32 research outputs found
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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Asymptotic ensemble stabilizability of the Bloch equation
In this paper we are concerned with the stabilizability to an equilibrium
point of an ensemble of non interacting half-spins. We assume that the spins
are immersed in a static magnetic field, with dispersion in the Larmor
frequency, and are controlled by a time varying transverse field. Our goal is
to steer the whole ensemble to the uniform "down" position. Two cases are
addressed: for a finite ensemble of spins, we provide a control function (in
feedback form) that asymptotically stabilizes the ensemble in the "down"
position, generically with respect to the initial condition. For an ensemble
containing a countable number of spins, we construct a sequence of control
functions such that the sequence of the corresponding solutions pointwise
converges, asymptotically in time, to the target state, generically with
respect to the initial conditions. The control functions proposed are uniformly
bounded and continuous
Hyperbolicity and curvature in dynamics and control
In this thesis, we will use some techniques developed in the frame of Optimal Control Theory and some tools of Hyperbolic Dynamics to investigate problems of Hamiltonian dynamics and infinite horizon optimal control. The intimate relation between Optimal Control Theory and Hamiltonian Dynamics became clear after the publication of Pontryagin Maximum Principle (PMP) in the 50s ([24]): this result in fact shows that the extremals of an optimal control problem have to be seeked among the solutions of a certain Hamiltonian system associated to the problem..
Minimum-time strong optimality of a singular arc: the multi-input non involutive case
We consider the minimum-time problem for a multi-input control-affine system, where we assume that the controlled vector fields generate a non-involutive distribution of constant dimension, and where we do not assume a-priori bounds for the controls. We use Hamiltonian methods to prove that the coercivity of a suitable second variation associated to a Pontryagin singular arc is sufficient to prove its strong-local optimality. We provide an application of the result to a generalization of Dubins problem
Geometric modeling of the movement based on an inverse optimal control approach
International audienceThe present paper analyses a class of optimal control problems on geometric paths of the euclidean space, that is, curves parametrized by arc length. In the first part we deal with existence and robustness issues for such problems and we define the associated inverse optimal control problem. In the second part we discuss the inverse optimal control problem in the special case of planar trajectories and under additional assumptions. More precisely we define a criterion to restrict the study to a convenient class of costs based on the analysis of experimentally recorded trajectories. This method applies in particular to the case of human locomotion trajectories
Analysis of optimal control models for the human locomotion
International audienceIn recent papers it has been suggested that human locomotion may be modeled as an inverse optimal control problem. In this paradigm, the trajectories are assumed to be solutions of an optimal control problem that has to be determined. We discuss the modeling of both the dynamical system and the cost to be minimized, and we analyse the corresponding optimal synthesis. The main results describe the asymptotic behavior of the optimal trajectories as the target point goes to infinity
Adiabatic control of the Schr\"odinger equation via conical intersections of the eigenvalues
In this paper we present a constructive method to control the bilinear
Schr\"odinger equation via two controls. The method is based on adiabatic
techniques and works if the spectrum of the Hamiltonian admits eigenvalue
intersections, and if the latter are conical (as it happens generically). We
provide sharp estimates of the relation between the error and the
controllability time