Implementation of convolutional perfectly matched layer for three‐dimensional hybrid implicit‐explicit finite‐difference time‐domain method

The hybrid implicit‐explicit (HIE) finite‐difference time‐domain (FDTD) method with the convolutional perfectly matched layer (CPML) is extended to a full three‐dimensional scheme in this article. To demonstrate the application of the CPML better, the entire derivation process is presented, in which the fine scale structure is changed from y‐direction to z‐direction of the propagation innovatively. The numerical examples are adopted to verify the efficiency and accuracy of the proposed method. Numerical results show that the HIE‐FDTD with CPML truncation has the similar relative reflection error with the FDTD with CPML method, but it is much better than the methods with Mur absorbing boundary. Although Courant‐Friedrich‐Levy number climbs to 8, the maximum relative error of the proposed HIE‐CPML remains more below than ?71 dB, and CPU time is nearly 72.1% less than the FDTD‐CPML. As an example, a low‐pass filter is simulated by using the FDTD‐CPML and HIE‐CPML methods. The curves obtained are highly fitted between two methods; the maximum errors are lower than ?79 dB. Furthermore, the CPU time saved much more, accounting for only 26.8% of the FDTD‐CPML method while the same example simulated.     

Implementation and optimization of GPU‐based parallel one‐step leapfrog ADI‐FDTD for far‐field scattering problems

The one‐step leapfrog alternative‐direction‐implicit finite‐difference time‐domain (ADI‐FDTD), free from the Courant‐Friedrichs‐Lewy (CFL) stability condition and sub‐step computations, is efficient when dealing with fine grid problems. However, solution of the numerous tridiagonal systems still imposes a great computational burden and makes the method hard to execute in parallel. In this paper, we proposed an efficient graphic processing unit (GPU)‐based parallel implementation of the one‐step leapfrog ADI‐FDTD for the far‐field EM scattering simulation of objects, in which we present and analyze the manners of calculation area division and thread allocation and a data layout transformation of z components is proposed to achieve better memory access mode, which is a key factor affecting GPU execution efficiency. The simulation experiment is carried out to verify the accuracy and efficiency of the GPU‐based implementation. The simulation results show that there is a good agreement between the proposed one‐step leapfrog ADI‐FDTD method and Yee's FDTD in solving the far‐field scattering problem and huge benefits in performance were encountered when the method was accelerated using GPU technology.     

Applications of anisotropic one‐step leapfrog HIE‐FDTD method in microwave circuit and antenna

To verify the effect of artificial anisotropy parameters in one‐step leapfrog hybrid implicit‐explicit finite‐difference time‐domain (FDTD) method, we calculated several microwave components with different characteristics. Introduced auxiliary field variable can reduce the program difficulty and improve the computational efficiency without additional computational time and memory cost. Analyses of the numerical results are proved that the calculation time is reduced to about one‐sixth compared to the traditional FDTD method for the same example simulated. The memory cost and relative error are remained at a good level. The numerical experiments for microwave circuit and antenna have been well demonstrated the method available.     

Separation principle for quasi‐one‐sided Lipschitz nonlinear systems with time delay

In this article, we address the problem of output stabilization for a class of nonlinear time‐delay systems. First, an observer is designed for estimating the state of nonlinear time‐delay systems by means of quasi‐one‐sided Lipschitz condition, which is less conservative than the one‐sided Lipschitz condition. Then, a state feedback controller is designed to stabilize the nonlinear systems in terms of weak quasi‐one‐sided Lipschitz condition. Furthermore, it is shown that the separation principle holds for stabilization of the systems based on the observer‐based controller. Under the quasi‐one‐sided Lipschitz condition, state observer and feedback controller can be designed separately even though the parameter (A,C) of nonlinear time‐delay systems is not detectable and parameter (A,B) is not stabilizable. Finally, a numerical example is provided to verify the efficiency of the main results.     

Reasoning tractably about explicit belief: A model‐theoretic approach

Existing epistemic logics such as the logic of implicit and explicit belief and the logic of awareness adopt a deductive‐theoretic approach for characterizing belief. In this approach, an agent represents the state of the world with a conjunction of axioms in its knowledge base (KB) and evaluates queries by trying to prove or disprove that they follow from KB. This paper presents a multivalued epistemic logic (MEL) that allows agents to reason both deductively and model theoretically about implicit and explicit belief. By characterizing an agent's KB with a class of finite models, the set of formulas that an agent believes can be determined by checking their validity in all these models. This rests on the fact that MEL has a complete axiomatization (sentences that are true in all these models will also be provable). In this paper, the soundness, completeness, and decidability of MEL are proven. Furthermore, a polynomial time model‐checking algorithm for determining the satisfiability of a sentence at a particular state in a given model of MEL is also presented. © 2000 John Wiley & Sons, Inc.     

Avoiding on‐screen metamerism in N‐primary displays

Abstract— The present paper describes a method for using more than three primaries in an additive‐primary display. The method ensures that each tristimulus specification can be produced in no more than one way, even if a non‐singular filter (i.e., one that does not reduce the dimensionality of color‐matching space) is interposed between the screen and the viewer. Starting with N primaries, the method uses only three at a time, but these may be composites — fixed linear combinations of the original N. As further insurance against on‐screen metamerism, a criterion on the primary spectra, based on the Binet‐Cauchy theorem, ensures that a triad of primaries keeps its right/left‐handed chromaticity ordering when a filter is interposed.     

Gain scheduled control for discrete‐time systems depending on bounded rate parameters

In this paper we consider a linear, discrete‐time system depending multi‐affinely on uncertain, real time‐varying parameters. A new sufficient condition for the stability of this class of systems, in terms of a feasibility problem involving linear matrix inequalities (LMIs), is obtained under the hypothesis that a bound on the rate of variation of the parameters is known. This condition, obtained by the aid of parameter dependent Lyapunov functions, obviously turns out to be less restrictive than that one obtained via the classical quadratic stability (QS) approach, which guarantees stability in presence of arbitrary time‐varying parameters. An important point is that the methodology proposed in this paper may result in being less conservative than the classical QS approach even in the absence of an explicit bound on the parameters rate of variation. Concerning the synthesis context, the design of a gain scheduled compensator based on the above approach is also proposed. It is shown that, if a suitable LMI problem is feasible, the solution of such problem allows to design an output feedback gain scheduled dynamic compensator in a controller‐observer form stabilizing the class of systems which is dealt with. The stability conditions are then extended to take into account L₂ performance requirements. Some numerical examples are carried out to show the effectiveness and to investigate the computational burden required by the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Computer simulation of polarization rotation characteristics of graphene

The magnetically biased graphene has the polarization rotation characteristics which is useful to design the polarizer. But this characteristic is difficult to simulate by using the finite‐difference time‐domain (FDTD) method, not only due to the graphene's thin layer which confines the time step size, but also because of graphene's isotropic surface conductivity when it is biased by static magnetic field. To solve this problem, this study presents an anisotropic hybrid implicit‐explicit FDTD method. This method uses auxiliary difference equations to represent graphene's conductivity, and removes the confinement of graphene's thickness on time step size by using hybrid implicit‐explicit technique. So, compared with FDTD method, the presented method can save a large number of computational time, which are validated by numerical examples.     

Input‐to‐state exponents and related ISS for delayed discrete‐time systems with application to impulsive effects

This paper aims to investigate the input‐to‐state exponents (IS‐e) and the related input‐to‐state stability (ISS) for delayed discrete‐time systems (DDSs). By using the method of variation of parameters and introducing notions of uniform and weak uniform M‐matrix, the estimates for 3 kinds of IS‐e are derived for time‐varying DDSs. The exponential ISS conditions with parts suitable for infinite delays are thus established, by which the difference from the time‐invariant case is shown. The exponential stability of a time‐varying DDS with zero external input cannot guarantee its ISS. Moreover, based on the IS‐e estimates for DDSs, the exponential ISS under events criteria for DDSs with impulsive effects are obtained. The results are then applied in 1 example to test synchronization in the sense of ISS for a delayed discrete‐time network, where the impulsive control is designed to stabilize such an asynchronous network to the synchronization.     

Key Time Steps Selection for Large‐Scale Time‐Varying Volume Datasets Using an Information‐Theoretic Storyboard

Key time steps selection is essential for effective and efficient scientific visualization of large‐scale time‐varying datasets. We present a novel approach that can decide the number of most representative time steps while selecting them to minimize the difference in the amount of information from the original data. We use linear interpolation to reconstruct the data of intermediate time steps between selected time steps. We propose an evaluation of selected time steps by computing the difference in the amount of information (called information difference) using variation of information (VI) from information theory, which compares the interpolated time steps against the original data. In the one‐time preprocessing phase, a dynamic programming is applied to extract the subset of time steps that minimize the information difference. In the run‐time phase, a novel chart is used to present the dynamic programming results, which serves as a storyboard of the data to guide the user to select the best time steps very efficiently. We extend our preprocessing approach to a novel out‐of‐core approximate algorithm to achieve optimal I/O cost, which also greatly reduces the in‐core computing time and exhibits a nice trade‐off between computing speed and accuracy. As shown in the experiments, our approximate method outperforms the previous globally optimal DTW approach [ TLS12 ] on out‐of‐core data by significantly improving the running time while keeping similar qualities, and is our major contribution.     

