Robust Control and Hot Spots in Dynamic Spatially Interconnected Systems

45 Pages Posted: 9 Jan 2011

See all articles by William A. Brock

William A. Brock

University of Wisconsin, Madison - Department of Economics; University of Missouri at Columbia - Department of Economics

Anastasios Xepapadeas

Athens University of Economics and Business; University of Bologna - School of Economics, Management, and Statistics

Date Written: 2010

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 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.

Keywords: Distributed Parameter Systems, Robust Control, Spatial Invariance, Hot Spot, Agglomeration

JEL Classification: C61, C65, Q22

Suggested Citation

Brock, William A. and Xepapadeas, Anastasios, Robust Control and Hot Spots in Dynamic Spatially Interconnected Systems (2010). FEEM Working Paper No. 155.2010, Available at SSRN: https://ssrn.com/abstract=1736486 or http://dx.doi.org/10.2139/ssrn.1736486

William A. Brock (Contact Author)

University of Wisconsin, Madison - Department of Economics ( email )

1180 Observatory Drive
Madison, WI 53706
United States
608-263-6655 (Phone)
608-263-3876 (Fax)

University of Missouri at Columbia - Department of Economics ( email )

118 Professional Building
Columbia, MO 65211
United States

Anastasios Xepapadeas

Athens University of Economics and Business ( email )

76 Patission Street
Athens, 104 34
Greece

University of Bologna - School of Economics, Management, and Statistics ( email )

Piazza Scaravilli 1
40126 Bologna, fc 47100
Italy

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