### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 5571-5576 |

Number of pages | 6 |

Journal | Proceedings of the National Academy of Sciences of the United States of America |

Volume | 114 |

Issue number | 22 |

DOIs | |

State | Published - May 30 2017 |

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### ASJC Scopus subject areas

- General

### Cite this

**Effective control of complex turbulent dynamical systems through statistical functionals.** / Majda, Andrew; Qi, Di.

Research output: Contribution to journal › Article

*Proceedings of the National Academy of Sciences of the United States of America*, vol. 114, no. 22, pp. 5571-5576. https://doi.org/10.1073/pnas.1704013114

}

TY - JOUR

T1 - Effective control of complex turbulent dynamical systems through statistical functionals

AU - Majda, Andrew

AU - Qi, Di

PY - 2017/5/30

Y1 - 2017/5/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85020009732&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85020009732&partnerID=8YFLogxK

U2 - 10.1073/pnas.1704013114

DO - 10.1073/pnas.1704013114

M3 - Article

AN - SCOPUS:85020009732

VL - 114

SP - 5571

EP - 5576

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 22

ER -