The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform
Sergei Avdonin - One of the best experts on this subject based on the ideXlab platform.
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Leaf peeling method for the wave equation on metric tree graphs
Inverse Problems & Imaging, 2021Co-Authors: Sergei Avdonin, Yuanyuan ZhaoAbstract:We consider the dynamical inverse problem for the wave equation on a metric tree graph and describe the dynamical Leaf Peeling (LP) method. The main step of the method is recalculating the Response Operator from the original tree to a peeled tree. The LP method allows us to recover the connectivity, potential function on a tree graph and the lengths of its edges from the Response Operator given on a finite time interval.
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Inverse problems for quantum trees II:Recovering matching conditions for star graphs
Inverse Problems & Imaging, 2010Co-Authors: Sergei Avdonin, Pavel Kurasov, Marlena NowaczykAbstract:The inverse problem for the Schrodinger Operator on a star graph is investigated. It is proven that such Schrodinger Operator, i.e. the graph, the real potential on it and the matching conditions at the central vertex, can be reconstructed from the Titchmarsh-Weyl matrix function associated with the graph boundary. The reconstruction is also unique if the spectral data include not the whole Titchmarsh-Weyl function but its principal block (the matrix reduced by one dimension). The same result holds true if instead of the Titchmarsh-Weyl function the dynamical Response Operator or just its principal block is known.
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The Boundary Control Approach to the Titchmarsh-Weyl m–Function. I. The Response Operator and the A–Amplitude
Communications in Mathematical Physics, 2007Co-Authors: Sergei Avdonin, Victor Mikhaylov, Alexei RybkinAbstract:We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the A−amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl m−function associated with the Schrodinger Operator H = −∂ x 2 + q(x) on L 2(0, ∞) with Dirichlet boundary condition at x = 0.
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the boundary control approach to the titchmarsh weyl m function i the Response Operator and the a amplitude
Communications in Mathematical Physics, 2007Co-Authors: Sergei Avdonin, Victor Mikhaylov, Alexei RybkinAbstract:We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the A−amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl m−function associated with the Schrodinger Operator H = −∂ x 2 + q(x) on L 2(0, ∞) with Dirichlet boundary condition at x = 0.
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Identification of $q(x)$ in $u_t=\Delta u-qu$ from Boundary Observations
SIAM Journal on Control and Optimization, 1995Co-Authors: Sergei Avdonin, Thomas I. SeidmanAbstract:We consider the problem of recovering the coefficient $q(x)$ in the equation $u_t=\Delta u-qu$ from boundary observations. Uniqueness of $q$ based on knowledge of the Neumann $\mapsto$ Dirichlet Response Operator is shown as an implication of (known) corresponding results concerning the inverse problem for the corresponding hyperbolic equation $w_{tt}=\Delta w-qw$. This is then reduced to use of the Response to a single input with some consideration of computational approximation.
Alexei Rybkin - One of the best experts on this subject based on the ideXlab platform.
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The Boundary Control Approach to the Titchmarsh-Weyl m–Function. I. The Response Operator and the A–Amplitude
Communications in Mathematical Physics, 2007Co-Authors: Sergei Avdonin, Victor Mikhaylov, Alexei RybkinAbstract:We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the A−amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl m−function associated with the Schrodinger Operator H = −∂ x 2 + q(x) on L 2(0, ∞) with Dirichlet boundary condition at x = 0.
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the boundary control approach to the titchmarsh weyl m function i the Response Operator and the a amplitude
Communications in Mathematical Physics, 2007Co-Authors: Sergei Avdonin, Victor Mikhaylov, Alexei RybkinAbstract:We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the A−amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl m−function associated with the Schrodinger Operator H = −∂ x 2 + q(x) on L 2(0, ∞) with Dirichlet boundary condition at x = 0.
Henrik Sandberg - One of the best experts on this subject based on the ideXlab platform.
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frequency domain analysis of linear time periodic systems
IEEE Transactions on Automatic Control, 2005Co-Authors: Henrik Sandberg, E MollerstedtAbstract:In this paper, we study convergence of truncated representations of the frequency-Response Operator of a linear time-periodic system. The frequency-Response Operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an Operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature.
