Vortex-based Control Algorithms

Vainchtein, Dmitri; Mezić, Igor

doi:10.1007/978-3-540-36085-8_9

Cited by 6 publications

(6 citation statements)

References 85 publications

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“…This approach will be described in more detail in the context of another control problem in Section 4.2; here we mention only that it also resulted in an optimal control in the form of a set of Dirac delta measures applied at the optimal phases of the vortex rotation. A generalization of this problem was considered by the same authors in [23] where the point vortices were replaced with elliptic vortex patches possessing more internal degrees of freedom. A solution of the associated problem of state estimation for a co-rotating vortex pair was proposed by Tadmor [88] and will be discussed in Section 5.…”

Section: Control Of Vortex Flows In Domains Without Boundariesmentioning

confidence: 99%

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Vortex dynamics models in flow control problems

Protas

2008

Nonlinearity

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In this paper we review the state of the art in the field of control of vortex dynamics. We focus on problems governed by two-dimensional incompressible Euler equations in domains both with and without boundaries. Following a comprehensive review of earlier approaches, we discuss how methods of modern control and optimization theory can be employed to solve control problems for vortex system. In addition, we also address the companion problem of the state estimation for vortex systems. While most of the discussion concerns point vortex systems, in the second part of the paper we also introduce a novel approach to the control of Euler flows involving finite-area vorticity distributions. The paper concludes with what, in the author's opinion, represent promising new research directions.

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Section: Control Of Vortex Flows In Domains Without Boundariesmentioning

confidence: 99%

“…Such vortex-based approaches to solution of flow control problem are currently also the subject of active research, and the purpose of the present article is to review the recent advances in this area. An earlier review of this field was written by Vainchtein and Mezić [23].…”

Section: Introductionmentioning

confidence: 99%

Vortex dynamics models in flow control problems

Protas

2008

Nonlinearity

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“…In most of the control problems, concerning realistic flows, the solution is achieved by means of simplified models such as point vortex [17]. There is a special interest in the use of control methods applied to vortex dynamics in the fields of geophysical fluid dynamics, aeronautic and hydrodynamic [16].…”

Section: Introductionmentioning

confidence: 99%

Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow

Balsa

Cots

Gergaud

et al. 2020

Lecture Notes in Electrical Engineering

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In this work we are interested in controlling the displacement of particles in interaction with N point vortices, in a two-dimensional fluid and neglecting the viscous diffusion. We want to drive a passive particle from an initial point to a final point, both given a priori, in a given finite time, the control being due to the possibility of impulsion in any direction of the plane. For the energy cost, the candidates as minimizers are given by the normal extremals of the Pontryagin Maximum Principle (PMP). The transcription of the PMP gives us a set of nonlinear equations to solve, the so-called shooting equations. We introduce these shooting equations and present numerical computations in the cases of N = 1, 2, 3 and 4 point vortices. In the integrable case N = 1, we give complete quadratures of the normal extremals.

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“…Point vortex are mathematical models used to describe the dynamic of vortex-dominated flows. These models are based on a low dimensional description of the flow features [1]. Vortex dynamics, based on point vortex models, have been employed in many science and engineering areas like geophysics, turbulence, superfluids or hydrodynamic [2,3,4,5,6].…”

Section: Introductionmentioning

confidence: 99%

“…It has emerged in recent years a special interest in the use of control theory applied to vortex dynamics. In most of the control problems, concerning realistic flows, the solution is achieved by means of simplified models such as point vortex [1]. In consequence, there is a special interest in the use of control methods applied to vortex dynamics, namely in the fields of geophysical fluid dynamics, aeronautics and hydrodynamics [7].…”

Section: Introductionmentioning

confidence: 99%

Control Problem in Passive Tracer Advection by Point Vortex Flow: A Case Study

Balsa¹,

Gama²,

Braz-César³

2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Vortex dynamics and passive tracers in vortex-dominated flows form a vast area of research that continues to attract the attention of numerous studies. Among these studies, it has emerged in recent times a special interest in the use of control theory applied to vortex dynamics. Point vortices are singular solutions of the two-dimensional incompressible Euler equations. These solutions correspond to the limiting case where the vorticity is completely concentrated on a finite number of spatial points, each with a prescribed strength/circulation. By definition, a passive tracer is a point vortex with zero circulation. We are concerned with the dynamics of a passive tracer advected by two-dimensional point vortex flow. More precisely, we want to drive a passive particle from an initial starting point to a final terminal point, both given a priori, in a given finite time. The flow is originated by the displacement of N viscous point vortices. More precisely, we look for the optimal trajectories that minimize the objective function that correspond to the energy expended in the control of the trajectories. The restrictions are essentially due to the ordinary differential equations that govern the displacement of the passive particle around the viscous point vortices. 3495 COMPDYN 2019 7 th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering M. Papadrakakis, M. Fragiadakis (eds.

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Vortex-based Control Algorithms

Cited by 6 publications

References 85 publications

Vortex dynamics models in flow control problems

Vortex dynamics models in flow control problems

Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow

Control Problem in Passive Tracer Advection by Point Vortex Flow: A Case Study

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