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Strong Local Optimality for Generalized L1 Optimal Control Problems

Author

Listed:
  • Francesca C. Chittaro

    (CNRS, LIS)

  • Laura Poggiolini

    (Università degli Studi di Firenze)

Abstract

In this paper, we analyze control-affine optimal control problems with a cost functional involving the absolute value of the control. The Pontryagin extremals associated with such systems are given by (possible) concatenations of bang arcs with singular arcs and with zero control arcs, that is, arcs where the control is identically zero. Here, we consider Pontryagin extremals given by a bang-zero control-bang concatenation. We establish sufficient optimality conditions for such extremals, in terms of some regularity conditions and of the coerciveness of a suitable finite-dimensional second variation.

Suggested Citation

  • Francesca C. Chittaro & Laura Poggiolini, 2019. "Strong Local Optimality for Generalized L1 Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 207-234, January.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:1:d:10.1007_s10957-018-1337-y
    DOI: 10.1007/s10957-018-1337-y
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    References listed on IDEAS

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    1. Dante Kalise & Karl Kunisch & Zhiping Rao, 2017. "Infinite Horizon Sparse Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 481-517, February.
    2. Georg Stadler, 2009. "Elliptic optimal control problems with L 1 -control cost and applications for the placement of control devices," Computational Optimization and Applications, Springer, vol. 44(2), pages 159-181, November.
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