Analysis of Dynamic Spatial Interaction Models by Means of Optimal Control

Abstract

This paper deals with the design of general classes of dynamic spatial interaction models. On the basis of a general (well‐behaved) multiperiod objective function and of a dynamic model representing the evolution of a spatial interaction system, an optimal control model is constructed. Particular attention is given to the equilibrium and stability conditions. It turns out that it is possible to identify steady‐state solutions for a dynamic spatial interaction model. Furthermore, it can also be demonstrated that the entropy model is a specific case of this spatial interaction system. A simple illustration for urban dynamics is given as well.