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A. Belyakov, Tz. Tsachev, V.M. Veliov:
"Optimal control of heterogeneous systems with endogenous domain of heterogeneity";
Applied Mathematics and Optimization, 64 (2011), 287 - 311.

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 satis¯es a di®erential 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 egularity conditions for the optimal control. A formula for the derivative of the objective function with respect to the control from L1 is presented together with a su±cient condition for its existence. A stylized economic example is investigated analytically and numerically.

optimal control, distributed control, heterogeneous systems, endogenous domain of heterogeneity, Pontryagin-type maximum principle, set-valued analysis

http://dx.doi.org/10.1007/s00245-011-9140-2

http://www.springerlink.com/content/q1w7x131764630t6/