Related papers: Time-optimal synthesis of SU(2) transformations fo…
We apply an extension of the Pontryagin Maximum Principle to derive time-optimal controls of two-level quantum systems by means of piecewise constant pulses. Global optimal solutions are obtained for state-to-state transfer in the cases…
In this paper we solve two equivalent time optimal control problems. On one hand, we design the control field to implement in minimum time the SWAP (or equivalent) operator on a two-level system, assuming that it interacts with an…
Focusing on the efficient probe and manipulation of single-particle spin states, we investigate the coupled spin and orbital dynamics of a spin 1/2 particle in a harmonic potential subject to ultrastrong spin-orbit interaction and external…
We show how to apply a generalization of Local control design to the problem of saturation of a spin 1/2 particle by magnetic fields in Nuclear Magnetic Resonance. The generalization of local or Lyapunov control arises from the fact that…
A class of optimal control problems of hybrid nature governed by semilinear parabolic equations is considered. These problems involve the optimization of switching times at which the dynamics, the integral cost, and the bounds on the…
We present an outline of a technique to associate certain methods from time optimal quantum control with various transforms on SU(3). Unitary operators are taken from certain time dependent Hamiltonians and transformation laws are derived.…
For $\alpha\in(0,\pi/2)$, let $(\Sigma)_\alpha$ be the control system $\dot{x}=(F+uG)x$, where $x$ belongs to the two-dimensional unit sphere $S^2$, $u\in [-1,1]$ and $F,G$ are $3\times3$ skew-symmetric matrices generating rotations with…
An analysis of the motion of a relativistic electron under a linear constraint in four dimensions is presented. Interesting results are given that show that the state of the electron is well defined under the formalism of time optimal…
The quantum navigation problem of finding the time-optimal control Hamiltonian that transports a given initial state to a target state through quantum wind, that is, under the influence of external fields or potentials, is analysed. By…
We consider an optimal control problem where the state is governed by a free boundary problem called the two-phase membrane problem and the control appears in the coefficients of the characteristic function of the positivity and negativity…
The basic module for the solution of the minimum time optimal control of a car-like vehicle is herein presented. The vehicle is subject to the effect of laminar (linear) and aerodynamic (quadratic) drag, taking into account the asymmetric…
In this paper we consider an optimal control problem governed by a time-dependent variational inequality arising in quasistatic plasticity with linear kinematic hardening. We address certain continuity properties of the forward operator,…
Finding minimal time and establishing the structure of the corresponding optimal controls which can transfer a given initial state of a quantum system into a given target state is a key problem of quantum control. In this work, this problem…
In this paper, we study the stabilization problem of quantum spin-1/2 systems under continuous-time measurements. In the case without feedback, we show exponential stabilization around the excited and ground state by providing a lower bound…
We consider the $\mathbb{H}_2$-optimal feedback control problem, for the case in which the plant is passive with bounded $\mathbb{L}_2$ gain, and the feedback law is constrained to be output-strictly passive. In this circumstance, we show…
In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…
We consider the problem of time-optimal control of quadrupole nucleus with the spin I=1 by NMR. In contrast to the conventional methods based on selective pulses, the control is implemented using nonselective pulses separated by free…
In this work, we formulate the problem of achieving in minimum-time perfect chiral resolution with bounded control fields, as an optimal control problem on two non-interacting spins-$1/2$. We assume the same control bound for the two Raman…
We study the optimal quantum control of heteronuclear two-qubit systems described by a Hamiltonian containing both nonlocal internal drift and local control terms. We derive an explicit formula to compute the minimum time required to steer…
We study a control problem governed by a semilinear parabolic equation with pointwise control and state constraints imposed at every point of the space-time cylinder. We obtain second order sufficient optimality conditions for local…