Improved single neuron controller for multivariable stochastic systems with non-Gaussianities and unmodeled dynamics

In this paper, a new adaptive control approach is presented for multivariate nonlinear non-Gaussian systems with unknown models. A more general and systematic statistical measure, called (h,?)$(h,?)$-entropy, is adopted here to characterize the uncertainty of the considered systems. By using the “sliding window” technique, the non-parameter estimate of the (h,?)$(h,?)$-entropy is formulated. Then, the improved neuron based controllers are developed for multivariate nonlinear non-Gaussian systems by minimizing the entropies of the tracking errors in closed loops. The condition to guarantee the strictly decreasing entropy of tracking error is presented. Moreover, the convergence in the mean-square sense has been analyzed for all the weights in the neural controllers. Finally, the comparative simulation results are presented to show that the performance of the proposed algorithm is superior to that of PID control strategy.     

Exchange of angular momentum in EMCD experiments

In energy loss magnetic chiral dichroism (EMCD) experiments a chiral electronic transition is induced that obeys the dipole selection rule for the magnetic quantum number Δm=±1$\mathrm{\Delta }m=\pm 1$ or Δ_Lz=±?$\mathrm{\Delta }{L}_z=\pm ?$. The incident plane electron wave is inelastically scattered and is detected in the diffraction plane, i.e. again in a plane wave state. Naïve reasoning suggests that the angular momentum _Lz$L_z$ of the probe electron has not changed in the interaction since plane waves have 〈_Lz〉=0$〈L_z〉=0$. This leads to the seeming contradiction that angular momentum is not conserved in the interaction. A closer inspection shows that the density matrix of the probe has indeed 〈_Lz〉=±?$〈L_z〉=\pm ?$ after a chiral interaction. However, 〈_Lz〉$〈L_z〉$ is not conserved when the probe electron propagates further to the exit surface of the specimen because the rigid lattice breaks rotational symmetry. Thus, the angular momentum of the photo electron that is created in a chiral electronic transition stems from both the probing electron and the crystal lattice.     

Effect of chromatic aberration on atomic-resolved spherical aberration corrected STEM images

The effect of the chromatic aberration (_Cc)$(C_c)$ coefficient in a spherical aberration (_Cs)$(C_s)$- corrected electromagnetic lens on high-resolution high-angle annular dark field (HAADF) scanning transmission electron microscope (STEM) images is explored in detail. A new method for precise determination of the _Cc$C_c$ coefficient is demonstrated, requiring measurement of an atomic-resolution one-frame through-focal HAADF STEM image. This method is robust with respect to instrumental drift, sample thickness, all lens parameters except _Cc$C_c$, and experimental noise. It is also demonstrated that semi-quantitative structural analysis on the nanometer scale can be achieved by comparing experimental _Cs$C_s$- corrected HAADF STEM images with their corresponding simulated images when the effects of the _Cc$C_c$ coefficient and spatial incoherence are included.     

Finite-time H∞ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals

This paper is concerned with the problem of finite-time _H∞$H_{\infty }$ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals. In order to reduce conservatism, a new Lyapunov–Krasovskii functional is constructed. Based on the derived condition, the reliable _H∞$H_{\infty }$ control problem is solved, and the system trajectory stays within a prescribed bound during a specified time interval. Finally, numerical examples are given to demonstrate the proposed approach is more effective than some existing ones.     

H∞ filtering for a class of discrete-time singular Markovian jump systems with time-varying delays

The problem of _H∞$H_{\infty }$ filtering for a class of discrete-time singular Markovian jump systems with time-varying delays is investigated in this paper. The transition probabilities under consideration are time-varying, i.e., Markovian chain is nonhomogeneous. By using the Lyapunov functional approach and reciprocally convex technique, a less conservative delay-dependent bounded real lemma is developed in terms of linear matrix inequalities. Moreover, a sufficient condition for the existence of the desired filter which guarantees the stochastic admissibility and the _H∞$H_{\infty }$ performance index of the resulting filtering error system is presented. Numerical examples are employed to show the usefulness of the proposed results.     

Decomposition of process damping ratios and verification of process damping model for chatter vibration

In the previous study, by the same authors, titled “A new process damping model (PDM) for chatter vibration (Measurement, 44 (8) (2011) 1342–1348)”, a new approach has been presented for obtaining process damping ratios (PDRs). This PDM has been constituted on the basis of the shear angle (φ)$(\phi )$ oscillations of the cutting tool and the alteration of the penetration forces when they penetrate into the wavy surface. Variation and quantity of PDR are predicted by reverse running analytical calculation procedure of traditional Stability Lobe Diagrams (SLDs). In this study, firstly, how the PDM in previous study results with different materials such as AISI-1050 and Al-7075 are examined. Then, two problems are solved: how much of the total PDR of cutting system is caused by the tool penetration and how much is caused by (φ)$(\phi )$ oscillation? Finally, verification of PDR values and PDM are performed by energy equations.     

Finite-time boundedness filtering for discrete-time Markovian jump system subject to partly unknown transition probabilities

This paper investigates the problem of finite-time boundedness filtering for discrete-time Markovian jump system subject partly unknown transition probabilities. By using the multiple Lyapunov function approach, a novel sufficient condition for finite-time bounded of _H∞$H_{\infty }$ filtering is derived and the system trajectory stays within a prescribed bound during a specified time interval. Finally, an example is provided to illustrate the usefulness and effectiveness of the proposed method.     

