A method is proposed to cool down atoms in a harmonic trap without phase-space compression as in a perfectly slow adiabatic expansion, i.e., keeping the same populations of instantaneous levels in the initial and final traps, but in a much shorter time. This may require that the harmonic trap become transiently an expulsive parabolic potential. The cooling times achieved are shorter than those ...

In this paper, a new numerical method is presented for solving the optimal control problems of Bang-Bang type with free or fixed terminal time. The method is based on Bezier polynomials which are presented in any interval as $[t_0,t_f]$. The problems are reduced to a constrained problems which can be solved by using Lagrangian method. The constraints of these problems are terminal state and con...

This paper deals with the study of the optimal control problem for the objective F (x, u, v) = ∫ T 0 f(x(t), x(t− h), ζ(t), u(t), v(t), t)dt, with x ∈ X, u ∈ U, v ∈ V ; X, U and V being vector spaces, and ζ(t) = ∫ h 0 R(t, τ )x(t− τ ) dτ , subject to the differential equation d dtx(t) = m(x(t), x(t− h), ζ(t), u(t), v(t), t) (0 6 t 6 T ), and the constraints g1(u(t), t) ∈ S1, g2(v(t), t) ∈ S2; n...

A fuzzy control irrigation system for cotton field is presented in this paper. The system is composed of host computer, slave computer controller, communication module, soil water sensors, valve controllers, and system software. A fuzzy control model is constructed to control the irrigation time and irrigation quantity for cotton filed. According to the water-required rules of different cotton ...

The problem of optimal feed-rate planning along a curved tool path for 3-axis CNC machines with a jerk limit for each axis is addressed. We prove that the optimal feed-rate planning must use “Bang-Bang” control, that is, at least one of the axes reaches its jerk bound throughout the motion. As a consequence, the optimal parametric velocity can be expressed as a piecewise analytic function of th...

A general form of the dynamics obtained as a limit of trajectories of singularly perturbed linear control systems is presented. The limit trajectories are described in terms of probability measure-valued maps. This allows to determine the extent to which the bang-bang principle for linear control systems is carried over to the singular limit.

The new approach applies standard regulator theory using appropriate transformations and thereby enables the problem to be solved more completely than has hitherto been possible. For example we consider the cases which arise when Q is singular, Particular attention is given to the limiting case as t, becomes infinite. For this case, conditions are presented for the asymptotic stability of the s...