Closed-Loop Turbulence Control: Progress and Challenges

Brunton, Steven L.; Noack, Bernd R.

doi:10.1115/1.4031175

Cited by 438 publications

(313 citation statements)

References 416 publications

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“…Another driving force is flow control. Simple control-oriented ROM are key enablers for model-based control design [8,40]. The application of linear control design methods to a CFD discretization constitutes, for instance, a immense numerical challenge.…”

Section: Introductionmentioning

confidence: 99%

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

Stankiewicz

Morzyński

Kotecki

et al. 2016

Theor. Comput. Fluid Dyn.

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We present a low-dimensional Galerkin model with state-dependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the three-dimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier-Stokes solution and converges to a periodic limit cycle. The investigated Galerkin models are based on the dynamic mode decomposition (DMD) and derive the dynamical system from first principles, the Navier-Stokes equations. A DMD model with training data from the initial linear transient fails to predict the limit cycle. Conversely, a model from limit-cycle data underpredicts the initial growth rate roughly by a factor 5. Key enablers for uniform accuracy throughout the transient are a continuous mode interpolation between both oscillatory fluctuations and the addition of a shift mode. This interpolated model is shown to capture both the transient growth of the oscillation and the limit cycle.

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Section: Introductionmentioning

confidence: 99%

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

Stankiewicz

Morzyński

Kotecki

et al. 2016

Theor. Comput. Fluid Dyn.

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“…It is worthwhile to briefly comment on a standard deterministic control strategy (7,8) for the L-96 model and its limitations. To control the instabilities about the mean state, it is natural to use the formulation in [11].…”

Section: Statistical Response For the Mean State From Statistical Linearmentioning

confidence: 99%

“…The linear response from the FDT forms a non-Markovian delayed control. Especially if we make the quasi-Gaussian approximation for [8] [that is, set…”

Section: Statistical Response For the Mean State From Statistical Linearmentioning

confidence: 99%

“…Control of these complex systems is a grand challenge, for example, in mitigating the effects of climate change (5, 6) or safe design of technology with fully developed shear turbulence. Control of flows in the transition to turbulence, where there is a small dimension of instabilities about a basic mean state, is an important and successful discipline (7,8). In complex turbulent dynamical systems, it is impossible to track and control the large dimension of instabilities, which strongly interact and exchange energy (9), and new control strategies are needed.…”

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confidence: 99%

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Effective control of complex turbulent dynamical systems through statistical functionals

Majda

2017

Proc. Natl. Acad. Sci. U.S.A.

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Turbulent dynamical systems characterized by both a highdimensional phase space and a large number of instabilities are ubiquitous among complex systems in science and engineering, including climate, material, and neural science. Control of these complex systems is a grand challenge, for example, in mitigating the effects of climate change or safe design of technology with fully developed shear turbulence. Control of flows in the transition to turbulence, where there is a small dimension of instabilities about a basic mean state, is an important and successful discipline. In complex turbulent dynamical systems, it is impossible to track and control the large dimension of instabilities, which strongly interact and exchange energy, and new control strategies are needed. The goal of this paper is to propose an effective statistical control strategy for complex turbulent dynamical systems based on a recent statistical energy principle and statistical linear response theory. We illustrate the potential practical efficiency and verify this effective statistical control strategy on the 40D Lorenz 1996 model in forcing regimes with various types of fully turbulent dynamics with nearly one-half of the phase space unstable.statistical energy principle | response theory | statistical control T urbulent dynamical systems characterized by both a highdimensional phase space and a large number of instabilities are ubiquitous among complex systems in science and engineering (1-4), including climate, material, and neural science. Control of these complex systems is a grand challenge, for example, in mitigating the effects of climate change (5, 6) or safe design of technology with fully developed shear turbulence. Control of flows in the transition to turbulence, where there is a small dimension of instabilities about a basic mean state, is an important and successful discipline (7,8). In complex turbulent dynamical systems, it is impossible to track and control the large dimension of instabilities, which strongly interact and exchange energy (9), and new control strategies are needed.The goal here is to propose an effective statistical control strategy for complex turbulent dynamical systems based on a recent statistical energy principle (10, 11) and statistical linear response theory (12-14). We illustrate the potential practical efficiency and verify this effective statistical control strategy on the 40D Lorenz 1996 (L-96) model in forcing regimes with various types of fully turbulent dynamics with nearly one-half of the phase space unstable.i) The statistical control theory proposed here has the goal and theoretical steps in its design. A) Goal and statistical energy. The statistical energy, E , is the sum of the energy of the statistical mean and the trace of the statistical covariance (10, 11). A turbulent dynamical system is subjected to poorly known external forcing, and the goal of the statistical control strategy is to find an effective deterministic feedback control to drive the statistical energy measured at some time...

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“…In contrast, as we will see, classification of a natural image may require only tens of measurements. More generally in engineering applications, machine learning and classification are becoming more widely used for modeling and control [1,27,33,7].…”

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confidence: 99%

Sparse Sensor Placement Optimization for Classification

Brunton¹,

Brunton²,

Proctor³

et al. 2016

SIAM J. Appl. Math.

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Abstract. Choosing a limited set of sensor locations to characterize or classify a high-dimensional system is an important challenge in engineering design. Traditionally, optimizing the sensor locations involves a brute-force, combinatorial search, which is NP-hard and is computationally intractable for even moderately large problems. Using recent advances in sparsity-promoting techniques, we present a novel algorithm to solve this sparse sensor placement optimization for classification (SSPOC) that exploits low-dimensional structure exhibited by many high-dimensional systems. Our approach is inspired by compressed sensing, a framework that reconstructs data from few measurements. If only classification is required, reconstruction can be circumvented and the measurements needed are orders-of-magnitude fewer still. Our algorithm solves an 1 minimization to find the fewest nonzero entries of the full measurement vector that exactly reconstruct the discriminant vector in feature space; these entries represent sensor locations that best inform the decision task. We demonstrate the SSPOC algorithm on five classification tasks, using datasets from a diverse set of examples, including physical dynamical systems, image recognition, and microarray cancer identification. Once training identifies sensor locations, data taken at these locations forms a low-dimensional measurement space, and we perform computationally efficient classification with accuracy approaching that of classification using full-state data. The algorithm also works when trained on heavily subsampled data, eliminating the need for unrealistic full-state training data.

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Closed-Loop Turbulence Control: Progress and Challenges

Cited by 438 publications

References 416 publications

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

Effective control of complex turbulent dynamical systems through statistical functionals

Sparse Sensor Placement Optimization for Classification

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