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Active volcanoes are associated with microearthquake (MEQ) hypocenters that form plane-oriented cluster distributions. These are faults delineating a magma injection system of dykes and sills. The Frac-Digger program was used to track fracking faults in the Kamchatka active volcanic belt and fore-arc region of Russia. In the case of magma laterally injected from volcanoes into adjacent structures, high-temperature hydrothermal systems arise, for example at Mutnovsky and Koryaksky volcanoes. Thermal features adjacent to these active volcanoes respond to magma injection events by degassing CO2 and by transient temperature changes. Geysers created by CO2-gaslift activity in silicic volcanism areas also flag magma and CO2 recharge and redistributions, for example at the Uzon-Geyserny, Kamchatka, Russia and Yellowstone, USA magma hydrothermal systems. Seismogenic faults in the Kamchatka fore-arc region are indicators of geofluid fracking, those faults can be traced down to 250 km depth, which is within the subduction slab below primary magma sources.

International audience; This work addresses the problem of robust stabilization of the concentrations of two different species of living organisms, which compete for a single limiting substrate in a bioreactor. This stabilization is performed using discontinuous feedback control laws that ensure the coexistence of all species. The control laws are designed considering bounded parametric uncertainties on the kinetic rates.

Discretization of continuous-time models is considered. Definition of SM for discrete-time systems is presented. The behavior under uncertainties of discrete-time systems, controlled by SM, is briefly discussed.

This chapter considers ordinary differential equations and inclusions, which are common mathematical models of control systems. In particular, elements of the theory of differential equations with discontinuous right-hand sides are presented. Problems of the existence and uniqueness of solutions as well as their continuous dependence on parameters are briefly studied. Some issues of modeling of control systems with uncertainties and disturbances are discussed.

International audience; This paper is concerned with finite-and fixed-time robust stabilization of uncertain multi-input nonlinear systems via the implicit Lyapunov function method. Instead of splitting the system into a linear nominal model and an additive perturbation which gathers nonlinearities, parametric uncertainties , and exogenous disturbances, the methodology hereby proposed preserves some nonlinear terms in the nominal system via an exact polytopic representation which leads to design conditions in the form of linear matrix inequalities. As a result, feasible solutions are found where former approaches fail; these solutions have more accurate settling-time estimates with reduced control effort. The corresponding control law includes well-known high-order sliding modes as a particular case. Numerical simulations are provided to illustrate the advantages of the proposal.

The concept of stability introduced in the famous thesis of Lyapunov [1] is one of the central notions of the modern control theory. Many problems of state estimation and control can be reduced to a stability analysis or to a stabilization of solutions of certain dynamical models. This chapter surveys stability notions for systems modeled by differential laws (ODEs, PDEs, evolution equations, and inclusion) and discusses some related convergence properties important for the analysis of homogeneous control systems.

The theory of evolution equations proposes a unified approach to a modeling and an analysis of dynamical systems governed by generalized differential laws. A state vector x in this case is an element of an infinite-dimensional Banach (or Hilbert) space \({\mathbb {B}}\).

This brief chapter introduces a reader in the problem of SMC designing the class of infinite-dimensional systems governed by a linear parabolic PDE containing uncertainties. The distributed unit signal is considered as a robust controller. The Lyapunov-Krasovskii functional is suggested for the analysis of the corresponding closed-loop dynamics.

International audience; The existence of a locally Lipschitz continuous homogeneous Lyapunov function is proven for a class of asymptotically stable homogeneous infinite dimensional systems with unbounded nonlinear operators.

A procedure of upgrading a linear observer to homogeneous (nonlinear) one is proposed and validated by experiment. The nonlinear observer design is based on the the concept of a linear geometric homogeneity. The simple procedure developed to apply the homogeneous nonlinear observer is based on the parameters provided by the linear observer, which is potential for many applications to improve their performance. A saturation function is introduced to guaranteed the improvement of estimation quality. Finally the theoretical results are confirmed by the QDrone platform of Quanser T M .

A discretization of continuous-time models is an important issue for the digital implementation of homogeneous control algorithms as well as for the numerical simulation of homogeneous controlled processes. This is a nontrivial task even in the finite-dimensional space. The explicit Euler discretization of a stable homogeneous system with nonzero degree is never globally asymptotically stable, but the implicit Euler discretization (being stable) does not preserve a convergence rate of the original continuous-time system. In other words, the classical discretization schemes are not appropriate for homogeneous models. This chapter introduces a new methodology of a consistent discretization, which allows all important properties of the continuous-time homogeneous system to be preserved in its discrete-time counterpart. The developed scheme is shown to be useful for the discretization of the homogeneous control algorithm designed in Chap. 9.

