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arXiv 2020年

作者： Frühauf, F. Scherzer, O. Leitão, A. Department of Computer Science Universität Innsbruck Technikerstraße 25 InnsbruckA-6020 Austria Radon Institute for Comput. Appl. Math. Austrian Academy of Sciences c/o Kepler Universität Linz LinzA-4040 Austria

We consider a regularization concept for the solution of ill–posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular appl.cation is level set regularization, where we develop a novel concept of minimizers. The proposed level set regularization is capable of handling changing topologies. A functional analytic framework explaining the splitting of topologies is given. The asymptotic limit of the level set regularization method is an evolution process, which is implemented numerically and the quality of the proposed algorithm is demonstrated by solving an inverse source *** Codes 65J20, 47A52 Copyright © 2020, The Authors. All rights reserved.

关键词： Topology

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Anti-synchronization of Two Different Hyperchaotic Systems with Fully Uncertain Parameters

Anti-synchronization of Two Different Hyperchaotic Systems w...

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International Conference on comput.tional Intelligence and Security

作者： jian-wen Feng Francis Austin He Ling An-ding Dai Coll. of Math. & Comput. Sci. Shenzhen Univ. Shenzhen China Dept. of Appl. Math. Hong Kong Polytech. Univ. Kowloon China Department of Applied Mathematics The Hong Kong Polytechnic University Kowloon Hong Kong Shenzhen University Shenzhen Guangdong CN

Based on the Lyapunov stability theory, the anti-synchronization between hyperchaotic Lorenz-Stenflo (LS) system and hyperchaotic Chen system with fully unknown parameters is investigated. An adaptive control law is derived for the case when the parameters of the drive and response systems to be synchronized are fully uncertain. Numerical simulation results are performed to show the effectiveness of the techniques.

关键词： Chaotic communication Control systems math.matics Lyapunov method Adaptive control Numerical simulation Equations comput.tional intelligence Security Helium

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Adaptive Synchronization Between Hyperchaotic Lorenz System and Chen System

Adaptive Synchronization Between Hyperchaotic Lorenz System ...

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International Conference on comput.tional Intelligence and Security

作者： Francis Austin Chen Xu Jian-wen Feng Wei-qiang Zhang Dept. of Appl. Math. Hong Kong Polytech. Univ. Kowloon China Inst. of Intell. Comput. Sci. Shenzhen Univ. Shenzhen China Hong Kong Polytechnic University Kowloon HK

This paper introduces the chaos synchronization between two different hyperchaotic systems with fully unknown parameters, i. e. the synchronization between hyperchaotic Lorenz system and hyperchaotic Chen system. Based on the Lyapunov stability theory, an adaptive control law is derived for the case when the parameters of the drive and response systems to be synchronized are fully uncertain. Finally, numerical simulation results are presented to show the effectiveness of the techniques.

关键词： Chaotic communication Adaptive control Control systems comput.tional intelligence Lyapunov method Numerical simulation Security Competitive intelligence math.matics Optical arrays

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STABILIZABILITY FOR NONAUTONOMOUS LINEAR PARABOLIC EQUATIONS WITH ACTUATORS AS DISTRIBUTIONS

arXiv

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arXiv 2023年

作者： Kunisch, Karl Rodrigues, Sérgio S. Walter, Daniel Johann Radon Institute for Comput. and Appl. Math. OAW Altenbergerstr. 69 Linz4040 Austria Institute for Mathematics and Scientific Computing 621 Heinrichstrasse 36 Graz8010 Austria Institute for Mathematics Humboldt University Rudower Chaussee 25 Berlin10117 Germany

The stabilizability of a general class of abstract parabolic-like equations is investigated, with a finite number of actuators. This class includes the case of actuators given as delta distributions located at given points in the spatial domain of concrete parabolic equations. A stabilizing feedback control operator is constructed and given in explicit form. Then, an associated optimal control is considered and the corresponding Riccati feedback is investigated. Results of simulations are presented showing the stabilizing performance of both explicit and Riccati *** Codes 93D15, 93B52, 93C20, 35K58 Copyright © 2023, The Authors. All rights reserved.

