Strong Local Optimality for Generalized L1 Optimal Control Problems

Francesca C. Chittaro () and Laura Poggiolini ()
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Francesca C. Chittaro: CNRS, LIS
Laura Poggiolini: Università degli Studi di Firenze

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 1, No 12, 207-234

Abstract: 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.

Keywords: Optimal control; Sufficient conditions; Hamiltonian methods; Sparse control; 49K15; 49K30 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-018-1337-y

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