The Experts below are selected from a list of 16575 Experts worldwide ranked by ideXlab platform
Masaru Ikehata - One of the best experts on this subject based on the ideXlab platform.
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the enclosure method for inverse obstacle scattering over a Finite Time Interval vi using shell type initial data
arXiv: Analysis of PDEs, 2019Co-Authors: Masaru IkehataAbstract:A simple idea of finding a domain that encloses an unknown discontinuity embedded in a body is introduced by considering an inverse boundary value problem for the heat equation. The idea gives a design of a special heat flux on the surface of the body such that from the corresponding temperature field on the surface one can extract the smallest radius of the sphere centered at an arbitrary given point in the whole space and enclosing unknown inclusions. Unlike before, the designed flux is free from a large parameter. An application of the idea to a coupled system of the elastic wave and heat equations are also given.
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The enclosure method for inverse obstacle scattering over a Finite Time Interval: V. Using Time-reversal invariance
Journal of Inverse and Ill-posed Problems, 2019Co-Authors: Masaru IkehataAbstract:The wave equation is Time-reversal invariant. The enclosure method using a Neumann data generated by this invariance is introduced. The method yields the minimum sphere that is centered at a given arbitrary point and encloses an unknown obstacle embedded in a known bounded domain from a single point on the graph of the so-called response operator on the boundary of the domain over a Finite Time Interval. The occurrence of the lacuna in the solution of the free space wave equation is positively used.
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The enclosure method for inverse obstacle scattering over a Finite Time Interval: IV. Extraction from a single point on the graph of the response operator
Journal of Inverse and Ill-posed Problems, 2017Co-Authors: Masaru IkehataAbstract:Now a final and maybe simplest formulation of the enclosure method applied to inverse obstacle problems governed by partial differential equations in a {\it spacial domain with an outer boundary} over a Finite Time Interval is fixed. The method employs only a single pair of a quite natural Neumann data prescribed on the outer boundary and the corresponding Dirichlet data on the same boundary of the solution of the governing equation over a Finite Time Interval, that is a single point on the graph of the so-called {\it response operator}. It is shown that the methods enables us to extract the distance of a given point outside the domain to an embedded unknown obstacle, that is the maximum sphere centered at the point whose exterior encloses the unknown obstacle. To make the explanation of the idea clear only an inverse obstacle problem governed by the wave equation is considered.
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Extracting the geometry of an obstacle and a zeroth-order coefficient of a boundary condition via the enclosure method using a single reflected wave over a Finite Time Interval
Inverse Problems, 2014Co-Authors: Masaru IkehataAbstract:This paper considers an inverse problem for the classical wave equation in an exterior domain. It is a mathematical interpretation of an inverse obstacle problem which employs the dynamical scattering data of an acoustic wave over a Finite Time Interval. It is assumed that the wave satisfies a Robin-type boundary condition with an unknown variable coefficient. The wave is generated from the initial data localized outside the obstacle and observed over a Finite Time Interval at the same place as the support of the initial data. It is already known that, using the enclosure method, one can extract the maximum sphere whose exterior encloses the obstacle, from the data. In this paper, it is shown that the enclosure method enables us to extract also: (i) a quantity which indicates the deviation of the geometry between the maximum sphere and the boundary of the obstacle at the first-reflection points of the wave; (ii) the value of the coefficient of the boundary condition at an arbitrary first-reflection point of the wave provided, for example, that the surface of the obstacle is known in a neighbourhood of the point. Further new knowledge is obtained as follows: the enclosure method can cover the case where the data are taken over a sphere whose centre coincides with that of the support of an initial datum, and yields results corresponding to (i) and (ii).
