Finite-horizon H∞ control for discrete time-varying systems with randomly occurring nonlinearities and fading measurements

This technical note deals with the H∞ control problem for a class of discrete time-varying nonlinear systems with both randomly occurring nonlinearities and fading measurements over a finite-horizon. The system measurements are transmitted through fading channels described by a modified stochastic Rice fading model. The purpose of the addressed problem is to design a set of time-varying controllers such that, in the presence of channel fading and randomly occurring nonlinearities, the H∞ performance is guaranteed over a given finite-horizon. The model transformation technique is first employed to simplify the addressed problem, and then the stochastic analysis in combination with the completing squares method are carried out to obtain necessary and sufficient conditions of an auxiliary index which is closely related to the finite-horizon H∞ performance. Moreover, the time-varying controller parameters are characterized via solving coupled backward recursive Riccati difference equations (RDEs). A simulation example is utilized to illustrate the usefulness of the proposed controller design scheme

Weight function for the quantum affine algebra Uq(sl^3)U_q(\hat{sl}_3)

We give a precise expression for the universal weight function of the quantum affine algebra $U_q(\hat{sl}_3)$. The calculations use the technique of projecting products of Drinfeld currents on the intersections of Borel subalgebras.Comment: 28 page

Overall properties of the Gaia DR1 reference frame

We compare quasar positions of the auxiliary quasar solution with ICRF2 sources using different samples and evaluate the influence on the {\it Gaia} DR1 reference frame owing to the Galactic aberration effect over the J2000.0-J20015.0 period. Then we estimate the global rotation between TGAS with {\it Tycho}-2 proper motion systems to investigate the property of the {\it Gaia} DR1 reference frame. Finally, the Galactic kinematics analysis using the K-M giant proper motions is performed to understand the property of {\it Gaia} DR1 reference frame. The positional comparison between the auxiliary quasar solution and ICRF2 shows negligible orientation and validates the declination bias of $\sim$$-0.1$\mas~in {\it Gaia} quasar positions with respect to ICRF2. Galactic aberration effect is thought to cause an offset $\sim$$0.01$\mas~of the $Z$ axis direction of {\it Gaia} DR1 reference frame. The global rotation between TGAS and {\it Tycho}-2 proper motion systems, obtained by different samples, shows a much smaller value than the claimed value $0.24$\masyr. For the Galactic kinematics analysis of the TGAS K-M giants, we find possible non-zero Galactic rotation components beyond the classical Oort constants: the rigid part $\omega_{Y_G} = -0.38 \pm 0.15$\masyr~and the differential part $\omega^\prime_{Y_G} = -0.29 \pm 0.19$\masyr~around the $Y_G$ axis of Galactic coordinates, which indicates possible residual rotation in {\it Gaia} DR1 reference frame or problems in the current Galactic kinematical model.Comment: 6 pages, 1 figure. Accepted for publication in A&

Physical implementation of holonomic quantum computation in decoherence-free subspaces with trapped ions

We propose a feasible scheme to achieve holonomic quantum computation in a decoherence-free subspace (DFS) with trapped ions. By the application of appropriate bichromatic laser fields on the designated ions, we are able to construct two noncommutable single-qubit gates and one controlled-phase gate using the holonomic scenario in the encoded DFS.Comment: 4 pages, 3 figures. To appear in Phys. Rev. A 74 (2006

A Survey on Multisensor Fusion and Consensus Filtering for Sensor Networks

Multisensor fusion and consensus filtering are two fascinating subjects in the research of sensor networks. In this survey, we will cover both classic results and recent advances developed in these two topics. First, we recall some important results in the development ofmultisensor fusion technology. Particularly, we pay great attention to the fusion with unknown correlations, which ubiquitously exist in most of distributed filtering problems. Next, we give a systematic review on several widely used consensus filtering approaches. Furthermore, some latest progress on multisensor fusion and consensus filtering is also presented. Finally, conclusions are drawn and several potential future research directions are outlined.the Royal Society of the UK, the National Natural Science Foundation of China under Grants 61329301, 61374039, 61304010, 11301118, and 61573246, the Hujiang Foundation of China under Grants C14002 and D15009, the Alexander von Humboldt Foundation of Germany, and the Innovation Fund Project for Graduate Student of Shanghai under Grant JWCXSL140

Internal stress wave measurements in solids subjected to lithotripter pulses

Semiconductor strain gauges were used to measure the internal strain along the axes of spherical and disk plaster specimens when subjected to lithotripter shock pulses. The pulses were produced by one of two lithotripters. The first source generates spherically diverging shock waves of peak pressure approximately 1 MPa at the surface of the specimen. For this source, the incident and first reflected pressure (P) waves in both sphere and disk specimens were identified. In addition, waves reflected by the disk circumference were found to contribute significantly to the strain fields along the disk axis. Experimental results compared favorably to a ray theory analysis of a spherically diverging shock wave striking either concretion. For the sphere, pressure contours for the incident P wave and caustic lines were determined theoretically for an incident spherical shock wave. These caustic lines indicate the location of the highest stresses within the sphere and therefore the areas where damage may occur. Results were also presented for a second source that uses an ellipsoidal reflector to generate a 30-MPa focused shock wave, more closely approximating the wave fields of a clinical extracorporeal lithotripter

Magnetic Reconnection resulting from Flux Emergence: Implications for Jet Formation in the lower solar atmosphere?

We aim at investigating the formation of jet-like features in the lower solar atmosphere, e.g. chromosphere and transition region, as a result of magnetic reconnection. Magnetic reconnection as occurring at chromospheric and transition regions densities and triggered by magnetic flux emergence is studied using a 2.5D MHD code. The initial atmosphere is static and isothermal, with a temperature of 20,000 K. The initial magnetic field is uniform and vertical. Two physical environments with different magnetic field strength (25 G and 50 G) are presented. In each case, two sub-cases are discussed, where the environments have different initial mass density. In the case where we have a weaker magnetic field (25 G) and higher plasma density ($N_e=2\times 10^{11}$ cm$^{-3}$), valid for the typical quiet Sun chromosphere, a plasma jet would be observed with a temperature of 2--3 $\times 10^4$ K and a velocity as high as 40 km/s. The opposite case of a medium with a lower electron density ($N_e=2\times 10^{10}$ cm$^{-3}$), i.e. more typical for the transition region, and a stronger magnetic field of 50 G, up-flows with line-of-sight velocities as high as 90 km/s and temperatures of 6 $\times$ 10$^5$ K, i.e. upper transition region -- low coronal temperatures, are produced. Only in the latter case, the low corona Fe IX 171 \AA\ shows a response in the jet which is comparable to the O V increase. The results show that magnetic reconnection can be an efficient mechanism to drive plasma outflows in the chromosphere and transition region. The model can reproduce characteristics, such as temperature and velocity for a range of jet features like a fibril, a spicule, an hot X-ray jet or a transition region jet by changing either the magnetic field strength or the electron density, i.e. where in the atmosphere the reconnection occurs.Comment: 11 pages, 13 figures, 2 table