Results 11 to 20 of about 25,187,934 (365)
A posteriori error estimates of hp spectral element method for parabolic optimal control problems
AIMS Mathematics, 2022 In this paper, we investigate the spectral element approximation for the optimal control problem of parabolic equation, and present a hp spectral element approximation scheme for the parabolic optimal control problem.
Zuliang Lu +5 more
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 2015 Significance Understanding dynamic constraints and balances in nature has facilitated rapid development of knowledge and enabled technology, including aircraft, combustion engines, satellites, and electrical power. This work develops a novel framework to
S. Brunton, J. Proctor, J. Kutz
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AIMS Mathematics, 2023 In this paper, we study the finite volume element method of bilinear parabolic optimal control problem. We will use the optimize-then-discretize approach to obtain the semi-discrete finite volume element scheme for the optimal control problem. Under some
Zuliang Lu +3 more
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Superconvergence for optimal control problems governed by semilinear parabolic equations
AIMS Mathematics, 2022 In this paper, we first investigate optimal control problem for semilinear parabolic and introduce the standard $ L^2(\Omega) $-orthogonal projection and the elliptic projection.
Chunjuan Hou +4 more
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Error estimates of variational discretization for semilinear parabolic optimal control problems
AIMS Mathematics, 2021 In this paper, variational discretization directed against the optimal control problem governed by nonlinear parabolic equations with control constraints is studied.
Chunjuan Hou +3 more
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Balanced truncation of perturbative representations of nonlinear systems [PDF]
, 2007 The paper presents a novel approach for a balanced truncation style of model reduction of a perturbative representation of a nonlinear system. Empirical controllability and observability gramians for nonlinear systems are employed to define a projection ...
Condon, Marissa, Grahovski, Georgi G.
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Balancing for unstable nonlinear systems [PDF]
, 1993 A previously obtained method of balancing for stable nonlinear systems is extended to unstable nonlinear systems. The similarity invariants obtained by the concept of LQG balancing for an unstable linear system can also be obtained by considering a past ...
Scherpen, J.M.A.
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Dynamic Design of a Quad-Stable Piezoelectric Energy Harvester via Bifurcation Theory
Sensors, 2022 The parameter tuning of a multi-stable energy harvester is crucial to enhancing harvesting efficiency. In this paper, the bifurcation theory is applied to quantitatively reveal the effects of structural parameters on the statics and dynamics of a quad ...
Qichang Zhang +4 more
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Frontiers in Materials, 2022 Wind energy is a typical foreseeable renewable energy source. This study constructs and optimizes a variable cross-section cantilever-based piezoelectric energy harvester for low-speed wind energy harvesting.
Kaiyuan Zhao +4 more
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Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis [PDF]
, 2008 By using the Duffing oscillator as a case study, this paper shows that the harmonic components in the nonlinear system response to a sinusoidal input calculated using the Nonlinear Output Frequency Response Functions (NOFRFs) are one of the solutions ...
Billings, S.A. +3 more
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