This paper is concerned with sufficient optimality condition for a Mayer problem with control-affine state equation and state constraints. Assuming that we are given an extremal constituted by the concatenation of a bang arc, a singular internal arc, a single boundary arc and a final bang arc, we provide a set of conditions that guarantee its strong local optimality. These conditions consists in a set of inequalities plus the coercivity of a suitable infinite-dimensional quadratic form (extended second variation).
Optimality Conditions for Control Problems Under Pure State Constraints / Poggiolini Laura; Chittaro Francesca. - In: SET-VALUED AND VARIATIONAL ANALYSIS. - ISSN 1877-0533. - STAMPA. - 33:(2025), pp. 39.0-39.0. [10.1007/s11228-025-00774-2]
Optimality Conditions for Control Problems Under Pure State Constraints
Poggiolini Laura
;
2025
Abstract
This paper is concerned with sufficient optimality condition for a Mayer problem with control-affine state equation and state constraints. Assuming that we are given an extremal constituted by the concatenation of a bang arc, a singular internal arc, a single boundary arc and a final bang arc, we provide a set of conditions that guarantee its strong local optimality. These conditions consists in a set of inequalities plus the coercivity of a suitable infinite-dimensional quadratic form (extended second variation).
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