Nonlinear H∞ observer design for one‐sided Lipschitz discrete‐time singular systems with time‐varying delay

This paper investigates the H_∞ observer design problem for a class of nonlinear discrete‐time singular systems with time‐varying delays and disturbance inputs. The nonlinear systems can be rectangular and the nonlinearities satisfy the one‐sided Lipschitz condition and quadratically inner‐bounded condition, which are more general than the traditional Lipschitz condition. By appropriately dealing with these two conditions and applying several important inequalities, a linear matrix inequality–based approach for the nonlinear observer design is proposed. The resulting nonlinear H_∞ observer guarantees asymptotic stability of the estimation error dynamics with a prescribed performance γ. The synthesis condition of H_∞ observer design for nonlinear discrete‐time singular systems without time delays is also presented. The design is first addressed for one‐sided Lipschitz discrete‐time singular systems. Finally, two numerical examples are given to show the effectiveness of the present approach.     

Robust H∞ sliding mode observer‐based fault‐tolerant control for One‐sided Lipschitz nonlinear systems

This paper presents fault tolerant controllers for a class of one‐sided Lipschitz nonlinear systems with external disturbances. A sliding mode observer (SMO) is integrated with the H_∞ filtering approach as the fault detection and isolation module. The problem is investigated in the presence of faults and disturbances simultaneously. The H_∞ ‐SMO is capable of approximating faults accurately, while reducing the effect of disturbances in the estimation of the state vector and occurred faults. Accordingly, using only a single SMO, the estimation error of the state vector and faults can be made simultaneously arbitrarily small. In addition, to deal with the weighted bilinear form appearing in the one‐sided Lipschitz condition, the quadratically inner bounded condition presented in the literature is employed in this paper as a useful solution. The proposed method guarantees the stability of the overall closed‐loop system, and after a short transient time, the estimation errors for state vector and fault signal converge to a small neighborhood of the origin. The effectiveness of the presented algorithm is confirmed in two examples including a single arm robot with a flexible joint and a numerical simulation.     

Computationally Efficient Algorithm For Frequency‐Weighted Optimal H∞ Model Reduction

In this paper, a frequency‐weighted optimal H_∞ model reduction problem for linear time‐invariant (LTI) systems is considered. The objective of this class of model reduction problems is to minimize H_∞ norm of the frequency‐weighted truncation error between a given LTI system and its lower order approximation. A necessary and sufficient solvability condition is derived in terms of LMIs with one extra coupling rank constraint, which generally leads to a non‐convex feasibility problem. Moreover, it has been shown that the reduced‐order model is stable when both stable input and output weights are included, and its state‐space data are given explicitly by the solution of the feasibility problem. An efficient model reduction scheme based on cone complementarity algorithm (CCA) is proposed to solve the non‐convex conditions involving rank constraint.     

Finite‐time boundedness of switched systems with time‐varying delays via sampled‐data control

In the framework of sampled‐data control, finite‐time boundedness (FTB) of switched systems with time‐varying delays is investigated. Sufficient conditions for FTB of switched systems with time‐varying delays via sampled‐data control are proposed. Moreover, considering the relationship between the sampling period and the mode‐dependent average dwell time, switching signals are designed. In addition, finite‐time weighted L₂‐gain (FTW‐L₂‐gain) of switched systems with time‐varying delays is proposed to measure their disturbance tolerance capacity within a finite‐time interval. Multiple Lyapunov‐Krasovskii functionals are applied to complete subsequent proofs in detail. Simulation results are exemplified to verify the proposed method.     

On mean‐square H∞ control for discrete‐time nonlinear stochastic systems with (x,u, v)‐dependent noises

In this paper, the H_∞ control problem is investigated for a general class of discrete‐time nonlinear stochastic systems with state‐, control‐, and disturbance‐dependent noises (also called (x, u, v)‐dependent noises). In the system under study, the system state, the control input, and the disturbance input are all coupled with white noises, and this gives rise to considerable difficulties in the stability and H_∞ performance analysis. By using the inequality techniques, a sufficient condition is established for the existence of the desired controller such that the closed‐loop system is mean‐square asymptotically stable and also satisfies H_∞ performance constraint for all nonzero exogenous disturbances under the zero‐initial condition. The completing square technique is used to design the H_∞ controller with hope to reduce the resulting conservatism, and a special algebraic identity is employed to deal with the cross‐terms induced by (x, u, v)‐dependent noises. Several corollaries with simplified conditions are presented to facilitate the controller design. The effectiveness of the developed methods is demonstrated by two numerical examples with one concerning the multiplier‐accelerator macroeconomic system.     

