Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

This work deals with the position control of selected patterns in reaction-diffusion systems. Exemplarily, the Schl\"{o}gl and FitzHugh-Nagumo model are discussed using three different approaches. First, an analytical solution is proposed. Second, the standard optimal control procedure is applied. The third approach extends standard optimal control to so-called sparse optimal control that results in very localized control signals and allows the analysis of second order optimality conditions.Comment: 22 pages, 3 figures, 2 table

A dynamic linear-programming approach to the planning of national settlement systems

In this paper the problem of planning human-settlement systems (HSS) is formulated in a dynamic linear-programming (DLP) framework. Such large time-dependent problems are treated both by optimal-control and linear-programming techniques. A multiregional population-growth model forms the state equation of the DLP problem. Budget, resource, and quality-of-life constraints are considered. The paper describes the formalization of the HSS planning problem and suggests methods for its solution.