Abstract

We prove second-order necessary optimality conditions for the so-called time crisis problem that comes up within the context of viability theory. It consists in minimizing the time spent by solutions of a controlled dynamics outside a given subset K of the state space. One essential feature is the discontinuity of the characteristic function involved in the cost functional. Thanks to a change of time and an augmentation of the dynamics, we relate the time crisis problem to an auxiliary Mayer control problem. This allows us to use the classical tools of optimal control for obtaining optimality conditions. Going back to the original problem, we deduce in that way second order optimality conditions for the time crisis problem.

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Keywords

  • Optimal control
  • Pontryagin maximum principle
  • second order optimality conditions

Mathematics Subject Classification

49J15, 49K15, 49J52, 34H05

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Suggested citation

T. Bayen, L. Pfeiffer. “Second-Order Analysis for the Time Crisis Problem.” Journal of Convex Analysis 27 (2020), No. 1, 139–163. https://doi.org/10.68381/jca27009

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Published by Heldermann Verlag, 2020. Rights now held by Banach Press.