In this article we establish first and second order sufficient optimality conditions for a class of single-input control-affine problems, in presence of a scalar state constraint. We consider strong-local optimality (that is, the C topology in the state space). The minimum-time and the Mayer problem are addressed. We restrict our analysis to extremals containing a bang arc, a single boundary arc, followed by a finite number of bang arcs. The sufficient conditions are expressed as a strengthened version of the necessary ones, plus the coerciveness of a suitable finite-dimensional quadratic form. The sufficiency of the given conditions is proven via Hamiltonian methods.
On the strong local optimality for state-constrained control-affine problems / Chittaro, F. C.; Poggiolini, L.. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 30:5(2023), pp. 0-0. [10.1007/s00030-023-00870-y]
On the strong local optimality for state-constrained control-affine problems
Chittaro F. C.;Poggiolini L.
2023-01-01
Abstract
In this article we establish first and second order sufficient optimality conditions for a class of single-input control-affine problems, in presence of a scalar state constraint. We consider strong-local optimality (that is, the C topology in the state space). The minimum-time and the Mayer problem are addressed. We restrict our analysis to extremals containing a bang arc, a single boundary arc, followed by a finite number of bang arcs. The sufficient conditions are expressed as a strengthened version of the necessary ones, plus the coerciveness of a suitable finite-dimensional quadratic form. The sufficiency of the given conditions is proven via Hamiltonian methods.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
