Mean-square filter design for stochastic polynomial systems with Gaussian and Poisson noises

This paper addresses the mean-square finite-dimensional filtering problem for polynomial system states with both, Gaussian and Poisson, white noises over linear observations. A constructive procedure is established to design the mean-square filtering equations for system states described by polynomial equations of an arbitrary finite degree. An explicit closed form of the designed filter is obtained in case of a third-order polynomial system. The theoretical result is complemented with an illustrative example verifying performance of the designed filter.     

原油芳烃的沉积环境指示作用

为了研究原油芳烃在沉积环境方面的指示作用,采用色谱-质谱仪对塔中地区海相原油、柴达木盆地咸水湖相原油、冀中坳陷淡水湖相原油以及吐哈盆地煤成油等31个原油样品进行了全油GC-MS分析.研究结果表明：芳构化二萜类的卡达烯和惹烯的丰度指示着高等植物输入强度,海相和咸水湖相原油卡达烯在萘系列中的质量分数小于0.24%,惹烯在菲系列中的质量分数小于1.21%,淡水湖相原油和煤成油中这两个值分别为0.12%～8.65%和0.71%～20.03%;硫芴和氧芴可能来自同一先质,而芴具有不同的成因,硫芴/氧芴可以反映氧化还原环境,海相和咸水湖相原油该值一般大于0.7,淡水湖相原油为0.48,煤成油小于0.14;硫芴/菲是区分海相原油（〉0.25）与陆相原油（〈0.2）最有效的参数;咸水湖相原油以高的三芳甾烷丰度（三芳甾烷系列/芳烃总量〉12%）和C26/C28（20S）三芳甾烷比值（〉0.45）为特征;煤成油中往往含有完整的苯并藿烷系列.     

Optimal filtering for linear systems with state and multiple observation delays

This article solves the optimal filtering problem for linear systems with state and multiple observation delays. The optimal estimate equation similar to the traditional Kalman–Bucy one is derived, and the system of equations for determining the filter gain matrix consists of an infinite set of equations. It is then demonstrated that a finite set of the filtering equations can be obtained in case of commensurable delays. In the example, the designed optimal filter is compared to the traditional Kalman–Bucy filter.     

On delay-dependent stability for a class of nonlinear stochastic delay-differential equations

Global asymptotic stability conditions for nonlinear stochastic systems with state delay are obtained based on the convergence theorem for semimartingale inequalities, without assuming the Lipschitz conditions for nonlinear drift functions. The Lyapunov–Krasovskii and degenerate functionals techniques are used. The derived stability conditions are directly expressed in terms of the system coefficients. Nontrivial examples of nonlinear systems satisfying the obtained stability conditions are given.     

动态概率神经网络及油气概率分布预测

传统概率神经网络(PNN)采用了前向径向基函数神经网络的局部化的、高斯型作用函数，虽然具有较好的分类能力，但也存在以下局限性：①如果学习样本增多，模式层的神经元个数也增多，导致运算矩阵的增大而使之几乎丧失处理大数据量实际资料的能力；②模式层到求和层的权值固定为常数，必然要求学习集合中各类样本的数量相等，从而会影响其接受实际数据的能力。为此文中引入了动态概率神经网络(DPNN)，它与传统PNN在结构上的区别在于：①模式层到求和层不以等权连接，权值由学习样本集的概率分布所确定；②学习样本集中各类样本的数量(各类在模式层的神经元个数)可以不相等。文中还介绍了DPNN算法。理论数据测试充分展示了DPNN结构具有动态调整、学习收敛快速、分类识别能力强大等特点。通过选取G油田实际资料的22种属性作为网络的输入向量，用DPNN进行分类识别得到了含油气概率分布图，可为预测有利油气圈闭及油水分布规律提供依据。     

On minmax filtering over discrete-continuous observations

This paper presents the minmax filtering problem for a state of a dynamic system under uncertainty conditions over discrete-continuous observations. The solution of the problem is based on the previously derived minmax filtering equations over continuous observations. Some mathematical tools concerning the problem are considered     

Optimal control for linear systems with multiple time delays in control input

This note presents the optimal linear-quadratic (LQ) regulator for a linear system with multiple time delays in the control input. Optimality of the solution is proved in two steps. First, a necessary optimality condition is derived from the maximum principle. Then, the sufficiency of this condition is established by verifying that it satisfies the Hamilton-Jacobi-Bellman equation. Using an illustrative example, the performance of the obtained optimal regulator is compared against the performance of the optimal LQ regulator for linear systems without delays and some other feasible feedback regulators that are linear in the state variables. Finally, the note establishes a duality between the solutions of the optimal filtering problem for linear systems with multiple time delays in the observations and the optimal LQ control problem for linear systems with multiple time delays in the control input.     

Mean-square H∞ filtering for stochastic systems: Application to a 2DOF helicopter

This paper designs the central finite-dimensional H_∞ filter for linear stochastic systems with integral-quadratically bounded deterministic disturbances, that is suboptimal for a given threshold γ with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. The original H_∞ filtering problem for a linear stochastic system is reduced to the corresponding mean-square H₂ filtering problem, using the technique proposed in Doyle (1989) [1]. In the example, the designed filter is applied to estimation of the pitch and yaw angles of a two degrees of freedom (2DOF) helicopter.