protocols are studied: with and without relative velocity measurements. For any positive damping coefficient of agents we propose a control protocol that ensures t...

Introduction: The COVID-19 pandemic which began in 2020 and has taken more than five million lives has become a threat to the very existence of mankind. Therefore, predicting the spread of COVID-19 in each individual country is a very urgent task. The complexity of its solution is due to the requirement for fast processing of large amounts of data...

This article provides a historical perspective of the field of adaptive control over the past seven decades and its intersection with learning. A chronology of key events over this large time-span, problem statements that the field has focused on, and key solutions are presented. Fundamental results related to stability and robustness of adaptive s...

The problem of synchronization in networks of linear systems with nonlinear diffusive coupling and a connected undirected graph is studied. By means of a coordinate transformation, the system is reduced to the form of mean-field dynamics and a synchronization-error system. The network synchronization conditions are established based on the stabilit...

This paper is devoted to the adaptive synchronization problem in the heterogeneous Hindmarsh–Rose neuronal networks. Heterogeneity is a natural property of biological neuronal networks, as each neuron has its own physiological characteristics, which may differ from other neurons within the population. Therefore, the study of the effect of heterogen...

The survey examines the current state of the speed gradient method, developed in the1970–80s for synthesizing control and adaptation algorithms in nonlinear systems, as well asnumerous applications of the method to solving scientific and engineering problems. Briefinformation about speed gradient algorithms and conditions of their applicability, op...

This article provides a historical perspective of the field of adaptive control over the past seven decades and its intersection with learning. A chronology of key events over this large time-span, problem statements that the field has focused on, and key solutions are presented. Fundamental results related to stability, robustness, and learning ar...

Presents information on the European Control Conference 2020.

In this paper, a method for forming the neuro-feedback (NFB) signal is suggested. The implementation of the method is based on the design of an adaptive model of subjects' neural activity in the form of a vector autoregression (VAR) model for capturing the spatio-temporal dynamics of an electroencephalogram (EEG). The adaptive model parameter adjus...

The paper deals with the navigation data exchange between two satellites moving in a swarm. It is focused on the reduction of the inter-satellite demanded communication channel capacity taking into account the dynamics of the satellites relative motion and possible erasures in the channel navigation data. The feedback control law is designed ensuri...

The paper is focused on the navigation data exchange between two satellites moved in a swarm. The feedback control law is designed ensuring regulation of the relative satellites motion. The adaptive binary coding/decoding procedure for data transmission over the limited capacity communication channel is proposed and studied for the cases of ideal a...

This work is primarily aimed at studying the reasons for the formation of the synchronous regimes of functioning of neural populations in the central nervous system of human or animal. It is well known that the synchronization of large number of the neurons in the central nervous system plays a key role in the formation of the brain waves. It was a...

We construct an adaptive controller for a linear minimum-phase system of an arbitrary relative degree with an unknown bounded disturbance and dynamically quantized measurements. The key novelty is the extension of the shunting method (parallel feedforward compensator) to plants with bounded disturbances. This method leads to an augmented system of...

The possibility to predict the spread of COVID-19 in Russia is studied. Particular goal is to predict the time instant when the number of infected achieves its maximum (peak). Such a partial prediction allows one to use simple epidemoics models: SIR and SEIR. Simplicity and small number of parameters are significant advantages of SIR and SEIR model...

This brief is devoted to the experimental study of possibilities for control of the phase shift between two vibration actuators. The control laws for frequency stabilization simultaneously with the prescribed phase shift between the rotors angular positions are proposed and experimentally studied by means of the mechatronic vibration test bed. It i...

Robustness of stability with respect to external perturbations is an important property characterizing the ability of the dynamics to counteract the influence of uncertainties. In the present paper such a property is investigated for the class of passive and strictly passive systems, which have several invariant compact and globally attracting subs...

This paper considers the discrete-time problem of deploying agents on a line segment under delay in communication channels and switching and also under incomplete information about the value of the delay and the law of switching. It is shown that neither delay nor switching affect the convergence of the agents' states to the uniform allocation on t...

The present investigation focuses on the output energy control of the nonlinear sine-Gordon model in a practical situation where only spatially sampled sensing and actuation are available. The speed-gradient method that has corroborated its utility for the sine-Gordon model, controlled through the manipulable parameters of the external field and bo...

Control theory in the USSR after WW2 achieved serious successes in such fields as optimal control, absolute stability, delay systems, pulse and relay control. Later there was a huge peak of breakthrough research on adaptation, learning and pattern recognition, starting at 1960th. Next approach to control under uncertainty relates to robustness; the...

Machine learning belongs to the crossroad of cybernetics (control science) and computer science. It is attracting recently an overwhelming interest, both of professionals and of the general public. In the talk a brief overview of the historical development of the machine learning field with a focus on the development of mathematical apparatus in it...

