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Robust Control and Hot Spots in Dynamic Spatially Interconnected Systems


  • William Brock

    (University of Wisconsin and Beijer Fellow)

  • Anastasios Xepapadeas

    (Athens University of Economics and Beijer Fellow)


This paper develops linear quadratic robust control theory for a class of spatially invariant distributed control systems that appear in areas of economics such as New Economic Geography, management of ecological systems, optimal harvesting of spatially mobile species, and the like. Since this class of problems has an infinite dimensional state and control space it would appear analytically intractable. We show that by Fourier transforming the problem, the solution decomposes into a countable number of finite state space robust control problems each of which can be solved by standard methods. We use this convenient property to characterize “hot spots” which are points in the transformed space that correspond to “breakdown” points in conventional finite dimensional robust control, or where instabilities appear or where the value function loses concavity. We apply our methods to a spatial extension of a well known optimal fishing model.

Suggested Citation

  • William Brock & Anastasios Xepapadeas, 2010. "Robust Control and Hot Spots in Dynamic Spatially Interconnected Systems," Working Papers 2010.155, Fondazione Eni Enrico Mattei.
  • Handle: RePEc:fem:femwpa:2010.155

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    More about this item


    Distributed Parameter Systems; Robust Control; Spatial Invariance; Hot Spot; Agglomeration;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • Q22 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Fishery

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