Volodymyr Lynnyk

• PhD
• Research Associate at The Czech Academy of Sciences

The consensus problem of a multi-agent system with nonlinear second-order underactuated agents is addressed. The essence of the approach can be outlined as follows: the output is redesigned first so that the agents attain the minimum-phase property. The second step is to apply the exact feedback linearization to the agents. This transformation divi...

A control design for a linear large-scale interconnected system composed of identical subsystems is presented in this paper. The control signal of all subsystems is sampled. For different subsystems, the sampling times are not identical. Nonetheless, it is assumed that a bound exists for the maximal sampling time. The control algorithm is designed...

The conditions for the synchronization of three interconnected generalized Lorenz systems are given. The interconnection topology contains a loop. It is shown that, under certain conditions on the strength of the coupling of the systems, the full synchronization of all three systems is guaranteed. The results are illustrated by an example.

We develop and test one relatively simple enhancement of the classical model reduction method applied to a class of chemical networks with mass conservation properties. Both methods, being (i) the standard quasi-steady-state approximation (QSSA) and (ii) the novel so-called delayed-QSSA (D-QSSA) method, first proposed by Vejchodsky (2014), are exte...

The well-known bottleneck of systems pharmacology, i.e., systems biology applied to pharmacology, refers to the determination of model parameters from experimentally measured datasets. This paper represents the development of our earlier studies devoted to the inverse (ill-posed) problems of model parameter identification. The key feature of this r...

A synchronization algorithm of nonlinear complex networks composed of nonlinear nodes is designed. The main idea is to apply the exact feedback linearization of every node first, then applying methods for synchronization of linear complex networks. The nodes need not admit full exact feedback linearization, however, they are supposed to be minimum-...

The brain is processing information 24 hours a day. There are millions of processes proceeding in it accompanied by various spectra of rhythms. This paper tests the hypothesis that the slow delta rhythm excites the gamma rhythm oscillations. Unlike other papers, we determine the slow rhythm spectrum not at the hypothesis stage but during the experi...

An algorithm for synchronization of a network composed of interconnected Hindmarsh–Rose neurons is presented. Delays are present in the interconnections of the neurons. Noise is added to the controlled input of the neurons. The synchronization algorithm is designed using convex optimization and is formulated by means of linear matrix inequalities v...

An algorithm is presented for leader-following synchronization of a multi-agent system composed of linear agents with time delay. The presence of different delays in various agents can cause a synchronization error that does not converge to zero. However, the norm of this error can be bounded and this boundary is presented. The proof of the main re...

The consensus problem of a multi-agent system with nonlinear agents is solved. It is assumed only the outputs of the agents are measurable, in order to obtain the estimate of the state, the nonlinear Luenberger observer is applied. The control of the agents is based on the exact feedback linearization. The method is illustrated by an example.

To solve the discrete nonlinear observer problem, it is necessary to find a solution of a certain functional equation. The existence conditions of this functional equation have already been well established, nevertheless, they are rather restrictive. Moreover, less attention was paid to the design of numerical methods to find its solution. In this...

This paper is aimed to develop and test one novel and unexplored enhancement of the classical model reduction method applied to a class of biochemical networks. Both methods, being (i) the standard quasi-steady-state approximation (QSSA), and (ii) the so-called delayed-QSSA methods are extensively presented. Specially, the numerical issues related...

In the paper, an algorithm for synchronization of a neural network composed of interconnected Hindmarsh-Rose neurons is proposed. The interconnections of the neurons are subject to delays and an additive noise is present. The convex optimization is the tool for finding the synchronization control, the result is formulated using linear matrix inequa...

Consensus synchronization problem was solved for a multi-agent system composed of identical underactuated system. The method is based on using a collocated feedback combined with a choice of the fictitious output so that the agents are minimum-phase with this output. Then, a synchronizing control is found based on the transformed variables. The res...

An observer for a nonlinear biological system — biomass production in a bioreactor —is proposed. The specific growth rate is estimated. The key point of the observer design is finding a solution of a certain partial differential equation. Conditions guaranteeing existence of its solution are presented. The solution is approximated using finite elem...

The generalized synchronization of the complex network consisting of nodes being the chaotic systems via the auxiliary system approach is studied here. More specifically, the applicability of the auxiliary system approach to detect the generalized synchronization in the complex network consisting of unidirectional coupled chaotic systems in the cyc...

A detailed mathematical analysis of the two-dimensional hybrid model for the lateral dynamics of walking-like mechanical systems (the so-called hybrid inverted pendulum) is presented in this article. The chaotic behavior, when being externally harmonically perturbed, is demonstrated. Two rather exceptional features are analyzed. Firstly, the unpert...

