caa a22 4500 445842180 CHVBK 20180317145348.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00245-011-9140-2 doi (NATIONALLICENCE)springer-10.1007/s00245-011-9140-2 Optimal Control of Heterogeneous Systems with Endogenous Domain of Heterogeneity [Elektronische Daten] [Anton Belyakov, Tsvetomir Tsachev, Vladimir Veliov] The paper deals with optimal control of heterogeneous systems, that is, families of controlled ODEs parameterized by a parameter running over a domain called domain of heterogeneity. The main novelty in the paper is that the domain of heterogeneity is endogenous: it may depend on the control and on the state of the system. This extension is crucial for several economic applications and turns out to rise interesting mathematical problems. A necessary optimality condition is derived, where one of the adjoint variables satisfies a differential inclusion (instead of equation) and the maximization of the Hamiltonian takes the form of "min-max”. As a consequence, a Pontryagin-type maximum principle is obtained under certain regularity conditions for the optimal control. A formula for the derivative of the objective function with respect to the control from L ∞ is presented together with a sufficient condition for its existence. A stylized economic example is investigated analytically and numerically. Springer Science+Business Media, LLC, 2011 Optimal control nationallicence Distributed control nationallicence Heterogeneous systems nationallicence Endogenous domain of heterogeneity nationallicence Pontryagin-type maximum principle nationallicence Set-valued analysis nationallicence Belyakov Anton ORCOS, Institute of Mathematical Methods in Economics, Vienna University of Technology, Argentinierstrasse 8/105-4, 1040, Vienna, Austria aut Tsachev Tsvetomir Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., Block 8, 1113, Sofia, Bulgaria aut Veliov Vladimir ORCOS, Institute of Mathematical Methods in Economics, Vienna University of Technology, Argentinierstrasse 8/105-4, 1040, Vienna, Austria aut Applied Mathematics & Optimization Springer-Verlag 64/2(2011-10-01), 287-311 0095-4616 64:2<287 2011 64 245 https://doi.org/10.1007/s00245-011-9140-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00245-011-9140-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Belyakov Anton ORCOS, Institute of Mathematical Methods in Economics, Vienna University of Technology, Argentinierstrasse 8/105-4, 1040, Vienna, Austria aut NATIONALLICENCE 700 1- Tsachev Tsvetomir Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., Block 8, 1113, Sofia, Bulgaria aut NATIONALLICENCE 700 1- Veliov Vladimir ORCOS, Institute of Mathematical Methods in Economics, Vienna University of Technology, Argentinierstrasse 8/105-4, 1040, Vienna, Austria aut NATIONALLICENCE 773 0- Applied Mathematics & Optimization Springer-Verlag 64/2(2011-10-01), 287-311 0095-4616 64:2<287 2011 64 245 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer