Bolza Optimal Control Problems with Linear Equations and Periodic Convex Integrands on Large Intervals

  • Alexander J. ZaslavskiEmail author
Part of the Advances in Mathematical Economics book series (MATHECON, volume 21)


We study the structure of approximate solutions of Bolza optimal control problems, governed by linear equations, with periodic convex integrands, on large intervals, and show that the turnpike property holds. To have this property means, roughly speaking, that the approximate optimal trajectories are determined mainly by the integrand, and are essentially independent of the choice of time intervals and data, except in regions close to the endpoints of the time interval. We also show the stability of the turnpike phenomenon under small perturbations of integrands and study the structure of approximate optimal trajectories in regions close to the endpoints of the time intervals.


Good trajectory-control pair Integrand Optimal control problem Overtaking optimal trajectory-control pair Turnpike property 


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© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Department of MathematicsThe Technion – Israel Institute of TechnologyHaifaIsrael

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