International audience; This work addresses the problem of robust stabilizationof the concentration of two different species competingfor a single limiting substrate. This stabilization is performedby means of discontinuous feedback control laws that ensurecoexistence of all species. The control laws are designed consideringbounded uncertainties on the kinetic rates.

International audience; A sufficient condition for output finite-time stability is presented. Based on this condition a scheme of adaptive finite-time control design is provided. The presented results are obtained with the use of homogeneity property. The theoretical results are supported by numerical examples.

International audience; Characterizations (necessary and sufficient conditions) of finite-time and fixed-time stability of evolution inclusions in Banach spaces are presented in terms of Lyapunov functionals.

International audience; The paper deals the method of Lyapunov exponents for a class of a generalized homogeneous systems. Homogeneous systems may have some sup-exponential and super-exponential grows. In this case, the method of Lyapunov exponents becomes non-informative, e.g. all Lyapunov exponents may equal to zero but the system is globally uniformly asymptotically stable. In this paper we propose an approach which allows us to analyze a behavior of such homogeneous systems by means of the method of Lyapunov exponents.

This paper considers the problem of local finite-time stabilization of the viscous Burgers equation. A boundary switched linear control with state dependent switching law is designed based on the Backstepping approach. The strategy builds on discontinuous kernels which render the control function a piecewise continuous one. It is proved that such a control stabilizes locally the viscous Burgers equation and that the settling time depends on initial conditions. A simulation result is provided to validate the theoretical results.

International audience; In this paper, the problem of state estimation of a bioreactor containing a single substrate and several competing species is studied. This scenario is well-known as a competition model, in which multiple species compete for the same nutrient. The goal is to estimate concentrations of the substrate and all species, considering the concentration of total biomass as measurement. To address such a challenge, the estimation scheme relies in the coupling of two estimation techniques: an asymptotic observer, which takes advantage of the model structure being independent of its kinetics, and a finite-time parameter estimation technique, which also drops the usual requirement of persistence of excitation.

International audience; The problem of a state feedback design for control of a quadrotor system under state and time constraints is studied. Convex embedding approach and Implicit Lyapunov function are employed to design a finite-time controller. The feedback gain is solved by a system of LMIs(Linear Matrix Inequalities). Theoretical results are supported with numerical simulation.

An algorithm of consistent implicit discretization for locally homogeneous finite-time stable system having discontinuity only at the origin is developed. It preserves finite-time stability property in the discrete-time models. The homogeneous domination approach is utilized for analysis of the discretized model. The scheme is demonstrated for a simplified model of a quadrotor control system.

In this paper, we study the finite-time stability of a class of nonlinear systems $\dot{x}=f({x})=H(x)b(x)$ , where $H$ is homogeneous and $b$ is bounded. We define the homogeneous extension of the non-homogeneous function $f$ and use this extension to prove that, under some conditions on b, if the system $\dot{x}\ =\ f(x)$ is globally asymptotically stable, then it is finite-time stable. An example of global asymptotic stable system with some additional conditions is presented in the last section to illustrate the obtained results.

This paper studies the robustness properties of homogeneous finite-time stable systems with respect to multiplicative perturbation for sufficiently small inputs. Robust stability conditions are presented for the systems admitting homogeneous approximation at the origin and at infinity. The utility of the obtained results is illustrated via robustness analysis of homogeneous observer with time-varying gains.

International audience; This paper deals with continuous boundary time-varying feedbacks for fixed-time stabilization of constant-parameter reaction-diffusion systems. The time of convergence can be prescribed and is independent of the initial condition of the system. The design of time-varying feedbacks is carried out by using the backstepping approach for which suitable characterizations for time-varying kernels are derived. Kernel solutions are given in terms of power series involving the exponential complete Bell polynomials for which we have exploited the Faà di Bruno formula. Moreover, by particularizing the characterization, one can recover kernel solutions in terms of the generalized Laguerre polynomials and the modified Bessel functions.