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A Bode sensitivity integral for linear time-periodic systems
2004Co-Authors: Henrik Sandberg, Bo BernhardssonAbstract:For linear time-invariant systems Bode's sensitivity integral is a well-known formula that quantifies some of thelimitations in feedback control. In this paper we show that a very similar formula holds for linear time-periodicsystems. We use the infinite-dimensional frequency-Response Operator called the harmonic transfer function to prove the result. It is shown that the harmonic transfer function isan analytic Operator and a trace class Operator under the assumption that the periodic system has roll-off 2. A periodic system has roll-off 2 if the first time-varying Markov parameter is equal to zero.
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Frequency-domain analysis of linear time-periodic systems
Proceedings of the 2004 American Control Conference, 2004Co-Authors: Henrik Sandberg, E Mollerstedt, Bo BernhardssonAbstract:In this paper we study how a system with a time-periodic impulse Response may be expanded into a sum of modulated time-invariant systems. This allows us to define a linear frequency-Response Operator for periodic systems, called the harmonic transfer function (HTF). Similar frequency-Response Operators have been derived before for sampled-data systems and periodic finite-dimensional state-space systems. The HTF is an infinite-dimensional Operator that captures the frequency coupling of a time-periodic system. The paper includes analysis of convergence of truncated HTFs. For this reason the concepts of input/output roll-off are developed and related to time-varying Markov parameters.
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Frequency-Domain Analysis of Linear Time-Periodic Systems
2003Co-Authors: Henrik SandbergAbstract:In this report we study how a time-varying system with a time-periodic integral kernel (impulse Response), g(t,\tau)=g(t+T,\tau+T), can be expanded into a sum of essentially time-invariant systems. This allows us to define a linear frequency Response Operator for periodic systems, called the Harmonic Transfer Function (HTF). The HTF is a direct analog of the transfer function for time-invariant systems, but it captures the frequency coupling of a time-periodic system. It can, for example, be used to compute the induced L_2-norm of periodic systems. The report also includes analysis of convergence of truncated HTFs, which is essential for practical computations as the HTF is an infinite-dimensional Operator.
Mihailo R Jovanovic - One of the best experts on this subject based on the ideXlab platform.
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Well-conditioned ultraspherical and spectral integration methods for resolvent analysis of channel flows of Newtonian and viscoelastic fluids
arXiv: Fluid Dynamics, 2020Co-Authors: Gokul Hariharan, Satish Kumar, Mihailo R JovanovicAbstract:Modal and nonmodal analyses of fluid flows provide fundamental insight into the early stages of transition to turbulence. Eigenvalues of the dynamical generator govern temporal growth or decay of individual modes, while singular values of the frequency Response Operator quantify the amplification of disturbances for linearly stable flows. In this paper, we develop well-conditioned ultraspherical and spectral integration methods for frequency Response analysis of channel flows of Newtonian and viscoelastic fluids. Even if a discretization method is well-conditioned, we demonstrate that calculations can be erroneous if singular values are computed as the eigenvalues of a cascade connection of the frequency Response Operator and its adjoint. To address this issue, we utilize a feedback interconnection of the frequency Response Operator with its adjoint to avoid computation of inverses and facilitate robust singular value decomposition. Specifically, in contrast to conventional spectral collocation methods, the proposed method (i) produces reliable results in channel flows of viscoelastic fluids at high Weissenberg numbers ($\sim 500$); and (ii) does not require a staggered grid for the equations in primitive variables. The developed approach can potentially be applied to related problems that involve stiff computations such as those arising in compressible high-speed flows.
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computation of frequency Responses for linear time invariant pdes on a compact interval
Journal of Computational Physics, 2013Co-Authors: Binh K Lieu, Mihailo R JovanovicAbstract:We develop mathematical framework and computational tools for calculating frequency Responses of linear time-invariant PDEs in which an independent spatial variable belongs to a compact interval. In conventional studies this computation is done numerically using spatial discretization of differential Operators in the evolution equation. In this paper, we introduce an alternative method that avoids the need for finite-dimensional approximation of the underlying Operators in the evolution model. This method recasts the frequency Response Operator as a two point boundary value problem and uses state-of-the-art automatic spectral collocation techniques for solving integral representations of the resulting boundary value problems with accuracy comparable to machine precision. Our approach has two advantages over currently available schemes: first, it avoids numerical instabilities encountered in systems with differential Operators of high order and, second, it alleviates difficulty in implementing boundary conditions. We provide examples from Newtonian and viscoelastic fluid dynamics to illustrate utility of the proposed method.
