Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group with the tracking error of the normalized Euclidean distance meeting predefined transient and steady‐state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low‐cost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form.     

Discrete‐time sector based hands‐off control for nonlinear system

This article presents a hands‐off control design for discrete‐time nonlinear system with a special type of nonlinear sector termed as “discrete‐time sector.” The design method to define the boundary of a discrete‐time sector is done with control‐Lyapunov function. The generalization of nonlinear system is viewed in the perspective of a comparison function. By means of a proposed sector, a switching control is designed such that no control action is experienced inside the sector thus, saving unnecessary control efforts. However, to study the robustness for discrete‐time system, a hands‐off control is modified to ensure the monotonic decrease in the energy of the system. Finally, the proposed approach is verified with the simulation results.     

Asymptotic stability of general linear methods for systems of linear neutral delay differential-algebraic equations

This paper is concerned with numerical stability of general linear methods (GLMs) for a system of linear neutral delay differential-algebraic equations. A sufficient and necessary condition for asymptotic stability of GLMs solving such system is derived. Based on this main result, we further investigate the asymptotic stability of linear multistep methods, Runge–Kutta methods, and block θ-methods, respectively. Numerical experiments confirm our theoretical result.     

Stabilisation of Schrödinger equation in dynamic boundary feedback with a memory-typed heat equation

In this work, we study the dynamic behaviour for a heat equation with exponential polynomial kernel memory to be a controller for a Schrödinger system. By introducing some new variables, the time-variant system is transformed into a time-invariant one. Remarkably, the resolvent of the closed-loop system operator is not compact anymore. The residual spectrum is shown to be empty and the continuous spectrum consisting of finite isolated points are obtained. It is shown that the sequence of generalised eigenfunctions forms a Riesz basis for the Hilbert state space. This deduces the spectrum-determined growth condition for the C ₀-semigroup, and the exponential stability is then established.     

Models for circular data from time series spectra

Circular data are those for which the natural support is the unit circle and its toroidal extensions. Numerous constructions have been proposed which can be used to generate models for such data. We propose a new, very general, one based on the normalization of the spectra of complex-valued stationary processes. As illustrations of the new construction's application, we study models for univariate circular data obtained from the spectra of autoregressive moving average models and relate them to existing models in the literature. We also propose and investigate multivariate circular models obtained from the high-order spectra of stationary stochastic processes generated using linear filtering with an autoregressive moving average response function. A new family of distributions for a Markov process on the circle is also introduced. Results for asymptotically optimal inference for dependent observations on the circle are presented which provide a new paradigm for inference with circular models. The application of one of the new families of spectra-generated models is illustrated in an analysis of wind direction data.     

东营凹陷深部储层流度属性提取及应用

东营凹陷深部储层埋深大、储层薄,为干燥环境下沉积的红层,采用常规储层描述与预测方法难以取得好的效果。在流度属性表征方法计算公式详细推导和流度属性本质含义解剖的基础上,根据研究区岩石物理参数和流体置换的特征,建立了含油层和干层的理论模型,发现将储层主频作为优势频率提取的流度属性,具有很好的有利储层识别度,含油砂体的流度属性能量团比干层及其它地层的能量要强。对东营凹陷深部实际三维工区数据进行目标处理,过井剖面的有利储层得到很好展示;沿层流度属性切片,其储层厚度、储层流体类型及其分布范围与井点图吻合度很高,进一步验证了方法的有效性。研究成果拓展了流度属性的应用范围(以往仅局限于低频),也为深部储层预测开辟了一条新的途径,具有重要的理论意义和较好的推广价值。     

Distribution-free composite Shewhart-GWMA Mann-Whitney charts for monitoring the process location

The Mann-Whitney (MW) statistic is one of the most recommended two-sample statistical tests when the assumption of normality fails to hold due to its robustness and fascinating properties especially when small sample sizes are involved. In order to improve the sensitivity of the generally weighted moving average (GWMA) monitoring scheme toward the detection of large shifts, in this paper, a new distribution-free phase II composite Shewhart-GWMA (CSG) scheme is proposed using the MW U statistic. The performance of the proposed scheme is investigated using the average run-length (ARL) and average extra quadratic loss (AEQL) values through extensive simulations. The performance of this newly proposed monitoring scheme is found to be superior when compared to numerous memory-type MW schemes (some existing and others introduced in this paper) in many situations. An illustrative example is given to demonstrate the implementation of the CSG MW U scheme using real-life data.     

水力压裂中多孔岩体的等效弹性常数应用

水力压裂调研结果认为，地下岩体中所含随机分布孔隙能够影响水力压裂的造缝过程。将多孔岩石的孔隙简化成规则排列的球形孔洞，采用渐近均匀化方法建立了等效弹性常数随孔隙比变化的关系；与基于Budiallsky自治理论得到的有效弹性常数进行比较，两曲线能较好地吻合；为水力压裂法准确地预测出水力压裂的造缝结果提供了可行方案。     

一类时滞四种群捕食被捕食系统的全局稳定性

对四种群的捕食-被捕食模型,利用解的存在性定理、正性定理、上下解方法和相应的单调迭代序列,研究了一类具有时滞的非线性反应扩散系统的牛曼初边值问题,得到了解的存在性和平衡态方程正解的全局渐近稳定性的充分条件.这个结果隐含着捕食-被捕食系统的共存是持久的,平凡解和所有半平凡解是不稳定的.     

Small‐b and Fixed‐b Asymptotics for Weighted Covariance Estimation in Fractional Cointegration

In a standard cointegrating framework, Phillips (1991) introduced the weighted covariance (WC) estimator of cointegrating parameters. Later, Marinucci (2000) applied this estimator to fractional circumstances and, like Phillips (1991), analysed the so‐called small‐b asymptotic approximation to its sampling distribution. Recently, an alternative limiting theory (fixed‐b asymptotics) has been successfully employed to approximate sampling distributions. With the purpose of comparing both approaches, we derive here the fixed‐b limit of WC estimators in a fractional setting, filling also some gaps in the traditional (small‐b) theory. We also provide some Monte Carlo evidence that suggests that the fixed‐b limit is more accurate.