Geodesic
Optimal Control of Heterogeneous Systems
Mathematics and Education in Mathematics, Tome 41 (2012) no. 1, pp. 70-82.

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The present paper is a survey on some results on optimal control of continuous heterogeneous systems, which were recently published in periodic journals. A dynamical system is called heterogeneous if each of its elements has specific dynamics. The heterogeneity of the systems we consider is described by a one- or two-dimensional parameter – each element of the system corresponds to a specific value of the parameter. The heterogeneous dynamical systems are used to model processes in economics, epidemiology, biology, social security (preventing the use of illicit drugs) etc. Here we consider models of optimal investment in education at the macroeconomic level [11], of restricting the damage caused by the spread of HIV [9], of markets for emission permits [3, 4] and optimal macroeconomic growth with endogenous improvement of the cutting-edge technologies [1]. *2010 Mathematics Subject Classification: 49K20, 92C60, 35Q91, 37N40, 91B69.
Keywords: Optimal Control, Continuous Heterogeneous Dynamical Systems, Applications in Economics and Epidemiology 
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Tsachev, Tsvetomir. Optimal Control of Heterogeneous Systems. Mathematics and Education in Mathematics, Tome 41 (2012) no. 1, pp. 70-82. http://geodesic.mathdoc.fr/item/MEM_2012_41_1_a2/