The desynchronization problems in oscillatory networks is considered. A new desynchronization notion is introduced and desynchronization conditions are provided. The desynchronization notion is formulated in terms of Yakubovich oscillatority of the auxiliary synchronization error system. As an example, the network of diffusively coupled FitzHugh-Na...

We construct an adaptive controller for a linear minimum-phase system of an arbitrary relative degree with an unknown bounded disturbance and dynamically quantized measurements. The key novelty is the extension of the shunting method (parallel feedforward compensator) to plants with bounded disturbances. This method leads to an augmented system of...

An attempt is made to use the simplest epidemic models: SIR and SEIR to predict the spread of COVID-19 in Russia. Simplicity and a small number of parameters are very significant advantages of SIR and SEIR models in conditions of a lack of numerical initial data and structural incompleteness of models. The forecast of distribution of COVID-19 in Ru...

The paper is devoted to the adaptive control problem of synchronization in the network of Hindmarsh-Rose neurons. The case of identical neurons was predominantly considered in the previous studies, which are concerned with the synchronization of the biological neuron models. However, the natural networks of biological neurons are heterogeneous, sin...

A new approach to the design of neurofeedback systems based on using Artificial Intelligence (AI) tools is proposed. The concept of control models of biological neural networks, and the setup including equipment and software tools developed in IPME RAS in order to implement the proposed concept is described. as well as the AI methods and programs p...

The desynchronization problems in oscillatory networks is considered. A new desynchronization notion is introduced and desynchronization conditions are provided. The desynchronization notion is formulated in terms of Yakubovich oscillatority of the auxiliary synchronization error system. As an example, the network of diffusively coupled FitzHugh-Na...

Dynamical processes in nature and technology are usually described by continuous-or discrete-time dynamical models, which have the form of nonlinear stochastic differential or difference equations. Hence, a topical problem is to develop effective methods for a simpler description of dynamical systems. The main requirement to simplification methods...

The influence of an external loading on nonlinear dynamic processes in a layer having a di-atomic crystalline structure is studied. An asymptotic procedure is developed to transform the solution of the initial two-dimensional problem to the solution to the coupled one-dimensional nonlinear equations for longitudinal macrostrains and variations in t...

We study the spatio-temporal dynamics of a multiplex network of delay-coupled FitzHugh–Nagumo oscillators with non-local and fractal connectivities. Apart from chimera states, a new regime of coexistence of slow and fast oscillations is found. An analytical explanation for the emergence of such coexisting partial synchronization patterns is given....

Introduction: The motion of many real world systems is described by essentially non-linear and non-stationary models. A number of approaches to the control of such plants are based on constructing an internal model of non-stationarity. However, the non-stationarity model parameters can vary widely, leading to more errors. It is only assumed in this...

The deployment of the agents over the line segment under protocols with communication delays and switching is studied. It is assumed that no information about the value of the communication delay and no information about switching policy in the communication graph is available. It is shown that neither delay values nor switching policy in a natural...

Introduction: The international RoboCup soccer tournaments for robots have been held since the mid-1990s and have attracted a lot of attention from universities all over the world. Their goal is to develop scientific and engineering research in the areas of robotics, artificial intelligence, computer vision, navigation, group and multi-agent intera...

New version of passification with respect to given input and output is proposed. It can be considered as an extension of passification introduced in (Fradkov, IEEE CDC 2008). Necessary and sufficient conditions for the proposed version of passification are obtained for linear SISO systems. Solution is based on KYP lemma and Meerov's results concern...

Biological systems are often composed of various heterogeneous units. It is an important problem to investigate how this heterogeneity affects the network dynamics, namely synchronization phenomenon. We study the heterogeneous networks of FitzHugh–Nagumo oscillators with diffusive coupling and present sufficient conditions for synchronization in th...

In the paper the energy control problems for Frenkel–Kontorova Model are posed and their connection to the pendula chains control is discussed. Speed-gradient based energy control algorithm is proposed and analyzed. Simulation results illustrating the convergence of the proposed algorithm are presented.

In this paper, we present and numerically study an adaptive coding procedure for data transfer among quadrotors moving in a formation. The quadrotor’s parameters are identified using experimental data from a digital communication channel with limited bandwidth. We compare the obtained results with theoretical expectations and illustrate the efficie...

The output energy control is developed for 1-D string model with fixed endpoints. It is considered a practical situation where a finite number of spatially-sampled sensing and actuation are available. First, the speed-gradient method is generalized in the present framework to pump/dissipate the energy of underlying model to a desired level provided...

A new control problem is posed and solved: regulation problem for the one-dimensional Klein-Gordon and semilinear wave equations with Neumann boundary conditions in the case when the control acts at both ends of the space interval (“two-point control”). A control algorithm based on the speed-gradient method is proposed. The global exponential stabi...

This paper studies the influence of the coupling type on the network desynchro-nization and proposes the algorithms to control it. We consider the FitzHugh-Nagumo network with random topology and different coupling values for different nodes. The simple mean field control which is similar for all nodes can be applicable for desynchronization of Fit...