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extracting the geometry of an obstacle and a zeroth order coefficient of a boundary condition via the enclosure method using a single reflected wave over a Finite Time Interval
arXiv: Analysis of PDEs, 2013Co-Authors: Masaru IkehataAbstract:This paper considers an inverse problem for the classical wave equation in an exterior domain. It is a mathematical interpretation of an inverse obstacle problem which employs the dynamical scattering data of acoustic wave over a Finite Time Interval. It is assumed that the wave satisfies a Robin type boundary condition with an unknown variable coefficient. The wave is generated by the initial data localized outside the obstacle and observed over a Finite Time Interval at the same place as the support of the initial data. It is already known that, using the enclosure method, one can extract the maximum sphere whose exterior encloses the obstacle, from the data. In this paper, it is shown that the enclosure method enables us to extract also: (i) a quantity which indicates the deviation of the geometry between the maximum sphere and the boundary of the obstacle at the first reflection points of the wave; (ii) the value of the coefficient of the boundary condition at an arbitrary first reflection point of the wave provided, for example, the surface of the obstacle is known in a neighbourhood of the point. Another new obtained knowledge is that: the enclosure method can cover the case when the data are taken over a sphere whose centre coincides with that of the support of an initial data and yields corresponding results to (i) and (ii).
N. Adachi - One of the best experts on this subject based on the ideXlab platform.
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A limiting property of the inverse of sampled-data systems on a Finite-Time Interval
IEEE Transactions on Automatic Control, 2001Co-Authors: T. Sogo, N. AdachiAbstract:If one considers a sampled-data system derived from a continuous-Time system with a relative degree of one or two on a Finite-Time Interval, it is not simple to predict the behavior of the output of the inverse of the sampled-data system as the sampling period goes to zero. This is because the number of sample points increases while the zeros of the pulse-transfer function tend to the boundary between the stable and unstable areas. The paper shows that the output of the sampled-data inverse systems converges to the output of the continuous-Time inverse systems independently of the stability of zeros.
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A limiting property of the inverse of sampled-data systems on a Finite Time Interval
Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171), 1998Co-Authors: T. Sogo, N. AdachiAbstract:If a sampled-data linear system is considered on a fixed Finite Time Interval, it is not a trivial matter to determine whether the output of the inverse of the system converges or diverges as the sampling period goes to 0 because the number of sample points increases while some zeros of the pulse transfer function tend to the boundary between the stable and unstable areas. This paper discusses the inverse of sampled-data systems obtained from linear continuous-Time systems of relative degree 2. It is demonstrated that the inverse of sampled-data systems converges to the inverse continuous-Time systems on a given Finite Time Interval, even if the system zeros are unstable.
T. Sogo - One of the best experts on this subject based on the ideXlab platform.
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A limiting property of the inverse of sampled-data systems on a Finite-Time Interval
IEEE Transactions on Automatic Control, 2001Co-Authors: T. Sogo, N. AdachiAbstract:If one considers a sampled-data system derived from a continuous-Time system with a relative degree of one or two on a Finite-Time Interval, it is not simple to predict the behavior of the output of the inverse of the sampled-data system as the sampling period goes to zero. This is because the number of sample points increases while the zeros of the pulse-transfer function tend to the boundary between the stable and unstable areas. The paper shows that the output of the sampled-data inverse systems converges to the output of the continuous-Time inverse systems independently of the stability of zeros.
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A limiting property of the inverse of sampled-data systems on a Finite Time Interval
Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171), 1998Co-Authors: T. Sogo, N. AdachiAbstract:If a sampled-data linear system is considered on a fixed Finite Time Interval, it is not a trivial matter to determine whether the output of the inverse of the system converges or diverges as the sampling period goes to 0 because the number of sample points increases while some zeros of the pulse transfer function tend to the boundary between the stable and unstable areas. This paper discusses the inverse of sampled-data systems obtained from linear continuous-Time systems of relative degree 2. It is demonstrated that the inverse of sampled-data systems converges to the inverse continuous-Time systems on a given Finite Time Interval, even if the system zeros are unstable.
Hao Shen - One of the best experts on this subject based on the ideXlab platform.
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hmm based asynchronous controller design of markovian jumping lur e systems within a Finite Time Interval
IEEE Transactions on Systems Man and Cybernetics, 2020Co-Authors: Rong Nie, Fei Liu, Xiaoli Luan, Hao ShenAbstract:This article study the asynchronous control problem for a class of discrete-Time Markovian jumping Lur'e systems (MJLSs) over the Finite-Time Interval. The partial accessibility of system modes with respect to the designed controller is described by a hidden Markov model (HMM). The asynchronous control law consists of two parts, i.e., the states and the nonlinearities involved in the dynamics of the controlled system. By selecting the appropriate Lyapunov functional and applying the modified sector condition, the Finite-Time stabilization conditions under the control constraints are derived. Finally, the effectiveness of the designed method is verified by an illustrative simulation.
