# Robust Control and Hot Spots in Dynamic Spatially Interconnected Systems

*William Brock* and
*Anastasios Xepapadeas* ()

No 1024, DEOS Working Papers from Athens University of Economics and Business

**Abstract:**
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 inÃƒï¿½Ã¯Â¿Â½nite 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 Ãƒï¿½Ã¯Â¿Â½nite state space robust control problems each of which can be solved by standard methods. We use this convenient property to characterize hot spotsÃƒï¿½Ã¯Â¿Â½which are points in the transformed space that correspond to Ãƒï¿½Ã¯Â¿Â½breakdownÃƒï¿½Ã¯Â¿Â½ points in conventional Ãƒï¿½Ã¯Â¿Â½nite 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 Ãƒï¿½Ã¯Â¿Â½shing model.

**Keywords:** Distributed parameter systems; robust control; spatial invariance; hot spot; agglomeration. (search for similar items in EconPapers)

**JEL-codes:** C61 C65 Q22 (search for similar items in EconPapers)

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**Related works:**

Working Paper: Robust Control and Hot Spots in Dynamic Spatially Interconnected Systems (2010)

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**Persistent link:** http://EconPapers.repec.org/RePEc:aue:wpaper:1024

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