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International audience; In this article we discuss how to control a parameter-dependent family of quantum systems. Our technique is based on adiabatic approximation theory and on the presence of curves of conical eigenvalue intersections of the controlled Hamiltonian. As particular cases, we recover chirped pulses for two-level quantum systems and counter-intuitive solutions for three-level stimulated Raman adiabatic passage (STIRAP). The proposed technique works for systems evolving both in finite-dimensional and infinite-dimensional Hilbert spaces. We show that the assumptions guaranteeing ensemble controllability are structurally stable with respect to perturbations of the parametrized family of systems.

In this paper we study local convergence of inexact Newton methods of the form $ {\big(}f(x_k)+ A_k(x_{k+1}-x_k)+F(x_{k+1}){\big)}\cap R_k(x_k) \neq \emptyset \ \ {with} \ \ A_k \in {\cal H}(x_k)$ for solving the generalized equation $f(x) +F(x) \ni 0$ in Banach spaces, where the function $f$ is continuous but not necessarily smooth and $F$ is a set-valued mapping with closed graph. The mapping $\cal H$ plays the role of a generalized set-valued derivative of $f$ which in finite dimensions may be represented by Clarke's generalized Jacobian, while in Banach spaces it may be identified with Ioffe's strict prederivative. The set-valued mappings $R_k$ represent inexactness. We utilize conditions divided into three groups: the first concerns the kind of nonsmoothness of the function $f$, the second involves metric regularity properties of an approximation of the mapping $f+F$, and the third is about the sequence of mappings $R_k$. Under various combinations of these conditions we show linear, superlinear, or ...

The minimum time control of the circular restricted three-body problem is considered. Controllability is proved on an adequate submanifold. Singularities of the extremal flow are studied by means of a stratification of the switching surface. Properties of homotopy maps in optimal control are framed in a simple case. The analysis is used to perform continuations on the two parameters of the problem: The ratio of the masses, and the magnitude of the control.

International audience; An algorithm for efficient solution of control constrained optimal control problems is proposed and analyzed. It is based on an active set strategy involving primal as well as dual variables. For discretized problems sufficient conditions for convergence in finitely many iterations are given. Numerical examples are given and the role of strict complementarity condition is discussed.