Kernel Correntropy Conjugate Gradient Algorithms Based on Half-Quadratic Optimization.

As a nonlinear similarity measure defined in the kernel space, the correntropic loss (C-Loss) can address the stability issues of second-order similarity measures thanks to its ability to extract high-order statistics of data. However, the kernel adaptive filter (KAF) based on the C-Loss uses the stochastic gradient descent (SGD) method to update its weights and, thus, suffers from poor performance and a slow convergence rate. To address these issues, the conjugate gradient (CG)-based correntropy algorithm is developed by solving the combination of half-quadratic (HQ) optimization and weighted least-squares (LS) problems, generating a novel robust kernel correntropy CG (KCCG) algorithm. The proposed KCCG with less computational complexity achieves comparable performance to the kernel recursive maximum correntropy (KRMC) algorithm. To further curb the growth of the network in KCCG, the random Fourier features KCCG (RFFKCCG) algorithm is proposed by transforming the original input data into a fixed-dimensional random Fourier features space (RFFS). Since only one current error information is used in the loss function of RFFKCCG, it can provide a more efficient filter structure than the other KAFs with sparsification. The Monte Carlo simulations conducted in the prediction of synthetic and real-world chaotic time series and the regression for large-scale datasets validate the superiorities of the proposed algorithms in terms of robustness, filtering accuracy, and complexity.

A novel 3D non-autonomous system with parametrically excited abundant dynamics and bursting oscillations.

In this paper, a novel non-autonomous chaotic system with rich dynamical behaviors is proposed by introducing parametric excitation to a Lorenz-like system, and the effect of the initial value of the excitation system on the resulting system dynamics is then thoroughly investigated. The attractors resulting from the proposed chaotic system will enter different oscillating states or have topological change when the initial value varies. Furthermore, some novel bursting oscillations and bifurcation mechanism are revealed. Stability and bifurcation of the proposed 3D non-autonomous system are comprehensively investigated to analyze the causes of the observed dynamics through a range of analytical methods, including bifurcation diagram, Lyapunov exponent spectrum, and sequence and phase diagrams. Software simulation and hardware experimentation are conducted in this study, which verify the dynamic behaviors of the proposed chaotic system. This study will create a new perspective and dimension of perceiving non-autonomous chaotic systems and exploring their applicability in real-world engineering applications.

A complex network theory analytical approach to power system cascading failure-From a cyber-physical perspective.

The modern electric power grid is evolving rapidly into such a state that distributed controllers and two-way energy and information flow are replacing the traditional paradigm of electricity distribution and energy management. Therefore, a power grid coupled with a communication network is playing a pivotal role in establishing modern electric power systems. Previous cascading failure analysis in power systems focused more on the physical network, while falling short of investigations on the coupling effect of interdependency of the integrated electricity and communication networks, i.e., cyber-physical power systems. To address such a pressing issue, this study introduces a novel stochastic cascading failure model, considering the interdependency between the cyber network and power network. A multiagent system and a novel protection relay model are incorporated into the proposed model. To apply the proposed analytical method, a test power system, the IEEE 68-bs power system, is used to study the impacts of a range of interdependencies and cyber network topological structures on the cascading failure. Simulation results show the necessity and effects of consideration of cyber communication network when investigating power system cascading failures. The study also provides useful information on robustness and vulnerability of a particular power grid, given different communication topologies and interdependencies.

Analysis and generation of chaos using compositely connected coupled memristors.

In large-scale high-density integrated circuits, memristors in close proximity to one another both influence, and are influenced by, the behavior of nearby memristors. However, the previous analyses of memristors-based circuit applications have seldom considered the possibility of coupling effects between memristors which invariably influences the response of all memristors, thus rendering much previous research as incomplete. In this paper, the circuit dynamics of memristive Chua's circuits are systematically analyzed based on a pair of compositely connected flux-controlled memristors characterized by cubic nonlinearity as a typical example. A theoretical analysis is undertaken and verified via MATLAB. While tuning the coupling strength, variations in circuit dynamics are characterized by phase portraits, bifurcation diagrams, and Lyapunov exponents. A new floating memristor emulator with coupling ports, described by cubic nonlinearity, is designed using off-the-shelf circuit devices and is shown to be successfully used in building chaotic circuits in hardware experiments, verifying theoretical results in simulations. This paper provides a new way through which memristors-based circuit dynamics can be influenced by tuning the coupling strength between memristors without changing other circuit parameters. It is further highlighted that when designing future memristors-based circuits, the coupling action between memristors should be considered if necessary and compensated when causing undesired circuit responses.

Formulation and Implementation of Nonlinear Integral Equations to Model Neural Dynamics Within the Vertebrate Retina.

Existing computational models of the retina often compromise between the biophysical accuracy and a hardware-adaptable methodology of implementation. When compared to the current modes of vision restoration, algorithmic models often contain a greater correlation between stimuli and the affected neural network, but lack physical hardware practicality. Thus, if the present processing methods are adapted to complement very-large-scale circuit design techniques, it is anticipated that it will engender a more feasible approach to the physical construction of the artificial retina. The computational model presented in this research serves to provide a fast and accurate predictive model of the retina, a deeper understanding of neural responses to visual stimulation, and an architecture that can realistically be transformed into a hardware device. Traditionally, implicit (or semi-implicit) ordinary differential equations (OES) have been used for optimal speed and accuracy. We present a novel approach that requires the effective integration of different dynamical time scales within a unified framework of neural responses, where the rod, cone, amacrine, bipolar, and ganglion cells correspond to the implemented pathways. Furthermore, we show that adopting numerical integration can both accelerate retinal pathway simulations by more than 50% when compared with traditional ODE solvers in some cases, and prove to be a more realizable solution for the hardware implementation of predictive retinal models.

A new chaotic oscillator with free control.

A novel chaotic system is explored in which all terms are quadratic except for a linear function. The slope of the linear function rescales the amplitude and frequency of the variables linearly while its zero intercept allows offset boosting for one of the variables. Therefore, a free-controlled chaotic oscillation can be obtained with any desired amplitude, frequency, and offset by an easy modification of the linear function. When implemented as an electronic circuit, the corresponding chaotic signal can be controlled by two independent potentiometers, which is convenient for constructing a chaos-based application system. To the best of our knowledge, this class of chaotic oscillators has never been reported.

Nonconvex integer optimal robust impulsive control strategy for first-order piecewise finite precision nonlinear random early detection algorithm.

There are two main contributions of this paper. First, this paper proposes a first-order piecewise finite precision nonlinear dynamical model for characterizing the average queue size of the random early detection (RED) algorithm. Second, this paper proposes a nonconvex integer optimal robust impulsive control strategy for stabilizing the average queue size. The objective of the control strategy is to determine the average queue size so that the average power of the impulsive control force is minimized subject to a constraint on the absolute difference between the actual average queue size and the theoretical average queue size at the equilibrium point. Computer numerical simulation results show that the proposed control strategy is effective and efficient for stabilizing the average queue size.