IDEAS home Printed from https://ideas.repec.org/p/luc/wpaper/26-01.html

Optimal Control of Diffusion Systems with State Constraints: Theory and Application to Land Restoration

Author

Listed:
  • Benteng Zou

    (DEM, Université du Luxembourg)

  • Carmen Camacho

    (Paris School of Economics)

  • Weihua Ruan

    (Purdue University Northwest, USA)

Abstract

"We develop an optimal control framework for infinite-dimensional systems with in- equality state constraints, extending the Pontryagin Maximum Principle to diffusion- driven dynamics with bounded states. The resulting conditions feature Radon-measure multipliers that characterize boundary behavior in distributed environments. As an illus- tration, we apply the framework to a model of land fertility evolving through reversible pollution and spatial diffusion. We show how discounting shapes optimal consumption, the activation of state constraints, and long-run spatial patterns. In the homogeneous case, explicit solutions identify conditions for full restoration or persistent degradation, while heterogeneous settings generate hybrid finite-horizon and long-run regimes. The framework provides general analytical tools for dynamic optimization problems with dif- fusion and bounded state variables."

Suggested Citation

  • Benteng Zou & Carmen Camacho & Weihua Ruan, 2026. "Optimal Control of Diffusion Systems with State Constraints: Theory and Application to Land Restoration," DEM Discussion Paper Series 26-01, Department of Economics at the University of Luxembourg.
    • Handle: RePEc:luc:wpaper:26-01
    as

    Download full text from publisher

    File URL: https://orbilu.uni.lu/handle/10993/67681
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O44 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Environment and Growth
    • Q15 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Land Ownership and Tenure; Land Reform; Land Use; Irrigation; Agriculture and Environment
    • Q56 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Environment and Development; Environment and Trade; Sustainability; Environmental Accounts and Accounting; Environmental Equity; Population Growth
    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:luc:wpaper:26-01. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Marina Legrand The email address of this maintainer does not seem to be valid anymore. Please ask Marina Legrand to update the entry or send us the correct address (email available below). General contact details of provider: https://edirc.repec.org/data/crcrplu.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.