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h_ infty h state estimation for stochastic jumping neural networks with fading channels over a Finite Time Interval
Neural Processing Letters, 2019Co-Authors: Liang Shen, Hao Shen, Mingming Gao, Yajuan Liu, Xia HuangAbstract:In the work, a class of Markov jump neural networks in the discrete-Time domain with fading channels are taken into account. The main aim is to investigate the $$H_{\infty }$$ state estimation issue when the Rice fading occurs in measured networks. In the first place, the analyses of the Finite-Time boundedness and the $$H_{\infty }$$ performance for the estimation error system with the aid of Finite-Time stability theory are presented. Some conditions which guarantee the solvability of the addressed problem are established. Furthermore, by applying an unique decoupling method, the gains of the presented estimator are obtained under the feasible solutions of the conditions derived before. Finally, the validity of the presented approach is verified by a numerical example.
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on asynchronous l 2 l filtering for networked fuzzy systems with markov jump parameters over a Finite Time Interval
Iet Control Theory and Applications, 2016Co-Authors: Yonghui Sun, Jing Wang, Hao ShenAbstract:In this study, the problem of asynchronous l 2 − l ∞ filtering is investigated for discrete-Time networked Takagi–Sugeno fuzzy Markov jump systems (FMJSs). The system measurements are transmitted over an unreliable communication network affected by sensor non-linearity and packet dropouts. The purpose is to design an asynchronous l 2 − l ∞ filter for discrete-Time FMJSs such that the resulting filtering error system is not only Finite-Time bounded for the given conditions, but also satisfies a prescribed l 2 − l ∞ performance. Some sufficient conditions for the existence of the asynchronous l 2 − l ∞ filter are presented, and the corresponding design problem is converted into a convex optimisation one. Finally, a numerical example and a modified inverted pendulum model are utilised to demonstrate the usefulness of our proposed approach.
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resilient h filtering for discrete Time uncertain markov jump neural networks over a Finite Time Interval
Neurocomputing, 2016Co-Authors: Mengshen Chen, Long Zhang, Hao ShenAbstract:In this paper, the resilient Finite-Time H ∞ filtering problem for discrete-Time uncertain Markov jump neural networks with packet dropouts is investigated. The purpose is to design a filter which is insensitive with respect to filter gain uncertainties subjects to an H ∞ performance level. The data packet dropouts phenomenon modeled by a stochastic Bernoulli distributed process is also considered. In terms of the linear matrix inequalities methodology, some sufficient conditions which guarantee that the filtering error system is Finite-Time bounded with a prescribed H ∞ performance level are established. Based on the conditions, an explicit expression for the desired filter is given. A numerical example is provided to illustrate the validness of the proposed scheme. HighlightsThe main contribution lies in some sufficient conditions provided to guarantee the filtering error system is Finite-Time bounded with a prescribed performance level.A resilient filter has been designed which can provide safe tuning margins and tolerate uncertainties in their coefficients. Therefore, the designed filter is more general than some existing ones.The packet dropouts phenomenon described by a stochastic Bernoulli distributed process is also considered which makes the desired filter structure more common.
P. Van Nieuwenhuizen - One of the best experts on this subject based on the ideXlab platform.
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Dimensional regularization of nonlinear sigma models on a Finite Time Interval
Physics Letters B, 2000Co-Authors: Fiorenzo Bastianelli, Olindo Corradini, P. Van NieuwenhuizenAbstract:Abstract We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a Finite Time Interval (“quantum mechanical path integrals in curved space”) dimensional regularization requires only a covariant Finite two-loop counterterm. This counterterm is nonvanishing and given by 1 8 ℏ 2 R .
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Dimensional regularization of nonlinear sigma models on a Finite Time Interval
Physics Letters B, 2000Co-Authors: Fiorenzo Bastianelli, Olindo Corradini, P. Van NieuwenhuizenAbstract:We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a Finite Time Interval (``quantum mechanical path integrals in curved space'') dimensional regularization requires only a covariant Finite two-loop counterterm. This counterterm is nonvanishing and given by R/8.Comment: 9 pages, 7 figures, LaTeX, minor changes in text and reference