关键词： Actuators

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Cooperative Design of Networked Observers for Stabilizing LTI Plants

Cooperative Design of Networked Observers for Stabilizing LT...

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IEEE International Symposium on Circuits and Systems

作者： Kexin Liu Henghui Zhu Jinhu Lu Maciej J. Ogorzalek LSC ISS Acad. Math. Syst. Sci. Chinese Academy of Sciences Beijing 100190 P. R. China Faculty Phys. Astronomy Appl. Comput. Sci. Jagiellonian University Krakow 30-059 Poland

ISBN: (纸本)9781479983926

With the rapid development of sensor networks in the last decade, the cooperative design for networked observers has received an increasing attention from engineering community. This paper aims at developing a unified framework for cooperative design of networked observers to stabilize LTI plants. Apart from the traditional centralized design of MIMO system, the proposed cooperative design approach only utilizes the local information of each sensor. For undirected networks, this paper obtains a sufficient and necessary condition for the existence of the parameters that lead to the stabilization of the LTI plant. In particular, we give the detailed design procedures for the parameters of networked observers, including feedback gains and the coupling strength. The numerical simulation is also given to validate the proposed theoretical results.

关键词： LTI Sensor networks design process Observers feedback gain local information. multiple input multiple output systems Stabilising

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Simultaneous Spectrum Sensing and Data Transmission for Multi-User MIMO Cognitive Radio Systems

Simultaneous Spectrum Sensing and Data Transmission for Mult...

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IEEE Global Communications Conference

作者： Nikolaos I. Miridakis Theodoros A. Tsiftsis George C. Alexandropoulos Merouane Debbah Dept. of Comput. Eng. Piraeus Univ. of Appl. Sci. Aegaleo Greece Sch. of Eng. Nazarbayev Univ. Astana Kazakhstan Math. & Algorithmic Sci. Lab. Huawei Technol. France Huawei France

ISBN: (纸本)9781509013296

We present a multi-user multiple-input multiple-output (MIMO) cognitive radio system consisting of a secondary receiver that deploys spatial multiplexing to decode signals from multiple secondary transmitters, under the presence of primary transmissions. The secondary receiver carries out minimum mean-squared error detection to decode the secondary data streams, while it performs spectrum sensing at the remaining signal to capture the potential presence of primary activity. Assuming Rayleigh fading as well as the realistic cases of channel fading time variation and channel estimation errors, we present novel closed-form expressions for important system measures, namely, the detection and false-alarm probabilities as well as the transmission power of the secondary nodes. The enclosed numerical results verify the accuracy of the presented analysis.

关键词： Sensors Receivers Channel estimation Transmitters Data communication Training Fading channels

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Fast normal‐mode approximation of tomographic arrival patterns

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The Journal of the Acoustical Society of America 1996年第4_SUPPLEMENT期100卷 2614-2614页

作者： E. K. Skarsoulis Inst. of Appl. and Comput. Math. F.O.R.T.H. 71110 Heraklion Crete Greece

The wave‐theoretic calculation of arrival patterns for the needs of ocean acoustic tomography is comput.tionally expensive due to the large number of comput.tion frequencies necessary for properly synthesizing a broadband signal in the time domain. A scheme for approximate fast normal‐mode calculations of broadband acoustic signals in the time domain is proposed, based on a second‐order Taylor expansion of eigenvalues and eigenfunctions with respect to frequency. For the case of a Gaussian impulse source, a closed‐form expression is obtained for the pressure in the time domain. Using perturbation theory, analytical expressions are derived for the first and second frequency derivatives of eigenvalues and eigenfunctions. The proposed approximation significantly accelerates arrival‐pattern calculations, since the eigenvalues, eigenfunctions, and their derivatives need to be calculated at a single frequency, the central frequency of the tomographic source. Furthermore, it offers a satisfactory degree of accuracy for the lower‐ and intermediate‐order modes. This is due to the fact that essential wave‐theoretic mechanisms such as dispersion and frequency dependence of mode amplitudes are contained in the representation up to a sufficient order. Numerical results demonstrate the efficiency of the method. [Work partially supported by EU/MAST.]

