Autonomous attitude using potential function method under control input saturation

The potential function method has been used extensively in nonlinear control for the development of feedback laws which result in global asymptotic stability for a certain prescribed operating point of the closed-loop system. It is a variation of the Lyapunov direct method in the sense that here the Lyapunov function, also called potential function, is constructed in such a way that the undesired points of the system state space are avoided. The method has been considered for the space applications where the systems involved are usually composed of the cascaded subsystems of kinematics and dynamics and the kinematic states are mapped onto an appropriate potential function which is augmented for the overall system by the use of the method of integrator backstepping. The conventional backstepping controls, however, may result in an excessive control effort that may be beyond the saturation bound of the actuators. The present paper, while remaining within the framework of conventional backstepping control design, proposes analytical formulation for the control torque bound being a function of the tracking error and the control gains. The said formulation can be used to tune to the control gains to bound the control torque to a prescribed saturation bound of the control actuators

A Theoretical Reappraisal of Branching Ratios and CP Asymmetries in the Decays B→(Xd,Xs)ℓ+ℓ−B \to (X_d,X_s) \ell^+ \ell^- and Determination of the CKM Parameters

We present a theoretical reappraisal of the branching ratios and CP asymmetries for the decays $B \to X_q \ell^+ \ell^-$, with $q=d,s$, taking into account current theoretical uncertainties in the description of the inclusive decay amplitudes from the long-distance contributions, an improved treatment of the renormalization scale dependence, and other parametric dependencies. Concentrating on the partial branching ratios $\Delta {\cal B}(B \to X_q \ell^+ \ell^-)$, integrated over the invariant dilepton mass region $1 {GeV}^2 \leq s \leq 6 {GeV}^2$, we calculate theoretical precision on the charge-conjugate averaged partial branching ratios $= (\Delta {\cal B}(B \to X_q \ell^+ \ell^-) + \Delta {\cal B}(\bar{B} \to \bar{X}_q \ell^+ \ell^-))/2$, CP asymmetries in partial decay rates $(a_{CP})_q=(\Delta {\cal B}(B \to X_q \ell^+ \ell^-) - \Delta {\cal B}(\bar{B} \to \bar{X}_q \ell^+ \ell^-))/(2 )$, and the ratio of the branching ratios $\Delta {\cal R} = /$. For the central values of the CKM parameters, we find $=(2.22^{+0.29}_{-0.30}) \times 10^{-6}$, $=(9.61^{+1.32}_{-1.47}) \times 10^{-8}$, $(a_{CP})_s =-(0.19^{+0.17}_{-0.19})$, $(a_{CP})_d =(4.40^{+3.87}_{-4.46})$, and $\Delta {\cal R} =(4.32 \pm 0.03)$. The dependence of $$ and $\Delta {\cal R}$ on the CKM parameters is worked out and the resulting constraints on the unitarity triangle from an eventual measurement of $\Delta {\cal R}$ are illustrated.Comment: 18 pages, 7 figures (require epsf.sty

Two New Pahlavi Inscriptions from Fars Province, Iran

First edition of two previously unknown Middle Persian inscriptions from the region of Fars in Iran

Invisibility and PT-symmetry

For a general complex scattering potential defined on a real line, we show that the equations governing invisibility of the potential are invariant under the combined action of parity and time-reversal (PT) transformation. We determine the PT-symmetric an well as non-PT-symmetric invisible configurations of an easily realizable exactly solvable model that consists of a two-layer planar slab consisting of optically active material. Our analysis shows that although PT-symmetry is neither necessary nor sufficient for the invisibility of a scattering potential, it plays an important role in the characterization of the invisible configurations. A byproduct of our investigation is the discovery of certain configurations of our model that are effectively reflectionless in a spectral range as wide as several hundred nanometers.Comment: 11 pages, 3 figures, revised version, accepted for publication in Phys.Rev.