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CDC/ECC - Computation of the frequency Responses for distributed systems with one spatial variable
IEEE Conference on Decision and Control and European Control Conference, 2011Co-Authors: Binh K Lieu, Mihailo R JovanovicAbstract:For a class of distributed systems with one spatial variable, we develop a method for computing the maximum singular value of the frequency Response Operator. This computation is typically done by resorting to finite-dimensional approximations of the underlying Operators. In this paper, we introduce an alternative approach that avoids the need for numerical approximation of the Operators in the evolution model. This involves two steps: (i) recasting the frequency Response Operator as a two point boundary value problem; and (ii) using state-of-the-art automatic spectral collocation techniques for solving the resulting boundary value problems with accuracy comparable to machine precision. We provide an example from viscoelastic fluid dynamics to illustrate the utility of the proposed method.
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Frequency Analysis and Norms of Distributed Spatially Periodic Systems
IEEE Transactions on Automatic Control, 2008Co-Authors: Makan Fardad, Mihailo R Jovanovic, Bassam BamiehAbstract:We investigate several fundamental aspects of the theory of linear distributed systems with spatially periodic coefficients. We develop a spatial-frequency domain representation analogous to the lifted or frequency Response Operator representation for linear time periodic systems. Using this representation, we introduce the notion of the H2 norm for this class of systems and provide algorithms for its computation. A stochastic interpretation of the H2 norm is given in terms of spatially cyclostationary random fields and spectral-correlation density Operators. When the periodic coefficients are viewed as feedback modifications of spatially invariant systems, we show how they can stabilize or destabilize the original systems in a manner analogous to vibrational control or parametric resonance in time periodic systems. Two examples from physics are provided to illustrate the main results.
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Frequency Analysis and Norms of Distributed
2008Co-Authors: Makan Fardad, Mihailo R Jovanovic, Bassam BamiehAbstract:We investigate several fundamental aspects of the theory of linear distributed systems with spatially periodic coef- ficients. We develop a spatial-frequency domain representation analogous to the lifted or frequency Response Operator representa- tion for linear time periodic systems. Using this representation, we introduce the notion of the norm for this class of systems and provide algorithms for its computation. A stochastic interpreta- tion of the norm is given in terms of spatially cyclostationary random fields and spectral-correlation density Operators. When the periodic coefficients are viewed as feedback modifications of spatially invariant systems, we show how they can stabilize or destabilize the original systems in a manner analogous to vibra- tional control or parametric resonance in time periodic systems. Two examples from physics are provided to illustrate the main results.
E Mollerstedt - One of the best experts on this subject based on the ideXlab platform.
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frequency domain analysis of linear time periodic systems
IEEE Transactions on Automatic Control, 2005Co-Authors: Henrik Sandberg, E MollerstedtAbstract:In this paper, we study convergence of truncated representations of the frequency-Response Operator of a linear time-periodic system. The frequency-Response Operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an Operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature.
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Frequency-domain analysis of linear time-periodic systems
Proceedings of the 2004 American Control Conference, 2004Co-Authors: Henrik Sandberg, E Mollerstedt, Bo BernhardssonAbstract:In this paper we study how a system with a time-periodic impulse Response may be expanded into a sum of modulated time-invariant systems. This allows us to define a linear frequency-Response Operator for periodic systems, called the harmonic transfer function (HTF). Similar frequency-Response Operators have been derived before for sampled-data systems and periodic finite-dimensional state-space systems. The HTF is an infinite-dimensional Operator that captures the frequency coupling of a time-periodic system. The paper includes analysis of convergence of truncated HTFs. For this reason the concepts of input/output roll-off are developed and related to time-varying Markov parameters.