Our focus mainly concerns solving the HamiltonJacobin-Bellman (HJB) equations derived from the nonlinear receding horizon control (RHC) schemes. A new numerical methods using the finite difference with sigmoidal transformation for computing the value function is developed. The developed numerical method is a stable and convergent algorithm for HJB equations. A fine optimization procedure is developed to increase the calculation accuracy with less time consumption. The value function is directly applied to the receding horizon controller design of some kind of nonlinear systems.
Detection of geographic concentration of economic activities at different spatial scales has long been of interest to researchers from spatial economics, regional science and economic geography. Using a unique dataset from the first industrial land use survey of its kind in China, this research is the first effort attempting to explore spatial distribution particularly geographic concentration of industries in China using firm-level data. Distancebased functions and spatial cluster analysis are employed to detect the spatial scales as well as the geographic locations of industrial concentration. The results indicate that four of the five selected industries are in general concentrated in southern Jiangsu at small spatial scales (less than 5 km), while the chemical industry demonstrates an overall spatial dispersion pattern relative to the distribution of all other industries. Most industrial clusters have a radius of less than 2.5 km containing 20%-60% of enterprises and 60%-86% of employees from each selected industry, with larger clusters showing relatively weaker concentration. This research demonstrates the connections and complementarity of different approaches, complementing previous studies that use distance-based functions with spatial scan statistics.
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