Optimal Control of Heterogeneous Systems with Endo

Authors: Anton O Belyakov Tsvetomir Tsachev Vladimir M Veliov

Publish Date: 2011/06/25

Volume: 64, Issue: 2, Pages: 287-311

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Abstract

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 “minmax” As a consequence a Pontryagintype 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

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