STRONG LOCAL MINIMIZERS IN OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS: SECOND-ORDER NECESSARY CONDITIONS

Hélène Frankowska (1) , Nikolai P. Osmolovskii (2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 IBS PAN - Systems Research Institute [Warsaw]

This paper is devoted to second-order necessary optimality conditions for strong local minima for a Mayer type optimal control problem with a general control constraint U ⊂ IR m , and state and final-point constraints described by a finite number of inequalities. We use the second order linearization of a relaxed differential inclusion associated to the control system to find a convex subset of second order tangents to the set of its trajectories. This leads to second-order necessary optimality conditions via a straightforward way, based on separation theorems.

Mots clés: differential inclusion; second-order necessary conditions; maximum principle; strong local minimum; second order tangents; Optimal control; state constraints

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Hélène Frankowska, Nikolai P. Osmolovskii. STRONG LOCAL MINIMIZERS IN OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS: SECOND-ORDER NECESSARY CONDITIONS. SIAM Journal on Control and Optimization, 2018, 56, pp.2353-2376. ⟨hal-02126111⟩