The Experts below are selected from a list of 9216 Experts worldwide ranked by ideXlab platform
Yoshitsugu Oono - One of the best experts on this subject based on the ideXlab platform.
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renormalization group and Singular Perturbations multiple scales boundary layers and reductive perturbation theory
Physical Review E, 1996Co-Authors: Lin Yuan Chen, Nigel Goldenfeld, Yoshitsugu OonoAbstract:Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary layers with technically difficult asymptotic matching, and WKB analysis. In contrast to conventional methods, the renormalization group approach requires neither ad hoc assumptions about the structure of perturbation series nor the use of asymptotic matching. Our renormalization group approach provides approximate solutions which are practically superior to those obtained conventionally, although the latter can be reproduced, if desired, by appropriate expansion of the renormalization group approximant. We show that the renormalization group equation may be interpreted as an amplitude equation, and from this point of view develop reductive perturbation theory for partial differential equations describing spatially extended systems near bifurcation points, deriving both amplitude equations and the center manifold. @S1063651X~96!00506-5#
Petr Siegl - One of the best experts on this subject based on the ideXlab platform.
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root system of Singular Perturbations of the harmonic oscillator type operators
Letters in Mathematical Physics, 2016Co-Authors: Boris Mityagin, Petr SieglAbstract:We analyze Perturbations of the harmonic oscillator type operators in a Hilbert space \({\mathcal{H}}\), i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.
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root system of Singular Perturbations of the harmonic oscillator type operators
Letters in Mathematical Physics, 2016Co-Authors: Boris Mityagin, Petr SieglAbstract:We analyze Perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues μk satisfying μk+1 − μk ≥ �> 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become even- tually simple and the root system contains a Riesz basis. Mathematics Subject Classification. 47A55, 47A70, 34L10.
Zoran Gajic - One of the best experts on this subject based on the ideXlab platform.
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order reduction of a wind turbine energy system via the methods of system balancing and Singular Perturbations
International Journal of Electrical Power & Energy Systems, 2020Co-Authors: Intessar Aliedani, Zoran GajicAbstract:Abstract In this paper we study the order reduction of a wind turbine model using the methods of balancing transformation and Singular Perturbations. We show that the order of the considered wind turbine model can be reduced from eight to six via the balancing transformation. Further reduction via the aforementioned method results in a significant jump in the error bound. In contrast, the method of Singular Perturbations shows that the order of the model can be further reduced to four, or two, and still provide very good approximations to the system model, in terms of its transient step response. Moreover, we show that the reduction in model order achieved via Singular Perturbations is superior to that achieved via balancing, when the linear-quadratic near-optimal controllers are considered and when wind turbulence and a large-signal disturbance are applied to the system.
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Model order reduction of an islanded microgrid using Singular Perturbations
2016 American Control Conference (ACC), 2016Co-Authors: Kliti Kodra, Zoran GajicAbstract:— In this paper we study model simplification of an islanded microgrid using system order reduction via Singular perturbation (SP) methods. A six-order islanded microgrid model used in a smart grid system is investigated. This model exhibits both lightly and highly damped, highly oscillatory behavior. While it is typical in power systems to use the slow subsystem obtained via SP to approximate the dynamics of the original system, simulation results on the islanded microgrid models show that the slow subsystem cannot approximate the original model well. We explicitly show that this system does not contain any slow dynamics implying that a poor approximation is produced by the slow subsystem obtained via SP. We show that the model investigated has two fast and four very fast modes. An excellent approximation can be obtained by using an approximate fourth-order model based on the very fast modes only. In addition, we also show that the reduced-order model obtained via the direct truncation (DT) method of the balanced model provides a very good approximation of the original system when the latter is truncated to order four.
Martino Bardi - One of the best experts on this subject based on the ideXlab platform.