International audience; In this paper, the problem of fixed-time stabilization of constant-parameter reaction-diffusion partial differential equations by means of continuous boundary time-varying feedbacks is considered. Moreover, the time of convergence can be prescribed in the design. The design of time-varying feedbacks is carried out based on the backstepping approach. Using a suitable target system with a time varying-coefficient, one can state that the resulting kernel of the backstepping transformation is time-varying and rendering the control feedback to be time-varying as well. Explicit representations of the kernel solution in terms of generalized Laguerre polynomials and modified Bessel functions are derived. The fixed-time stability property is then proved. A simulation example is presented to illustrate the main results.

The article presents results of studies aimed to develop parameters for preventive gas removal of mine bedrocks occur during the layer mining of the Third potash formation in conditions of Belaruskali JSC mines. Development of parameters for preventive gas removal of bedrocks was carried out based on results of mine experimental studies of gas content, gas dynamic characteristics of bedrocks and experimental studies of dynamics of pressure of free gases under different mine industrial conditions of layer mining at the Third potash formation. A method of mine experimental research consider quantitative assessment of the indicators such as gas content of bedrocks on free gases, initial velocity of gas emission from bedrocks, pressure of free gases of bedrocks. Study of dynamics of change in time of pressure of free gases in bedrocks of the preparatory excavations were carried out in excavation poles of long faces that mine layers 2, 2-3 and 3 of the Third formation. That was done with help of measuring stations (packers) equipped for measuring the pressure of free gases in the measuring chambers by digital manometers. Based on results of mine experimental studies, regularities of formation of focuses of gas dynamic phenomena in bedrocks were established. Regularities consider various mining conditions of layer operation of the Third potash layer. Parameters of preventive gas removal drilling of wells into the bedrocks of preparatory excavations for long faces that mine layers 2, 2-3 and 3 of the Third potash layer in various geological and mining conditions have been developed. Parameters consider established regularities of formation of focuses of gas dynamic phenomena in bedrocks. Parameters of preventive gas removal drilling for various technological schemes for operation of the Third layer include a list of excavations in the long faces where preventive gas removal drilling should be applied and diameter, depth and distance between the degassing wells. Introduction of schemes of preventive drilling of degassing wells into the bedrocks of preparatory excavations of long faces that mine layers 2, 2-3, 3 of the Third potash layer allows to increase safety of mining operations at the mines of Belaruskali JSC.

This paper presents feedback sensitivity functions analysis of implicit Lyapunov function-based control system in case of finite-time stabilization problem. The Gang of Four is chosen as a feedback sensitivity tool. The results can be used for parametric tuning of control algorithms in order to guarantee desired closed-loop sensitivity specifications. The obtained results are supported by numerical examples.

This paper deals with the design of a robust control for linear systems with external disturbances using a homogeneous differentiator-based observer based on a implicit Lyapunov function approach. Sufficient conditions for stability of the closed-loop system in the presence of external disturbances are obtained and represented by linear matrix inequalities. The parameter tuning for both controller and observer is formulated as a semi-definite programming problem with linear matrix inequalities constraints. Simulation results illustrate the feasibility of the proposed approach and some improvements with respect to the classic linear observer approach.

The thermal, hydrogeological, and chemical processes affecting Kamchatka geothermal reservoirs were studied by using isotope and geochemistry data: (1) The Geysers Valley hydrothermal reservoirs; (2) The Paratunsky low temperature reservoirs; (3) The North-Koryaksky hydrothermal system; (4) The Mutnovsky high temperature geothermal reservoir; (5) The Pauzhetsky geothermal reservoir. In most cases water isotope in combination with Cl- transient data are found to be useful tool to estimate reservoirs natural and disturbed by exploitation recharge conditions, isotopes of carbon-13 (in CO2) data are pointed either active magmatic recharge took place, while SiO2 and Na-K geothermometers shows opposite time transient trends (Paratunsky, Geysers Valley) suggest that it is necessary to use more complicated geochemical systems of water/mineral equilibria.

The paper studies the problem of minimax control design for linear evolution equations in Hilbert spaces with measurement noise and additive exogenous disturbances. The key result of the paper is an algorithm, generating a control in an output-feedback form, which steers the state of the system as close as possible to a given sliding hyperplane, asymptotically as time goes to infinity. The control is designed in the state space of the minimax filter, and guarantees that the state of the filter will be exactly on the sliding surface, and the state of the plant will belong to an ellipsoid centered at the filter's state vector for large enough time. The optimality of the designed feedback and estimation error is proven. The feedback is represented by means of the unique solution of an algebraic Riccati equation. The theory is then applied to design a minimax control for linear hereditary systems subject to noise and disturbances. This is achieved by projecting the hereditary system onto a finite dimensional subspace of the corresponding state space by means of a finite-volume approximation method, designing feedback in the state space of the resulting finite dimensional system. The solution of the operator Riccati equation is obtained using a (modified) Kleinman-Newton method. The efficacy of the proposed algorithm is illustrated by a numerical example for a time-delay linear systems with constant point delays.

