arXiv subjects

Francesca Chittaro

Publications and source records attributed to Francesca Chittaro.

7 recordsLinked to original sources

arXiv2021

Singular extremals in L^1 optimal control problems: sufficient optimality conditions

In this paper we are concerned with generalised L 1-minimisation problems, i.e. Bolza problems involving the absolute value of the control with a control-affine dynamics. We establish sufficient conditions for the strong local optimality of extremals given by the concatenation of bang, singular and inactive (zero) arcs. The sufficiency of such conditions is proven by means of Hamiltonian methods. As a byproduct of the result, we provide an explicit invariant formula for the second variation along the singular arc.

math.OC↗

arXiv2018

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.

math.OC↗

arXiv2018

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.

math.OC↗

arXiv2017

Towards generic adiabatic elimination for bipartite open quantum systems

We consider a composite open quantum system consisting of a fast subsystem coupled to a slow one. Using the time-scale separation, we develop an adiabatic elimination technique to derive at any order the reduced model describing the slow subsystem. The method, based on an asymptotic expansion and geometric singular perturbation theory, ensures the physical interpretation of the reduced second-order model by giving the reduced dynamics in a Lindblad form and the state reduction in Kraus map form. We give explicit second-order formulas for Hamiltonian or cascade coupling between the two subsystems. These formulas can be used to engineer, via a careful choice of the fast subsystem, the Hamiltonian and Lindbald operators governing the dissipative dynamics of the slow subsystem.

quant-ph↗

arXiv2015

Approximate controllability via adiabatic techniques for the three-inputs controlled Schr{ö}dinger equation

We consider a system described by a controlled bilinear Schr{ö}dinger equation with three external inputs. We provide a constructive method to approximately steer the system from a given energy level to a superposition of energy levels corresponding to a given probability distribution. The method is based on adiabatic techniques and works if the spectrum of the Hamiltonian admits eigenvalue intersections, with respect to variations of the controls, and if the latter are conical. We provide sharp estimates of the relation between the error and the controllability time, and we show how to improve these estimates by selecting special control paths.

math.OC↗

arXiv2014

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.

math.OC↗

arXiv2011

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.

math.OC↗