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Tangent linear and second‐order models from the Born and Rytov approximations

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The Journal of the Acoustical Society of America 2006年第5_SUPPLEMENT期119卷 3248-3248页

作者： Emmanuel Skarsoulis George Piperakis George Makrakis Inst. of Appl. & Comput. Math. FORTH P.O. Box 1385 711 10 Heraklion Greece Univ. of Crete Crete Greece

Adjoint and higher‐order methods for the solution of inverse problems in underwater acoustics rely on tangent linear and higher‐order models of the forward propagation problem, with respect to the underlying parameters of interest. The use of Born and Rytov approximations is examined for the representation of perturbations of the Green’s function and perturbations of the phase, respectively, caused by range‐dependent variations of the sound‐speed distribution about a range‐independent background environment. Using the normal‐mode representation for the background Green’s function and appl.ing the stationary‐phase approach in combination with analytic evaluation at singular points, closed‐form expressions are derived for the first‐ and second‐order perturbations of the Green’s function, generalizing previous perturbation results derived under the assumption of range independence. The resulting expressions for the phase show the second‐order character of the phase (and the associated travel times) in the case of range‐dependent, zero‐mean sound‐speed perturbations.

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Sensitivity kernels of finite‐frequency travel times in ocean acoustic tomography

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The Journal of the Acoustical Society of America 2004年第5_SUPPLEMENT期115卷 2617-2617页

作者： Emmanuel K. Skarsoulis Bruce D. Cornuelle Inst. of Appl. and Comput. Math. FORTH 711 10 Heraklion Crete Greece Scripps Inst. of Oceanogr. La Jolla CA 92093

Wave theoretic modeling is appl.ed to obtain travel‐time sensitivity kernels representing the amount by which travel times are affected by localized sound‐speed variations anywhere in the medium. In the ray approximation travel times are sensitive to medium changes only along the corresponding eigenrays. In the wave‐theoretic approach the perturbations of peak arrival times are expressed in terms of pressure perturbations, which are further related with the underlying sound‐speed perturbations using the first Born approximation. In this way, an integral representation of travel‐time perturbations is obtained in terms of sound‐speed perturbations; the associated kernel represents the spatial sensitivity of travel times to sound‐speed perturbations. The appl.cation of the travel‐time sensitivity kernel to an ocean acoustic waveguide gives a picture close to the ray‐theoretic one in the high‐frequency case but significantly differs at lower frequencies. Low‐frequency travel times are sensitive to sound‐speed changes in areas surrounding the eigenrays, but not on the eigenrays themselves, where the sensitivity is zero. Further, there are areas of positive sensitivity, where, e.g., a sound‐speed increase results in a counter‐intuitive increase of arrival times. These findings are confirmed by independent forward calculations.

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Reconstructing the seafloor properties from acoustic reflection data

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The Journal of the Acoustical Society of America 2005年第4B_SUPPLEMENT期89卷 1883-1883页

作者： John S. Papadakis Michael I. Taraoudakis Panagiotis J. Papadakis Foundation for Res. and Technol.‐Hellas Inst. of Appl. and Comput. Math. P.O. Box 1527 711 10 Iraklion Crete Greece

The determination of the structure of the seafloor using measurements of the acoustic reflected power is an important inverse hydroacoustic problem with many appl.cations in ocean geophysics. A realistic description of the seafloor includes many sedimentary layers over a harder substrate. Assuming that a rough estimation of the thicknesses of the various layers is available (by suitable subbottom profiling) the important thing is to recover the properties of the various layers, that is, the density, the sound velocity, and the attenuation coefficient. A simple scheme for the reconstruction of the seabottom is presented based on the assumption that reliable reflection coefficient measurements from a broadband acoustic source are available. The scheme is based on a systematic variation of the geoacoustic parameters of a background bottom model, so as the calculated reflection coefficient converges to the measured data. It is shown that data from various frequencies are necessary in order to obtain satisfactory results. [Work supported by EEC/MAST program.]

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