A discord is a refinement of the concept of an anomalous subsequence of a time series. The task of discovering discords is applied in a wide range of subject areas involving time series: medicine, economics, climate modeling, and others. In this paper, we propose a novel parallel algorithm for discord discovery using Intel MIC (Many Integrated Core) accelerators in the case when time series fit in the main memory. We achieve parallelization through thread-level parallelism and OpenMP technology. The algorithm employs a set of matrix data structures to store and index the subsequences of a time series and to provide an efficient vectorization of computations on the Intel MIC platform. Moreover, the algorithm exploits the ability to independently computing Euclidean distances between subsequences of a time series. The algorithm iterates subsequences in two nested loops; it parallelizes the outer and the inner loops separately and differently, depending on both the number of running threads and the cardinality of the sets of subsequences scanned in the loop. The experimental evaluation shows the high scalability of the proposed algorithm.

A stable BiI3 monosheet has been grown for the first time on the (0001) surface of the topological insulator Bi2Se3 as confirmed by scanning tunnelling microscopy, surface X-ray diffraction, and X-ray photoemision spectroscopy. BiI3 is deposited by molecular beam epitaxy from the crystalline BiTeI precursor that undergoes decomposition sublimation. The key fragment of the bulk BiI3 structure, a 2 [I—Bi—I] layer of edge-sharing BiI6 octahedra, is preserved in the ultra-thin film limit, but exhibits large atomic relaxations. The stacking sequence of the trilayers and alternations of the Bi—I distances in the monosheet are the same as in the bulk BiI3 structure. Momentum resolved photoemission spectroscopy indicates a direct band gap of 1.2 eV. The Dirac surface state is completely destroyed and a new flat band appears in the band gap of the BiI3 film that could be interpreted as an interface state., This work is supported by the DFG through SPP 1666 (Topological Insulators) and ERANET Chemistry program. The authors thank Arthur Ernst for providing the DFT calculations of the relaxed BiI3 double-layer film. We thank F. Weiss for technical support. The authors thank the staff of the ESRF and Elettra for their help and hospitality during their visit in Grenoble and Trieste, and G. Zamborlini, M. Jugovac and V. Feyer (PGI-6) for assistance, in using the NanoESCA beamline.

International audience; Numeric approximations to the solutions of asymptotically stable homogeneous systems by Euler method, with a step of discretization scaled by the state norm, are investigated (for the explicit and implicit integration schemes). It is proven that for a sufficiently small discretization step the convergence of the approximating solutions to zero can be guaranteed globally in a finite or a fixed time depending on the degree of homogeneity of the system, but in an infinite number of discretization iterations. The maximal admissible step can be estimated by analyzing the system properties on the sphere. It is shown that the absolute and relative errors of the discretizations are globally bounded functions, thus the approximations approaching the solutions with the step converging to zero. In addition, it is established that the proposed discretization approach preserves robustness with respect to exogenous perturbations. Efficiency of the designed discretization algorithms is demonstrated in simulations.

40 years ago W. Haupin stressed that anode overvoltages on the carbon materials have a scatter more than 300 mV under the same current density. This is a reason to attempt to find out the reason for greater differences because decreasing the overvoltage promises high energy saving. Experiments in lab.cells in galvanostatic conditions have been conducted to determine the overvoltages for the smelter anodes used in Sayanogorsk and Boguchany smelters (Russia) (more than 80 curves currents-overvoltages are received). Overvoltages are compared with other carbon block properties. Recommendations to use these values as a parameter of carbon block quality were made.

International audience; This paper considers the problem of finite-time stabilization of coupled reaction-diffusion partial differential equations by means of boundary time-varying feedbacks; moreover, the time of convergence can be prescribed in the design. The design of time-varying feedbacks is carried out based on the backstepping approach. Selecting a suitable target system with time varying-coefficients, the resulting kernel of the backstepping transformation is time-varying which provides the control feedback to be time-varying as well. The target system turns out to be fixed-time stable and two cases for the control design are pointed out in order to obtain either boundedness or fixed-time convergence of the original system. A simulation example is presented to illustrate the results.

