Anisotropy of inter-band transitions and band structure of Cs3Zn6B9O21 nonlinear optical crystals

Polarized optical functions near the fundamental absorption edge of novel Cs₃Zn₆B₉O₂₁ nonlinear optical crystals possessing a wide UV transparency down to 190 nm were investigated. The anisotropy of optical functions is not well studied yet which restrains the further strategy of the formation on its base of solid state compounds with desirable properties. The studies were performed using a band structure calculations as well as the experimental measurements of fundamental polarized UV absorption edge and X-ray photoelectron spectra of the studied crystals. The experimental data were used for evaluation of scissor factors of the band structure. The results of the calculations were compared with the XPS and polarized absorption optical spectra of the investigated crystals. The introduction of the scissor factor was performed in order to obtain a sufficient agreement with experiment. The observed anisotropy of absorption may be explained by the anisotropy of carrier effective masses.     

An Adaptive Pseudospectral Method for Constrained Dynamic Optimization Problems in Chemical Engineering

An adaptive pseudospectral method with two novel strategies is proposed to solve constrained dynamic optimization problems in chemical engineering. The first strategy is to introduce slope information in designing appropriate subintervals, so that the approach becomes more efficient to track the optimal control profiles. The second strategy is to redistribute the collocation points based on the approximation error, thus ensuring the accuracy of the method. Two constrained dynamic optimization problems with multiple control variables are tested as illustrations, and the proposed approach is compared with other methods. The research results reveal the effectiveness of the proposed method in improving the solution accuracy of dynamic optimization problems.     

Detection in sea clutter based on nonlinear ARCH model

In this paper, a complex nonlinear autoregressive conditional heteroscedasticity (CNARCH) model is proposed to model sea clutter. For heteroscedastic model, since the likelihood function is not obtained from explicit probability density function (PDF) expression, it is typically referred to as a quasi-likelihood function. The corresponding quasi-maximum likelihood estimation (QMLE) of the model parameters is derived. Furthermore, the corresponding detection algorithm is derived based on this model. We also conduct the simulations of both synthetic and practical data, demonstrate that the proposed model offers higher accuracy in detection, than the linear ARCH model, when used in the sea clutter.     

A numerical method for multipoint boundary value problems with application to a restricted three body problem

A type of parallel shooting method is proposed for the solution of nonlinear multipoint boundary value problems. It extends the usual quasilinearization method and a previous shooting method developed for such problems, and reduces to usual multiple shooting techniques for two point boundary value problems. The effectiveness of the method for stiff problems is illustrated by an application to the problem of finding periodic solutions of a restricted three body problem with given Jacobian constant and unknown period.     

Fast NMPC schemes for regulatory and economic NMPC – A review

In this paper, NMPC schemes based on fast update methods (fast NMPC schemes) are reviewed that strive to provide a fast but typically suboptimal update of the control variables at each sampling instant with negligible computational delay. The review focuses on schemes that employ one of two subclasses of fast update methods developed for direct solution approaches, the suboptimal update methods and the sensitivity-based update methods. The connections and similarities of the fast update methods, the elements of the fast NMPC, the control architecture as well as the fast NMPC schemes as a whole are highlighted to support the assessment of the benefits and limitations of each individual scheme. In this way, this review facilitates the choice of a suitable fast NMPC scheme within the vast amount of fast NMPC schemes available in literature.     

New results for delay-dependent stability of linear systems with time-varying delay

The asymptotic stability problem for a class of linear systems with time-varying delays is studied using a generalized discretized Lyapunov functional approach. The kernel of the functional, which is a function of two variables, is chosen as piecewise linear. The conditions of the Lyapunov functional and its derivative are written in terms of linear matrix inequalities (LMIs). New delay-dependent stability criteria are proposed by simplifying the derived LMIs. Numerical examples show that the results obtained by these new criteria significantly improve the estimate of stability limit over the existing results in the literature.     

Stability and positive observer design for positive 2D discrete-time system with multiple delays

This paper addresses the problems of stability and positive observation for positive two-dimensional (2D) discrete-time systems in Roesser model with multiple delays. A novel proof is provided for the necessary and sufficient conditions of asymptotic stability for the positive 2D systems. Based on the obtained results, necessary and sufficient conditions are proposed for the existence of a 2D positive observer. All the proposed conditions are in terms of linear matrix inequalities.     

Particle swarm optimization based nonlinear active noise control under saturation nonlinearity

In this paper, a method is proposed to overcome the saturation non-linearity linked to the microphones and loudspeakers of active noise control (ANC) system. The reference microphone gets saturated when the acoustic noise at the source increases beyond the dynamic limits of the microphone. When the controller tries to drive the loudspeaker system beyond its dynamic limits, the saturation nonlinearity is also introduced into the system. The secondary path which is generally estimated with a low level auxiliary noise by a linear transfer function does not model such saturation nonlinearity. Therefore, the filtered-x least mean square (FXLMS) algorithm fails to perform when the noise level is increased. For alleviating the saturation nonlinearity effect a nonlinear functional expansion based ANC algorithm is proposed where the particle swarm optimization (PSO) algorithm is suitably applied to tune the parameters of a filter bank based functional link artificial neural network (FLANN) structure, named as PSO based nonlinear structure (PSO-NLS) algorithm. The proposed algorithm does not require any computation of secondary path estimate filtering unlike other conventional gradient based algorithms and hence has got computational advantage. The computer simulation experiments show its superior performance compared to the FXLMS, filtered-s LMS and genetic algorithms under saturation present at both at secondary and reference paths. The paper also includes a sensitivity analysis to study the effect of different parameters on ANC performance.     

Robust boundary stabilization of a vibrating rectangular plate using disturbance adaptation

This paper considers robust boundary control with disturbance adaptation to stabilize the vibration of a rectangular plate under disturbances with unknown upper‐bounds. Disturbances are considered to be distributed both over the plate interior domain and along the boundary (in‐domain and boundary distributed disturbances). Applying Hamilton's principle, the dynamics of the plate is represented in the form of a fourth‐order partial differential equation subject to static and dynamic boundary conditions. The proposed model considers the membrane effect of axial force and the effect of actuator mass dynamics on the plate vibration. A robust boundary control is established that stabilizes the plate in presence of both in‐domain and boundary disturbances. A rigorous Lyapunov stability analysis shows that the vibration of the plate is uniformly ultimately bounded and converges to the vicinity of zero by proper selection of control gains. For the vanishing in‐domain disturbances, it is seen that exponential stability is achieved by the proposed control. Next, a disturbance adaptation law is introduced to stabilize the plate vibration in response to disturbances with unknown bounds, and the stability of the robust boundary control with disturbance adaptation is studied using Lyapunov. Simulation results verify the efficiency of the suggested control. Copyright © 2016 John Wiley & Sons, Ltd.     

Synthesis of multi-variate Volterra systems by a topological assemblage scheme

The Volterra series expansion is widely employed to represent the input–output relationship of nonlinear dynamical systems. Such a representation is based on the Volterra frequency-response functions (VFRF), which can be calculated from the governing equations of the system by the harmonic probing method. This operation is straightforward for simple systems, but may become very complicated for multi-variate or high-order systems. An alternative technique for the evaluation of the VFRFs of multi-variate systems is presented here generalizing a previously reported technique that focused on uni-variate cases. Additionally, it is extended to derive, within the same framework, a set of associated linear equations (ALE). Examples of a 2-dof system with polynomial nonlinearities, a wind-excited cable and a 2-dof system subjected to ocean waves are utilized to demonstrate applications of the proposed technique.