Fault Isolation for Nonlinear Systems Using Flexible Support Vector Regression

While support vector regression is widely used as both a function approximating tool and a residual generator for nonlinear system fault isolation, a drawback for this method is the freedom in selecting model parameters. Moreover, for samples with discordant distributing complexities, the selection of reasonable parameters is even impossible. To alleviate this problem we introduce the method of flexible support vector regression (F-SVR), which is especially suited for modelling complicated sample distributions, as it is free from parameters selection. Reasonable parameters for F-SVR are automatically generated given a sample distribution. Lastly, we apply this method in the analysis of the fault isolation of high frequency power supplies, where satisfactory results have been obtained

Dependence of resting-state-based cerebrovascular reactivity (CVR) mapping on spatial resolution

Cerebrovascular reactivity (CVR) is typically assessed with a carbon dioxide (CO2) stimulus combined with BOLD fMRI. Recently, resting-state (RS) BOLD fMRI has been shown capable of generating CVR maps, providing a potential for broader CVR applications in neuroimaging studies. However, prior RS-CVR studies have primarily been performed at a spatial resolution of 3–4 mm voxel sizes. It remains unknown whether RS-CVR can also be obtained at high-resolution without major degradation in image quality. In this study, we investigated RS-CVR mapping based on resting-state BOLD MRI across a range of spatial resolutions in a group of healthy subjects, in an effort to examine the feasibility of RS-CVR measurement at high resolution. Comparing the results of RS-CVR with the maps obtained by the conventional CO2-inhalation method, our results suggested that good CVR map quality can be obtained at a voxel size as small as 2 mm isotropic. Our results also showed that, RS-CVR maps revealed resolution-dependent sensitivity. However, even at a high resolution of 2 mm isotropic voxel size, the voxel-wise sensitivity is still greater than that of typical task-evoked fMRI. Scan duration affected the sensitivity of RS-CVR mapping, but had no significant effect on its accuracy. These findings suggest that RS-CVR mapping can be applied at a similar resolution as state-of-the-art fMRI studies, which will broaden the use of CVR mapping in basic science and clinical applications including retrospective analysis of previously collected fMRI data

Generalized Combination Complex Synchronization for Fractional-Order Chaotic Complex Systems

Based on two fractional-order chaotic complex drive systems and one fractional-order chaotic complex response system with different dimensions, we propose generalized combination complex synchronization. In this new synchronization scheme, there are two complex scaling matrices that are non-square matrices. On the basis of the stability theory of fractional-order linear systems, we design a general controller via active control. Additionally, by virtue of two complex scaling matrices, generalized combination complex synchronization between fractional-order chaotic complex systems and real systems is investigated. Finally, three typical examples are given to demonstrate the effectiveness and feasibility of the schemes

A New Fractional-Order Chaotic Complex System and Its Antisynchronization

We propose a new fractional-order chaotic complex system and study its dynamical properties including symmetry, equilibria and their stability, and chaotic attractors. Chaotic behavior is verified with phase portraits, bifurcation diagrams, the histories, and the largest Lyapunov exponents. And we find that chaos exists in this system with orders less than 5 by numerical simulation. Additionally, antisynchronization of different fractional-order chaotic complex systems is considered based on the stability theory of fractional-order systems. This new system and the fractional-order complex Lorenz system can achieve antisynchronization. Corresponding numerical simulations show the effectiveness and feasibility of the scheme

Synchronization of Fractional-Order Complex Chaotic Systems Based on Observers

By designing a state observer, a new type of synchronization named complex modified projective synchronization is investigated in a class of nonlinear fractional-order complex chaotic systems. Combining stability results of the fractional-order systems and the pole placement method, this paper proves the stability of fractional-order error systems and realizes complex modified projective synchronization. This method is so effective that it can be applied in engineering. Additionally, the proposed synchronization strategy is suitable for all fractional-order chaotic systems, including fractional-order hyper-chaotic systems. Finally, two numerical examples are studied to show the correctness of this new synchronization strategy

Synchronization of Fractional-Order Chaotic Systems with Model Uncertainty and External Disturbance

This paper is concerned with complete synchronization of fractional-order chaotic systems with both model uncertainty and external disturbance. Firstly, we propose a new dynamic feedback control method for complete synchronization of fractional-order nominal systems (without both uncertainty and disturbance). Then, a new uncertainty and disturbance estimator (UDE)-based dynamic feedback control method for the fractional-order systems with both uncertainty and disturbance is presented, by which the synchronization problem of such fractional-order chaotic systems is realized. Finally, the fractional-order Lorenz system is used to demonstrate the practicability of the proposed results

Generalized Combination Complex Synchronization for Fractional-Order Chaotic Complex Systems

Based on two fractional-order chaotic complex drive systems and one fractional-order chaotic complex response system with different dimensions, we propose generalized combination complex synchronization. In this new synchronization scheme, there are two complex scaling matrices that are non-square matrices. On the basis of the stability theory of fractional-order linear systems, we design a general controller via active control. Additionally, by virtue of two complex scaling matrices, generalized combination complex synchronization between fractional-order chaotic complex systems and real systems is investigated. Finally, three typical examples are given to demonstrate the effectiveness and feasibility of the schemes

On the Asymptotic Properties of Nonlinear Third-Order Neutral Delay Differential Equations with Distributed Deviating Arguments

This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. Several new theorems are obtained which ensure that every solution to this equation either is oscillatory or tends to zero. Two illustrative examples are included