Abstract:
The network and plant can be regarded as a controlled time-varying system because of the random induced delay in the networked control systems. The cerebellar model articulation controller (CMAC) neural network and a PD controller are combined to achieve the forward feedback control. The PD controller parameters are adjusted adaptively by fuzzy reasoning mechanism, which can optimize the control effect by reducing the uncertainty caused by the network-induced delay. Finally, the simulations show that the control method proposed can improve the performance effectively. 1. Introduction Networked control system (NCS) is a distributed and networked real-time feedback control system which combine communication network and control system [1]. Due to the irregularly multiple nodes shared network and data flowing change, information exchange time delay occurred inevitably, which is the network-induced delay [2]. The network-induced delay will cause system poor control quality and bad performance, even unstable [3–5]. Therefore, the induced delay is one of the most issues in the network control system [6–9]. Based on the influence of the induced delay in the network control system, a cycle time delay network using augmented deterministic discrete time model method is proposed by [10] to control the linear continuous controlled object. In [11] based on the queue management network, the queuing methodology is put forward to turn random time delay into fixed-length time delay. The buffer queue method is designed based on probability predictor delay compensation, according to the problem of random delay in the network control system [12]. Zhang et al. [13] studied the stability of network control system with constant delay. Wu et al. [14] propose a delay-dependent sufficient condition by applying the delay partitioning approach for the asymptotic stability with an H∞ error performance for the error system. Wu and Zheng [15] addressed the L2-L∞ dynamic output feedback (DOF) control problem for a class of nonlinear fuzzy ItO stochastic systems with time-varying delay. Yue et al. [16] established the new network control system model considering network-varying delay, packet loss, and wrong sequence. Peng et al. [17] researched on network control system with interval variable delay and reduced complexity by introducing Jessen inequality. Wu et al. [18] investigated the problems of stability analysis and stabilization for a class of discrete-time Takagi-Sugeno fuzzy systems with time-varying state delay. Wu et al. [19] proposed sufficient conditions to guarantee the

Abstract:
The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for computing both Caputo and (modified) Riemann-Liouville (RL) fractional pseudospectral differentiation matrices (F-PSDMs) of any order at general Jacobi-Gauss-Lobatto (JGL) points. We show that in the Caputo case, it suffices to compute F-PSDM of order $\mu\in (0,1)$ to compute that of any order $k+\mu$ with integer $k\ge 0,$ while in the modified RL case, it is only necessary to evaluate a fractional integral matrix of order $\mu\in (0,1).$ Secondly, we introduce suitable fractional JGL Birkhoff interpolation problems leading to new interpolation polynomial basis functions with remarkable properties: (i) the matrix generated from the new basis yields the exact inverse of F-PSDM at "interior" JGL points; (ii) the matrix of the highest fractional derivative in a collocation scheme under the new basis is diagonal; and (iii) the resulted linear system is well-conditioned in the Caputo case, while in the modified RL case, the eigenvalues of the coefficient matrix are highly concentrated. In both cases, the linear systems of the collocation schemes using the new basis can solved by an iterative solver within a few iterations. Notably, the inverse can be computed in a very stable manner, so this offers optimal preconditioners for usual fractional collocation methods for fractional differential equations (FDEs). It is also noteworthy that the choice of certain special JGL points with parameters related to the order of the equations can ease the implementation. We highlight that the use of the Bateman's fractional integral formulas and fast transforms between Jacobi polynomials with different parameters, are essential for our algorithm development.

Abstract:
In this paper, an stability theorem is proposed for a fractional state space system based on Lyapunov stability theory. Controller can be achieved easily by this theory without calculating any equilibrium point. The fractional unified chaotic system is used to improve the stability theorem. The effectiveness of the theory is verified by the simulation results.

Abstract:
In this paper, based on output linearization feedback control,the nonlinear function of the chaotic system is linearized, then the complex synchronization of the nonlinear chaotic system is converted into the stable problem of the linearization system. Then a nonlinear controller is given by pole assignment. Furthermore based on the scheme above, a system of secure communication is proposed. One channel of the system is output of the chaotic transmitter, the other one transmits the information-bearing signal. Finally a numerical example is used to show the effectiveness of the proposed technique.

Abstract:
In order to improve the complexity of chaotic signals, a new fractional-order four-dimensional hyperchaotic system is presented. Some dynamical properties of the system are investigated. The circuit implementation of this new system is simulated using Multisim. The results prove that chaos actually exists in the system with order as low as 3.2. A simple linear feedback controller is designed, and the simulation results are presented to demonstrate the effectiveness of the method.

Abstract:
An adaptive tracking control based on zero phase error is presented.First,state-variable filters based on the state equations for reference model with transfer function being 1 are introduced.Then,an adaptive law with generalized output error is designed.The structure of the controller is relatively simple and it has better servo performance.Finally,the simulation results show that the method can improve the performance of the dynamic system with unknown parameters or time_varying parameters.

Abstract:
The coordinate transformation offers a remarkable way to design cloaks that can steer electromagnetic fields so as to prevent waves from penetrating into the {\em cloaked region} (denoted by $\Omega_0$, where the objects inside are invisible to observers outside). The ideal circular and elliptic cylindrical cloaked regions are blown up from a point and a line segment, respectively, so the transformed material parameters and the corresponding coefficients of the resulted equations are highly singular at the cloaking boundary $\partial \Omega_0$. The electric field or magnetic field is not continuous across $\partial\Omega_0.$ The imposition of appropriate {\em cloaking boundary conditions} (CBCs) to achieve perfect concealment is a crucial but challenging issue. Based upon the principle that finite electromagnetic fields in the original space must be finite in the transformed space as well, we obtain CBCs that intrinsically relate to the essential "pole" conditions of a singular transformation. We also find that for the elliptic cylindrical cloak, the CBCs should be imposed differently for the cosine-elliptic and sine-elliptic components of the decomposed fields. With these at our disposal, we can rigorously show that the governing equation in $\Omega_0$ can be decoupled from the exterior region $\Omega_0^c$, and the total fields in the cloaked region vanish. We emphasize that our proposal of CBCs is different from any existing ones.

Abstract:
We report in this paper a fast and accurate algorithm for computing the exact spherical nonreflecting boundary condition (NRBC) for time-dependent Maxwell's equations. It is essentially based on a new formulation of the NRBC, which allows for the use of an analytic method for computing the involved inverse Laplace transform. This tool can be generically integrated with the interior solvers for challenging simulations of electromagnetic scattering problems. We provide some numerical examples to show that the algorithm leads to very accurate results.

Abstract:
This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle-triangle mapping proposed in the conference note [21]. Here, we provide some new insights into the originality and distinctive features of the mapping, and show that this transform only induces a logarithmic singularity, which allows us to devise a fast, stable and accurate numerical algorithm for its removal. Consequently, any triangular element can be treated as efficiently as a quadrilateral element, which affords a great flexibility in handling complex computational domains. Benefited from the fact that the image of the mapping includes the polynomial space as a subset, we are able to obtain optimal $L^2$- and $H^1$-estimates of approximation by the proposed basis functions on triangle. The implementation details and some numerical examples are provided to validate the efficiency and accuracy of the proposed method. All these will pave the way for developing an unstructured TSEM based on, e.g., the hybridizable discontinuous Galerkin formulation.