Stabilization of a nonlinear large scale interconnected system is investigated. The system is linearized by the exact feedback linearization, then a procedure to reduce the complexity of the system is applied. This allows to find a controller for the linearized problem as a solution of an optimization problem whose dimension is equal to the dimensi...

This paper deals with a control of coupled nonlinear identical systems that admit full exact feedback input-output linearization. The subsystems are linearized using this nonlinear transformation. In the next step, an auxiliary low-dimensional system is derived whose stability implies stability of the original large-scale system. The control law is...

A simple hybrid mechanical system, tentatively called as the hybrid inverted pendulum, is studied. This study is motivated by the problem of the lateral stability of the planar walking strategies applied to a more realistic settings. Using numerical simulations, the influence of the lateral harmonic perturbations is studied as well. Some complex fe...

The problem of the consensus of multi-agent systems with identical nonlinear agents admitting exact feedback linearization is solved. A small-dimensional problem (with dimension of only one agent) is derived whose solution is used to solve the consensus problem with a large number of agents. This auxiliary problem is formulated using linear matrix...

Dynamics of the so-called hybrid inverted pendulum is studied here. Motivation is the lateral stability of the planar walking strategies applied to more realistic settings. The influence of the lateral harmonic forcing of the hybrid inverted pendulum is analyzed. It is shown numerically that reasonable sized forcing imposes the bounded oscillatory...

This paper focuses on the design of the novel chaotic masking scheme via message embedded synchronization. A general class of the systems allowing the message embedded synchronization is presented here, moreover, it is shown that the generalized Lorenz system belongs to this class. Furthermore, the secure encryption scheme based on the message embe...

An approach to generate the pseudo random number sequences from a single generalized Lorenz system (GLS) is proposed in this paper. New algorithms are introduced for the binary sequence generation based on the GLS. Basic statistical tests and security analysis of the pseudo random number generators (PRNG) based on the GLS are also provided. The res...

This paper studies synchronization of a dynamic complex network consisting of nodes being generalized Lorenz chaotic systems and connections created with transmitted synchronizing signals. The focus is on the robustness of the network synchronization with respect to its topology. The robustness is analyzed theoretically for the case of two nodes wi...

This paper implements and analyzes the well-known message embedded synchronization scheme for the case of the generalized Lorenz system. Such a synchronization may be used for chaotic masking scheme using a single channel only. This method was already discussed in the earlier literature for the particular classes of systems. In this paper, a more g...

This paper describes the chaos shift keying method based on the second derivative desynchronization error and provides its security analysis, especially against the attacks by power and return map analysis. Desynchronization chaos shift keying method (DECSK) uses methods to detect the correct bit by detecting the wrong bit. Various modifications ar...

This paper studies yet another improvement of the anti-synchronization chaos shift keying scheme for the secure encryption and decryption of the digital data. A new concept of the detection of the correct binary value in the receiver is introduced here. The proposed method requires very reasonable amount of data to encrypt and time to decrypt one b...

A modified version of the Chaos Shift Keying (CSK) scheme for secure encryption and decryption of data will be discussed. The classical CSK method determines the correct value of binary signal through checking which initially unsynchronized system is getting synchronized. On the contrary, the new Anti-synchronization CSK (ACSK) scheme determines th...

This paper studies a new modification of the anti-synchronization chaos shift keying scheme for the secure encryption and decryption of data. A new concept of the detection of the correct/incorect binary value in the receiver is used. The method proposed here requires very reasonable amount of data to encrypt and time to decrypt a single bit. Basic...

The aim of this paper is to study synchronization of a dynamical complex network consisting of nodes being generalized Lorenz chaotic systems and connections are created with transmitted synchronizing signals. Focus is on the robustness of the network synchronization with respect to its connectional structure. This robustness is analyzed theoretica...

This paper studies the application of the observer-based chaos synchronization in the so-called generalized Lorenz systems to secure encryption. More precisely, a modified version of the chaos shift keying (CSK) scheme for secure encryption and decryption of data is proposed. Recall, that the classical CSK method determines the correct value of bin...

This paper studies possible application of the observer based chaos synchronization to secure encryption. Unlike common approaches that use continuous time synchronized chaos foe the so-called chaotic masking, the chaos shift keying (CSK) is being used here. CSK uses piece of synchronized chaotic signal to encode directly a given symbol.

In this paper, a modified version of the Chaos Shift Keying (CSK) scheme for secure encryption and decryption of data is proposed. The proposed scheme uses the effect of anti-synchronization, rather than synchronization. More specifically, the classical CSK method determines the correct value of binary signal through checking which unsynchronized s...