4 research outputs found
Numerical Solution of the Dynamic Programming Equation for the Optimal Control of Quantum Spin Systems
The purpose of this paper is to describe the numerical solution of the
Hamilton-Jacobi-Bellman (HJB) for an optimal control problem for quantum spin
systems. This HJB equation is a first order nonlinear partial differential
equation defined on a Lie group. We employ recent extensions of the theory of
viscosity solutions from Euclidean space to Riemannian manifolds to interpret
possibly non-differentiable solutions to this equation. Results from
differential topology on the triangulation of manifolds are then used to
develop a finite difference approximation method, which is shown to converge
using viscosity solution techniques. An example is provided to illustrate the
method.Comment: 11 pages, 5 figure
Hybrid Impulsive Control for Closed Quantum Systems
The state transfer problem of a class of nonideal quantum systems is investigated. It is known that traditional Lyapunov methods may fail to guarantee convergence for the nonideal case. Hence, a hybrid impulsive control is proposed to accomplish a more accurate convergence. In particular, the largest invariant sets are explicitly characterized, and the convergence of quantum impulsive control systems is analyzed accordingly. Numerical simulation is also presented to demonstrate the improvement of the control performance
Hybrid Impulsive Control for Closed Quantum Systems
The state transfer problem of a class of nonideal quantum systems is investigated. It is known that traditional Lyapunov methods may fail to guarantee convergence for the non-ideal case. Hence, a hybrid impulsive control is proposed to accomplish a more accurate convergence. In particular, the largest invariant sets are explicitly characterized, and the convergence of quantum impulsive control systems is analyzed accordingly. Numerical simulation is also presented to demonstrate the improvement of the control performance
Minimum time control of spin systems via Dynamic programming
In this article we show how dynamic programming can be applied to the time optimal control of spin systems. This is done by recasting the system in two ways: (i) As an adjoint system along the lines of[1], (ii) As an impulsive control problem. We illustrate the dynamic programming methodology using numerical examples