Structural stability of bang-bang trajectories with a double switching time in the minimum time problem

In this paper we consider the problem of structural stability of strong local optimisers for the minimum time problem in the case when the nominal problem has a bang-bang strongly local optimal control which exhibits a double switch

Strong local optimality for generalized L1 optimal control problems

In this paper, we analyse 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 inactivated arcs, that is, arcs where the control is identically zero. Here we consider Pontryagin extremals given by a bang-inactive-bang concatenation. We establish sufficient optimality conditions for such extremals, in terms of some regularity conditions and of the coercivity of a suitable finite-dimensional second variation.Comment: Journal of Optimization Theory and Applications, Springer Verlag, In pres

Constrained bang-bang-singular extremals

International audienceBy means of Hamiltonian methods we give sufficient conditions for the strong local optimality of a Pontryagin extremal for a Mayer problem where both the end points of admissible trajectories are constrained to smooth manifolds of the state space. The extremal is given by the concatenation of two bang arcs and a partially singular one. Our sufficient conditions amount to regularity conditions on the extremal and the coercivity of a suitable quadratic form

Strong local optimality for a bang-bang-singular extremal: the fixed-free case

International audienceIn this paper we give sufficient conditions for a Pontryagin extremal trajectory, consisting of two bang arcs followed by a partially or totally singular one, to be a strong local minimizer for a Mayer problem. The problem is defined on R n and the end-points constraints are of fixed-free type. We use a Hamiltonian approach and its connection with the second order conditions in the form of a LQ accessory problem. An example is proposed. All the results are coordinate free so they also hold on a manifold