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On feedback strengthening of the maximum principle for measure differential equations

Author

Listed:
  • Maxim Staritsyn

    (Siberian Branch of the Russian Academy of Sciences)

  • Stepan Sorokin

    (Siberian Branch of the Russian Academy of Sciences)

Abstract

For a class of nonlinear nonconvex impulsive control problems with states of bounded variation driven by Borel measures, we derive a new type non-local necessary optimality condition, named impulsive feedback maximum principle. This optimality condition is expressed completely within the objects of the impulsive maximum principle (IMP), while employs certain “feedback variations” of impulsive control. The obtained optimality condition is shown to, potentially, discard non-optimal IMP-extrema, and can be viewed as a deterministic non-local iterative algorithm for optimal impulsive control.

Suggested Citation

  • Maxim Staritsyn & Stepan Sorokin, 2020. "On feedback strengthening of the maximum principle for measure differential equations," Journal of Global Optimization, Springer, vol. 76(3), pages 587-612, March.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:3:d:10.1007_s10898-018-00732-3
    DOI: 10.1007/s10898-018-00732-3
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    References listed on IDEAS

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    1. Elena Goncharova & Maxim Staritsyn, 2012. "Optimization of Measure-Driven Hybrid Systems," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 139-156, April.
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