2,312 publications from this institution
In this paper, a smart NN control scheme is proposed. This scheme is designed such that the current control action can utilize the knowledge that the NN learned from the past control process. A chaotic signal is employed as the reference signal to improve the generalization ability of the NN in the training phase of the scheme, where the complex chaotic signal offers much more information for NN learning thereby significantly improving the efficiency of the NN generalization. Compared with most of the adaptive neural controllers, the smart neural controller (in the operational phase) is a static and low-order controller, and thus needs much less computational resources, and is more feasible in practical implementation. Simulation studies are included to demonstrate the effectiveness of the new control scheme.
No abstract is provided for this article.
We apply the modified extended Kalman filter to develop a learning algorithm for feedforward networks. The resulting algorithm improves the existing extended Kalman filter based scheme in both speed of convergence and accuracy of estimation.
Abstract: This paper is concerned with the problem of finite-time synchronization incomplex networks with stochastic noise perturbations. By using a novel finite-timeL-operator differential inequality and other inequality techniques, some novel sufficientconditions are obtained to ensure finite-time stochastic synchronization for the complexnetworks concerned, where the coupling matrix need not be symmetric. The effectsof control parameters on synchronization speed and time are also analyzed, and thesynchronization time in this paper is shorter than that in the existing literature. The resultshere are also applicable to both directed and undirected weighted networks without anyinformation of the coupling matrix. Finally, an example with numerical simulationsis givento demonstrate the effectiveness of the proposed method.Keywords: chaotic complex networks; finite-time synchronization; stochasticsynchronization; L-operator differential inequality; stochastic disturbance1. IntroductionIn recent years, complex networks have been shown to exist in many different areas in the realword [1], such as Internet networks, the Word Wide Web, food chains, relationship networks, andso on. A complex network is composed of a set of interconnected nodes, where the nodes andconnections can represent anything. According to different ways of connections and whether there are
In this work, we study the realization and bifurcation of Boolean functions of four variables via a Cellular Neural Network (CNN). We characterize the basic relations between the genes and the offsets of an uncoupled CNN as well as the basis of the binary input vectors set. Based on the analysis, we have rigorously proved that there are exactly 1882 linearly separable Boolean functions of four variables, and found an effective method for realizing all linearly separable Boolean functions via an uncoupled CNN. Consequently, any kind of linearly separable Boolean function can be implemented by an uncoupled CNN, and all CNN genes that are associated with these Boolean functions, called the CNN gene bank of four variables, can be easily determined. Through this work, we will show that the standard CNN invented by Chua and Yang in 1988 indeed is very essential not only in terms of engineering applications but also in the sense of fundamental mathematics.
We present a direct solution to the problem of constructing a stochastic matrix with prescribed eigenspectrum, widely referred to as the stochastic inverse eigenvalue problem. The solution uses Markov state disaggregation to construct a Markov chain with the associated stochastic transition matrix possessing the required eigenspectrum. Existing solutions that follow the same approach are limited to constructing matrices with real-valued eigenspectra. The novel solution directly constructs matrices with complex-valued eigenspectra by applying a new disaggregation technique in tandem with a technique from a previous solution. Due to this generalization, the novel solution is able to successfully model physical systems from a larger family. Furthermore, the novel solution constructs the matrix in a finite and predetermined number of iterations, and without numerical approximation. The solution is demonstrated by deriving an expression for a set of 4 × 4 stochastic matrices sharing the same prescribed complex-valued eigenspectrum and indexed by a real parameter.
Based on multi-carrier transmission and multi-level chaos shift keying modulation, a novel multi-carrier chaos shift keying (MC-CSK) modulation system is proposed and designed in this paper. The new system adopts multiple subcarriers, on which all chaotic basis signals along with multiple data-bearing signals are transmitted simultaneously. The data-bearing signals and their references, though sharing the same subcarriers, are separated by I/Q channels. As a consequence, the MC-CSK system can achieve higher bit rate and better spectral efficiency compared with the MC-DCSK system. It can also dispense with chaos synchronization and threshold shifting that are required in conventional CSK systems, and achieve a delay-line-free design in both transmitters and receivers. Also, the performance of the proposed system is further improved by normalizing all chaotic basis signals and making them strictly orthogonal using the Gram-Schmidt algorithm. Moreover, the bit error rates (BERs) of the MC-CSK system over additive white Gaussian noise and multipath Rayleigh fading channels are derived. Finally, simulations are performed under different channel conditions and the effects of system parameters on the BER performance are evaluated. Both analytical and simulation results confirm that the MC-CSK system outperforms differential CSK (DCSK) and MC-DCSK systems in BER performance, except a rare case when the number of subcarriers is very small.
Consider the following two spatially generalized Logistic systems with two different real parameters: xm+1,n+ωxm,n+1=1−μ1[(1+ω)xmn]2 and ym+1,n+ωym,n+1=1−μ2[(1+ω)ymn]2, where ω is a constant. We introduce an analytical method for generalized synchronization of these two spatially chaotic systems. We specify a range of the coupling constant in the generalized synchronization, and characterize a nonlinear function for synchronization stability.
This note points out that the assertions of (Chen's attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system, CHAOS 23, 033108 (2013)) are groundless and incorrect. The failure of that criticism actually supports the strong standing of the Chen system.
The intrinsic dynamics of the Lorenz system are confined in the positive half-space with respect to the vertical axis due to a limiting threshold effect. To break such a threshold effect, a novel piecewise Lorenz system is introduced, equipped with a staircase function and an even symmetric piecewise-linear function. The new system is autonomous, and yet, it can generate various grid multiwing butterfly chaotic attractors without requiring any external forcing. A module-based circuit is designed for implementation, with experiments reported for verification and demonstration.
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, one kind of intermittency generated by a discontinuous system is studied. Although this system, which is composed of two switched subsystems coupled with a high strength, is nonsmooth, the mechanism of this kind of intermittency can be analyzed with several explicit relations between the intermittency characteristics and the system control parameters. In particular, estimates of “steady-state” values of the system (in the laminar phases) and a critical value for this intermittency can be derived, which are helpful in relevant control systems design. Moreover, some power laws for the observed intermittency are obtained and discussed. </para>
Halo‐chaos in high‐current accelerator has become one of the key issues because it can cause excessive radioactivity from the accelerators and significantly limits the applications of the new accelerators in industrial and other fields. Some general engineering methods for chaos control have been developed, but they generally are unsuccessful for halo‐chaos suppression due to many technical constraints. In this article, controllability condition for beam halo‐chaos is analyzed qualitatively. Then Particles‐in‐Cell (PIC) simulations explore the nature of beam halo‐chaos formation. A nonlinear control method and wavelet function feedback controller are proposed for controlling beam halo‐chaos. After control of beam halo‐chaos for initial proton beam with water bag distributions, the beam halo strength factor H is reduced to zero, and other statistical physical quantities of beam halo‐chaos are doubly reduced. The results show that the developed methods in this paper are very effective for proton beam halo‐chaos suppression. Potential application of the halo‐chaos control method is finally pointed out.
