27 research outputs found
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
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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