Spin–charge separation and electron pairing instabilities in Hubbard nanoclusters

Electron charge and spin pairing instabilities in various cluster geometries for attractive and repulsive electrons are studied exactly under variation of interaction strength, electron doping and temperature. The exact diagonalization, level crossing degeneracies, spin–charge separation and separate condensation of paired electron charge and opposite spins yield intriguing insights into the origin of magnetism, ferroelectricity and superconductivity seen in inhomogeneous bulk nanomaterials and various phenomena in cold fermionic atoms in optical lattices. Phase diagrams resemble a number of inhomogeneous, coherent and incoherent nanoscale phases found recently in high-_Tc$T_c$ cuprates, manganites and multiferroic nanomaterials probed by scanning tunneling microscopy. Separate condensation of electron charge and spin degrees at various crossover temperatures offers a new route for superconductivity, different from the BCS scenario. The calculated phase diagrams resemble a number of inhomogeneous paired phases, superconductivity, ferromagnetism and ferroelectricity found in Nb and Co nanoparticles. The phase separation and electron pairing, monitored by electron doping and magnetic field surprisingly resemble incoherent electron pairing in the family of doped high-_Tc$T_c$ cuprates, ruthenocuprates, iron pnictides and spontaneous ferroelectricity in multiferroic materials.     

Energy-filtered transmission electron microscopy based on inner-shell ionization

We demonstrate that energy-filtered transmission electron microscopy (EFTEM) based on inner-shell ionization can contain atomic resolution information. We present a comparison between experimental data and simulation for the EFTEM image of the _N4,5${\mathrm{N}}_{4,5}$ edge (threshold energy 99 eV) of lanthanum in _LaB6${\mathrm{LaB}}_6$ in which direct interpretation of the location of the lanthanum columns is possible. Our first principles approach is based on calculating transition potentials for inelastic scattering. For our case study, the localization of the transition potentials is such that elastic contrast is only weakly preserved in the EFTEM image. This is not always the case, but we show how the approach based on calculating the elastic wave function and the transition potentials can provide insight about when direct interpretation may and may not be possible. In our test specimen, the direct interpretation fails for thicker specimens when the long tails of the transition potential from multiple adjacent sites leads to significant image features other than at the sites of the element of interest. We can thus anticipate instances where direct interpretation may be more reliable, such as looking for a single impurity in an otherwise well known sample.     

Stabilization of an inverted pendulum-cart system by fractional PI-state feedback

This paper deals with pole placement PI-state feedback controller design to control an integer order system. The fractional aspect of the control law is introduced by a dynamic state feedback as u(t)=_Kpx(t)+_KIIα(x(t))$u\left(t\right)=K_{p}x\left(t\right)+K_I{\mathfrak{I}}_{\alpha }\left(x\right(t\left)\right)$. The closed loop characteristic polynomial is thus fractional for which the roots are complex to calculate. The proposed method allows us to decompose this polynomial into a first order fractional polynomial and an integer order polynomial of order n−1$n-1$ (n being the order of the integer system). This new stabilization control algorithm is applied for an inverted pendulum-cart test-bed, and the effectiveness and robustness of the proposed control are examined by experiments.     

H∞ mode-dependent fault detection filter design for stochastic Markovian jump systems with time-varying delays and parameter uncertainties

This paper deals with the problem of robust _H∞$H_{\infty }$ fault detection for a class of stochastic Markovian jump systems (SMJSs) The aim is to design a linear mode-dependent fault detection filter such that the fault detection system is not only stochastically asymptotically stable in the large, but also satisfies a prescribed _H∞-norm$H_{\infty }\mathrm{-}\mathrm{norm}$ level for all admissible uncertainties. By using Lyapunov stability theory and generalized Itô formula, some novel mode-dependent and delay-dependent sufficient conditions in terms of linear matrix inequality (LMI) are proposed to insure the existence of the desired fault detection filter. A simulation example and an industrial nonisothermal continuous stirred tank reactor (CSTR) system are employed to show the effectiveness of the proposed method.     

Elastic–plastic contact analysis of an ellipsoid and a rigid flat

The work presents a finite element model (FEM) of the equivalent von-Mises stress and displacements that are formed for the different ellipticity contact of an ellipsoid with a rigid flat. The material is modeled as elastic perfectly plastic and follows the von-Mises yield criterion. The smaller the ellipticity of the ellipsoid is, the larger the depth of the first yield point from the ellipsoid tip happens. The FEM produces contours for the normalized normal and radial displacement as functions of the different interference depths. The evolution of plastic region in the asperity tip for a sphere (k_e=1) and an ellipsoid with different ellipticities $(k_e=\frac{1}{2}\mathrm{and}\frac{1}{5})$ is shown with increasing interferences. It is interesting to note the behavior of the evolution of the plastic region in the ellipsoid tip for different ellipticities, k_e, is different. The developments of the plastic region on the contact surface are shown in more details in Fig. 7. When the dimensionless contact pressure is up to 2.5, the uniform contact pressure distribution is almost prevailing in the entire contact area. It can be observed clearly that the normalized contact pressure ascends slowly from the center to the edge of the contact area for a sphere (k_e=1), almost has uniform distribution prevailing the entire contact area for an ellipsoid $(k_e=\frac{1}{2})$, and descends slowly from the center to the edge of the contact area for an ellipsoid $(k_e=\frac{1}{5})$.