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An optimal control model for cloud seeding in a deterministic and stochastic environment.

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Title: An optimal control model for cloud seeding in a deterministic and stochastic environment.
Authors: Misra, Arvind Kumar1 (AUTHOR), Tripathi, Amita1 (AUTHOR) amita4utripathi@gmail.com
Source: Optimal Control - Applications & Methods. Nov2020, Vol. 41 Issue 6, p2166-2189. 24p.
Subjects: Cloud condensation nuclei, Snowpack augmentation, Rain-making, Hamilton-Jacobi-Bellman equation, Stability theory
Geographic Terms: India
Abstract: Summary: To promote artificial rain in India and other such developing countries, in this article, we have proposed and analyzed a nonlinear mathematical model for cloud seeding by considering that aerosols are introduced proportional to the density of water vapors present in the atmosphere. The model is analyzed using Lyapunov's stability theory of differential equations. To reduce the cost of cloud seeding, an optimal control strategy is designed by incorporating four control parameters. We have shown the existence and uniqueness of solution of this optimal control problem, using Pontryagins Maximum Principle. To minimize the cost in making artificial rain, the optimal control problem provides the strategy for the rate of introduction of aerosols in the atmosphere. To capture the effects of environmental noise on control strategies, the model in deterministic framework is converted into stochastic framework. In this regard, the Hamilton‐Jacobi‐Bellman equation for stochastic control cost function has been formed. The stochastic analysis implies that the control strategy is effective in reducing the cost and increasing rainfall. [ABSTRACT FROM AUTHOR]
Copyright of Optimal Control - Applications & Methods is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22Optimal+Control+-+Applications+%26+Methods%22">Optimal Control - Applications & Methods</searchLink>. Nov2020, Vol. 41 Issue 6, p2166-2189. 24p.
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  Data: <searchLink fieldCode="DE" term="%22Cloud+condensation+nuclei%22">Cloud condensation nuclei</searchLink><br /><searchLink fieldCode="DE" term="%22Snowpack+augmentation%22">Snowpack augmentation</searchLink><br /><searchLink fieldCode="DE" term="%22Rain-making%22">Rain-making</searchLink><br /><searchLink fieldCode="DE" term="%22Hamilton-Jacobi-Bellman+equation%22">Hamilton-Jacobi-Bellman equation</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22India%22">India</searchLink>
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  Label: Abstract
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  Data: Summary: To promote artificial rain in India and other such developing countries, in this article, we have proposed and analyzed a nonlinear mathematical model for cloud seeding by considering that aerosols are introduced proportional to the density of water vapors present in the atmosphere. The model is analyzed using Lyapunov's stability theory of differential equations. To reduce the cost of cloud seeding, an optimal control strategy is designed by incorporating four control parameters. We have shown the existence and uniqueness of solution of this optimal control problem, using Pontryagins Maximum Principle. To minimize the cost in making artificial rain, the optimal control problem provides the strategy for the rate of introduction of aerosols in the atmosphere. To capture the effects of environmental noise on control strategies, the model in deterministic framework is converted into stochastic framework. In this regard, the Hamilton‐Jacobi‐Bellman equation for stochastic control cost function has been formed. The stochastic analysis implies that the control strategy is effective in reducing the cost and increasing rainfall. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Optimal Control - Applications & Methods is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1002/oca.2648
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 24
        StartPage: 2166
    Subjects:
      – SubjectFull: Cloud condensation nuclei
        Type: general
      – SubjectFull: Snowpack augmentation
        Type: general
      – SubjectFull: Rain-making
        Type: general
      – SubjectFull: Hamilton-Jacobi-Bellman equation
        Type: general
      – SubjectFull: Stability theory
        Type: general
      – SubjectFull: India
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      – TitleFull: An optimal control model for cloud seeding in a deterministic and stochastic environment.
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            NameFull: Misra, Arvind Kumar
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            NameFull: Tripathi, Amita
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            – D: 01
              M: 11
              Text: Nov2020
              Type: published
              Y: 2020
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              Value: 41
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