Geometrical and topological methods in optimal control theory

Vakhrameev, S. A.

doi:10.1007/bf02362893

Cited by 12 publications

(3 citation statements)

References 817 publications

(112 reference statements)

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“…Ideas on nontrivial topological properties of various systems can be found in many areas of research such as nonlinear dynamics [1], control system theory [2], biology [3], data analysis [4], etc. In physics and material science, these ideas have found applications to the socalled topological insulators, which have recently drawn considerable attention due to their unusual properties.…”

Section: Introductionmentioning

confidence: 99%

Reconfigurable Microwave Photonic Topological Insulator

Goryachev

Tobar

2016

Phys. Rev. Applied

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Using full 3D finite element simulation and underlining Hamiltonian models, we demonstrate reconfigurable photonic analogues of topological insulators on a regular lattice of tunable posts in a re-entrant 3D lumped element type system. The tunability allows dynamical in-situ change of media chirality and other properties via alteration of the same parameter for all posts, and as a result, great flexibility in choice of bulk/edge configurations. Additionally, one way photon transport without an external magnetic field is demonstrated. The ideas are illustrated by using both full finite element simulation as well as simplified harmonic oscillator models. Dynamical reconfigurability of the proposed systems paves the way to a new class of systems that can be employed for random access, topological signal processing and sensing.

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Section: Introductionmentioning

confidence: 99%

Reconfigurable Microwave Photonic Topological Insulator

Goryachev

Tobar

2016

Phys. Rev. Applied

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“…We refer to [22, theorem 12.4] for a proof of the Pontryagin maximum principle, together with an account of the appropriate regularity assumption assumed on the various curves. We refer for example to [23,24] for extended reviews on optimal control theory. For application to our problem, we shall make crucial use of the fact that conditions (5.4), (5.5) and (5.7) can be obtained as the critical points of the variational principle…”

Section: C(x(t) U(t)) Dt (51) Subject To the Conditionsẋ (T) = X(x(mentioning

confidence: 99%

Section: (T) ∈ (T X(t) S T ) •mentioning

confidence: 99%

Dynamics and optimal control of flexible solar updraft towers

et al. 2015

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The use of solar chimneys for energy production was suggested more than 100 years ago. Unfortunately, this technology has not been realized on a commercial scale, in large part due to the high cost of erecting tall towers using traditional methods of construction. Recent works have suggested a radical decrease in tower cost by using an inflatable self-supported tower consisting of stacked toroidal bladders. While the statics deflections of such towers under constant wind have been investigated before, the key for further development of this technology lies in the analysis of dynamics, which is the main point of this paper. Using Lagrangian reduction by symmetry, we develop a fully three-dimensional theory of motion for such towers and study the tower's stability and dynamics. Next, we derive a geometric theory of optimal control for the tower dynamics using variable pressure inside the bladders and perform detailed analytical and numerical studies of the control in two dimensions. Finally, we report on the results of experiments demonstrating the remarkable stability of the tower in real-life conditions, showing good agreement with theoretical results.

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