Coordination of discrete‐time multi‐agent systems via relative output feedback

This paper investigates the joint effects of agent dynamic and network topology on the consensusability of linear discrete‐time multi‐agent systems via relative output feedback. An observer‐based distributed control protocol is proposed. A necessary and sufficient condition for consensusability under this control protocol is given, which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the eigenratio of the undirected communication graph affect consensusability. As a special case, multi‐agent systems with discrete‐time double integrator dynamics are discussed where a simple control protocol directly using two‐step relative position feedback is provided to reach a consensus. Finally, the result is extended to solve the formation and formation‐based tracking problems. The theoretical results are illustrated by simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

Fast Mean‐Curvature Flow via Finite‐Elements Tracking

In this paper, we present a novel approach for efficiently evolving meshes using mean‐curvature flow. We use a finite‐elements hierarchy that supports an efficient multigrid solver for performing the semi‐implicit time‐stepping. Although expensive to compute, we show that it is possible to track this hierarchy through the process of surface evolution. As a result, we provide a way to efficiently flow the surface through the evolution, without requiring a costly initialization at the beginning of each time‐step. Using our approach, we demonstrate a factor of nearly seven‐fold improvement over the non‐tracking implementation, supporting the evolution of surfaces consisting of 1M triangles at a rate of just a few seconds per update.     

Improving Shift‐Reduce Phrase‐Structure Parsing with Constituent Boundary Information

Shift‐reduce parsing enjoys the property of efficiency because of the use of efficient parsing algorithms like greedy/deterministic search and beam search. In addition, shift‐reduce parsing is much simpler and easy to implement compared with other parsing algorithms. In this article, we explore constituent boundary information to improve the performance of shift‐reduce phrase‐structure parsing. In previous work, constituent boundary information has been used to speed up chart parsers successfully. However, whether it is useful for improving parsing accuracy has not been investigated. We propose two different models to capture constituent boundary information, based on which two sets of novel features are designed for a shift‐reduce parser. The first model is a boundary prediction model that uses a classifier to predict the boundaries of constituents. We use automatically parsed data to train the classifier. The second one is a Tree Likelihood Model that measures the validity of a constituent by its likelihood which is calculated on automatically parsed data. Experimental results show that our proposed method outperforms a strong baseline by 0.8% and 1.6% in F‐score on English and Chinese data, respectively, achieving the competitive parsing accuracies on Chinese (84.8%) and English (90.8%). To our knowledge, this is the first time for shift‐reduce phrase‐structure parsing to advance the state‐of‐the‐art with constituent boundary information.     

H∞ stabilization for networked semi‐Markovian jump systems with randomly occurring uncertainties via improved dynamic event‐triggered scheme

This paper aims to solve the H_∞ stabilization problem for networked semi‐Markovian jump systems subject to randomly occurring uncertainties by an improved event‐triggered technique. A new measurement error that is defined as the difference value between the latest transmitted data and the mean value of both current data and latest transmitted data is introduced into the event‐triggered condition. Compared with traditional dynamic event‐triggered scheme, more unexpected data could be avoided to be transmitted, which is demonstrated in the simulation through sufficient comparison experiments. Furthermore, by employing a Lyapunov‐Krasovskii functional method and a free‐weighting matrix method, sufficient conditions are derived to guarantee the stabilization of the closed‐loop semi‐Markovian jump time‐delay system with uncertainties and a prescribed performance index. Then, a codesign method for H_∞ controller gains and event‐triggered parameters is presented. Finally, simulations are given to verify the effectiveness of our improved dynamic event‐triggered scheme.     

Periodically Time‐Varying Memory State‐Feedback for Robust H2 Control of Uncertain Discrete‐Time Linear Systems

This study is concerned with the synthesis of periodically time‐varying memory state‐feedback controllers (PTVMSFCs) for discrete‐time linear systems. In our preceding studies, we have already established a solid theoretical basis for linear matrix inequality (LMI)‐based (robust) H _∞‐PTVMSFCs synthesis, and the goal of this paper is to extend those results to the H ₂ performance criterion. In the H ₂ case, the main difficulty stems from the fact that we have to ensure the existence of common auxiliary variables for multiple LMI conditions that are related to the Lyapunov inequality and the inequalities for bounding traces that characterize the H ₂ norm. We can overcome this difficulty and derive a necessary and sufficient LMI condition for the optimal H ₂‐PTVMSFC synthesis. On the basis of this result, we also consider robust H ₂‐PTVMSFC synthesis for LTI systems with parametric uncertainties.