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ergodicity stabilization and Singular Perturbations for bellman isaacs equations
2010Co-Authors: Olivier Alvarez, Martino BardiAbstract:The authors study Singular Perturbations of optimal stochastic control problems and differential games arising in the dimension reduction of system with multiple time scales. They analyze the uniform convergence of the value functions via the associated Hamilton-Jacobi-Bellman-Isaacs equations, in the framework of viscosity solutions. The crucial properties of ergodicity and stabilization to a constant that the Hamiltonian must possess are formulated as differential games with ergodic cost criteria. They are studied under various different assumptions and with PDE as well as control-theoretic methods. The authors also construct an explicit example where the convergence is not uniform. Finally they give some applications to the periodic homogenization of Hamilton-Jacobi equations with non-coercive Hamiltonian and of some degenerate parabolic PDEs. Table of Contents: Introduction and statement of the problem; Abstract ergodicity, stabilization, and convergence; Uncontrolled fast variables and averaging; Uniformly nondegenerate fast diffusion; Hypoelliptic diffusion of the fast variables; Controllable fast variables; Nonresonant fast variables; A counterexample to uniform convergence; Applications to homogenization; Bibliography. (MEMO/204/960)
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ergodicity stabilization and Singular Perturbations for bellman isaacs equations
2010Co-Authors: Olivier Alvarez, Martino BardiAbstract:The authors study Singular Perturbations of optimal stochastic control problems and differential games arising in the dimension reduction of system with multiple time scales. They analyze the uniform convergence of the value functions via the associated Hamilton-Jacobi-Bellman-Isaacs equations, in the framework of viscosity solutions. The crucial properties of ergodicity and stabilization to a constant that the Hamiltonian must possess are formulated as differential games with ergodic cost criteria. They are studied under various different assumptions and with PDE as well as control-theoretic methods. The authors also construct an explicit example where the convergence is not uniform. Finally they give some applications to the periodic homogenization of Hamilton-Jacobi equations with non-coercive Hamiltonian and of some degenerate parabolic PDEs. Table of Contents: Introduction and statement of the problem; Abstract ergodicity, stabilization, and convergence; Uncontrolled fast variables and averaging; Uniformly nondegenerate fast diffusion; Hypoelliptic diffusion of the fast variables; Controllable fast variables; Nonresonant fast variables; A counterexample to uniform convergence; Applications to homogenization; Bibliography. (MEMO/204/960)
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Singular Perturbations of nonlinear degenerate parabolic pdes a general convergence result
Archive for Rational Mechanics and Analysis, 2003Co-Authors: Olivier Alvarez, Martino BardiAbstract:The main result of the paper is a general convergence theorem for the viscosity solutions of Singular perturbation problems for fully nonlinear degenerate parabolic PDEs (partial differential equations) with highly oscillating initial data. It substantially generalizes some results obtained previously in [2]. Under the only assumptions that the Hamiltonian is ergodic and stabilizing in a suitable sense, the solutions are proved to converge in a relaxed sense to the solution of a limit Cauchy problem with appropriate effective Hamiltonian and initial data. In its formulation, our convergence result is analogous to the stability property of Barles and Perthame. It should thus reveal a useful tool for studying general Singular perturbation problems by viscosity solutions techniques. A detailed exposition of ergodicity and stabilization is given, with many examples. Applications to homogenization and averaging are also discussed.
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viscosity solutions methods for Singular Perturbations in deterministic and stochastic control
Siam Journal on Control and Optimization, 2001Co-Authors: Olivier Alvarez, Martino BardiAbstract:Viscosity solutions methods are used to pass to the limit in some penalization problems for first order and second order, degenerate parabolic, Hamilton--Jacobi--Bellman equations. This characterizes the limit of the value functions of Singularly perturbed optimal control problems for deterministic systems and for controlled degenerate diffusions. The results apply to cases where the usual order reduction method does not give the correct limit, and to systems with fast state variables depending nonlinearly on the control. Some connections with ergodic control and periodic homogenization are discussed.
Lin Yuan Chen - One of the best experts on this subject based on the ideXlab platform.
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renormalization group and Singular Perturbations multiple scales boundary layers and reductive perturbation theory
Physical Review E, 1996Co-Authors: Lin Yuan Chen, Nigel Goldenfeld, Yoshitsugu OonoAbstract:Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary layers with technically difficult asymptotic matching, and WKB analysis. In contrast to conventional methods, the renormalization group approach requires neither ad hoc assumptions about the structure of perturbation series nor the use of asymptotic matching. Our renormalization group approach provides approximate solutions which are practically superior to those obtained conventionally, although the latter can be reproduced, if desired, by appropriate expansion of the renormalization group approximant. We show that the renormalization group equation may be interpreted as an amplitude equation, and from this point of view develop reductive perturbation theory for partial differential equations describing spatially extended systems near bifurcation points, deriving both amplitude equations and the center manifold. @S1063651X~96!00506-5#