International audience; Conditions for the existence and convergence to zero of numeric approximations with state-depend step of discretization to solutions of asymptotically stable homogeneous systems are obtained for the explicit and implicit Euler integration schemes. It is shown that for a sufficiently small discretization step the convergence of the approximating solutions to zero can be guaranteed globally in a finite or a fixed time, but in an infinite number of discretization iterations. It is proven that the absolute and relative errors of the respective discretizations are globally bounded functions. Efficiency of the proposed discretization algorithms is demonstrated by the simulation of the super-twisting system.

International audience; The interval estimation design is studied for a second-order delay differential equation with position delayed measurements, uncertain input and initial conditions. The proposed method contains two consecutive interval observers. The first one estimates the interval of admissible values for the position without delay for each instant of time using new delay-dependent conditions on positivity. Then derived interval estimates of the position are used to design the second observer estimating an interval of admissible values for the velocity of the considered dynamical system. The results are illustrated by numerical experiments for an example.

International audience; In the present paper, the stability criterion for generalized homogeneous differential inclusions is obtained that may simplify the control design procedure in some particular cases. Robust dynamical feedback control law is designed for homogeneous differential inclusions. Performance of the resulting dynamical feedback is illustrated by numerical simulation.

This article presents a theoretical framework to study finite-time and fixed-time input-to-state stability of nonlinear systems using the implicit Lyapunov function formulation. This approach allows to determine stability, robustness and convergence type of a given system without relying in an explicit Lyapunov function.

In the Comment on our publication [Phys. Rev. B 95, 180202(R) (2017)], R. A. Gordon claims that our main conclusion is not valid, namely that gold atoms deposited in situ on the (0001) surface of s ...

В статье представлены результаты археологических раскопок кургана №1 могильника Уйбат-Чарков (Усть-Абаканский район Республики Хакасия) и их научная интерпретация. Этот курган датируется ранним уйбатским этапом окуневской культуры и может рассматриваться как эталонный памятник этого периода (эпоха ранней бронзы). В ходе его исследования были обнаружены 17 могил, различных, в том числе уникальных конструкций. Центральное погребение было совершено в яме глубиной около4,5 метров. Большое научное значение имеет обнаружение в этом кургане трех захоронений в катакомбах. Это подтверждает наблюдения специалистов о связях окуневской культуры с катакомбной культурно-исторической общностью. В ходе исследований была обнаружена серия фрагментов плит с традиционными изображениями окуневской культуры. Особое значение имеет личина «джойского» типа, обнаруженная на одной из плит в закладе катакомбы. Ранее предполагалось, что эти изображения датируются финалом окуневской культуры. Новая находка позволяет связать этот тип изображений с ранним уйбатским этапом и во многом пересмотреть представления о развитии окуневского искусства. На основании серии из пяти радиоуглеродных дат непотревоженной могилы-11 был определен приблизительный возраст кургана – XXV-XXIII вв. до н.э. В связи с исследованиями этого памятника можно вновь вернуться к рассмотрению проблемы происхождения окуневской культуры. Наблюдается большое число аналогий с памятниками позднеямного и ямно-катакомбного времени Северо-Западного Прикаспия., The article presents the results of archaeological excavations of burial mound no. 1 of the Uibat-Charkov burial ground (Ust-Abakan district of the Republic of Khakassia) and their scientific interpretation. This mound dates from the early Uibat stage of the Okunevskaya culture and can be regarded as a reference site of that period (the Early Bronze Age). In the course of its research, various 17 graves were found including unique structures. The central burial was made in a pit about 4.5 meters in depth. Of great scientific importance is the discovery in this mound of three burials in the catacombs. This is confirmed by the observations of specialists on the links between the Okunevskaya culture and the catacomb culturalhistorical community. During the research, the discovery was made of a series of fragments of plates with traditional images of the Okunevskaya culture. Of particular importance is the face of the “Joy” type, found on one of the catacomb’s plates. Earlier it was assumed that these images are dated by the finale of the Okunevskaya culture. A new find allows us to relate this type of images to the early Uibat stage and to revise the ideas about the development of Okunev art in many respects. Based on a series of five radiocarbon dates of the undisturbed grave-11, the approximate age of the mound was determined by 25th–28th centuries BC. In connection with the research of this site, one can again return to the problem of the origin of the Okunevskaya culture. There is a large number of analogies with the sites of the Late-Pit Grave and the Pit Grave -Catacomb time of the North-Western Caspian.