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
    ---><---

    References listed on IDEAS

    as
    1. Boucekkine, R. & Camacho, C. & Fabbri, G., 2013. "Spatial dynamics and convergence: The spatial AK model," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2719-2736.
    2. Stephen J. Redding & Esteban Rossi-Hansberg, 2017. "Quantitative Spatial Economics," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 21-58, September.
    3. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2021. "From firm to global-level pollution control: The case of transboundary pollution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 331-345.
    4. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2021. "From firm to global-level pollution control: The case of transboundary pollution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 331-345.
    5. Boucekkine, Raouf & Camacho, Carmen & Zou, Benteng, 2009. "Bridging The Gap Between Growth Theory And The New Economic Geography: The Spatial Ramsey Model," Macroeconomic Dynamics, Cambridge University Press, vol. 13(1), pages 20-45, February.
    6. Chichilnisky, Graciela & Heal, Geoffrey & Beltratti, Andrea, 1995. "The Green Golden Rule," Economics Letters, Elsevier, vol. 49(2), pages 175-179, August.
    7. C. V. Pao, 1992. "Nonlinear Parabolic and Elliptic Equations," Springer Books, Springer, number 978-1-4615-3034-3, October.
    8. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "Growth and agglomeration in the heterogeneous space: a generalized AK approach," Journal of Economic Geography, Oxford University Press, vol. 19(6), pages 1287-1318.
    9. Daron Acemoglu & Philippe Aghion & Leonardo Bursztyn & David Hemous, 2012. "The Environment and Directed Technical Change," American Economic Review, American Economic Association, vol. 102(1), pages 131-166, February.
    10. Nicholas Stern, 2008. "The Economics of Climate Change," American Economic Review, American Economic Association, vol. 98(2), pages 1-37, May.
    11. Partha Dasgupta, 2008. "Discounting climate change," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 141-169, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Torre, Davide La & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Transboundary pollution externalities: Think globally, act locally?," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    2. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "A dynamic theory of spatial externalities," Games and Economic Behavior, Elsevier, vol. 132(C), pages 133-165.
    3. Philippe Aghion & Antoine Dechezleprêtre & David Hémous & Ralf Martin & John Van Reenen, 2016. "Carbon Taxes, Path Dependency, and Directed Technical Change: Evidence from the Auto Industry," Journal of Political Economy, University of Chicago Press, vol. 124(1), pages 1-51.
    4. Tsangaris, Spyridon & Xepapadeas, Anastasios & Yannacopoulos, Athanasios N. & Salvati, Luca, 2024. "Spatial externalities, R&D spillovers, and endogenous technological change," Regional Science and Urban Economics, Elsevier, vol. 109(C).
    5. Buchholz Wolfgang & Heindl Peter, 2015. "Ökonomische Herausforderungen des Klimawandels," Perspektiven der Wirtschaftspolitik, De Gruyter, vol. 16(4), pages 324-350, December.
    6. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "Managing spatial linkages and geographic heterogeneity in dynamic models with transboundary pollution," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    7. Albeverio, Sergio & Mastrogiacomo, Elisa, 2022. "Large deviation principle for spatial economic growth model on networks," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    8. Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2023. "Spatial growth theory: Optimality and spatial heterogeneity," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    9. Boucekkine, R. & Fabbri, G. & Federico, S. & Gozzi, F., 2020. "Control theory in infinite dimension for the optimal location of economic activity: The role of social welfare function," Working Papers 2020-02, Grenoble Applied Economics Laboratory (GAEL).
    10. Fausto Gozzi & Marta Leocata & Giulia Pucci, 2024. "Network-Based Optimal Control of Pollution Growth," Papers 2406.15338, arXiv.org, revised Jan 2026.
    11. Carmen Camacho & Alexandre Cornet, 2021. "Diffusion of soil pollution in an agricultural economy. The emergence of regions, frontiers and spatial patterns," PSE Working Papers halshs-02652191, HAL.
    12. Calvia, Alessandro & Gozzi, Fausto & Leocata, Marta & Papayiannis, Georgios I. & Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2024. "An optimal control problem with state constraints in a spatio-temporal economic growth model on networks," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    13. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2020. "Optimal location of economic activity and population density: The role of the social welfare function," AMSE Working Papers 2003, Aix-Marseille School of Economics, France.
    14. William Brock & Anastasios Xepapadeas, 2020. "Climate change policy under spatial heat transport and polar amplification," Chapters, in: Graciela Chichilnisky & Armon Rezai (ed.), Handbook on the Economics of Climate Change, chapter 7, pages 127-166, Edward Elgar Publishing.
    15. Herb Kunze & Davide La Torre & Simone Marsiglio, 2019. "A Multicriteria Macroeconomic Model with Intertemporal Equity and Spatial Spillovers," Papers 1911.08247, arXiv.org.
    16. Carmen Camacho & Alexandre Cornet, 2021. "Diffusion of soil pollution in an agricultural economy. The emergence of regions, frontiers and spatial patterns," Working Papers halshs-02652191, HAL.
    17. Boucekkine, R. & Fabbri, G. & Federico, S. & Gozzi, F., 2020. "Control theory in infinite dimension for the optimal location of economic activity: The role of social welfare function," Working Papers 2020-02, Grenoble Applied Economics Laboratory (GAEL).
    18. Herb Kunze & Davide Torre & Simone Marsiglio, 2022. "Sustainability and spatial spillovers in a multicriteria macroeconomic model," Annals of Operations Research, Springer, vol. 311(2), pages 1067-1084, April.
    19. Raouf Boucekkine & Carmen Camacho & Weihua Ruan, 2025. "Endogenous Growth, Spatial Dynamics and Convergence: A Refinement," Annals of Economics and Statistics, GENES, issue 159, pages 79-106.
    20. Davide Torre & Danilo Liuzzi & Simone Marsiglio, 2024. "Epidemic outbreaks and the optimal lockdown area: a spatial normative approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 349-411, February.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.