Probability densities for conditional statistics in the cubic sensor problem

This paper applies the techniques of Malliavin’s stochastic calculus of variations to Zakai’s equation for the one-dimensional cubic sensor problem in order to study the existence of densities of conditional statistics. Let {X _t} be a Brownian motion observed by a cubic sensor corrupted by white noise, and let denote the unnormalized conditional estimate of φ(X _i ). If φ₁,...,φ _n are linearly independent, and if , it is shown that the probability distribution of admits a density with respect to Lebesgue measure for anyn. This implies that, at any fixed time, the unnormalized conditional density cannot be characterized by a finite set of sufficient statistics. Research supported in part by NSF Grant No. MCS-8301880 and by the Institute for Mathematics and It Applications, Minneapolis, Minnesota.     

具有随机丢包的网络化多自主体系统的一致性

研究具有随机丢包的网络化多自主体系统的均方一致性问题,其中不同自主体间的通信通道具有相同的丢包情况并且均服从马尔可夫(Markov)分布。首先,利用系统变换和迭代方法,得到了系统达到均方一致的一个初等充要条件。然后,利用矩阵理论和图论知识,如果拓扑图含有有向生成树,则可以将系统的均方一致性转化成一个线性Markov跳变系统的均方稳定性,并且可以建立线性矩阵不等式形式的均方可镇定准则。最后,通过相应的仿真实例说明了所得结论的可行性。     

加载速率对结构钢力学性能和断裂韧度的影响

在常温下进行了常用建筑结构钢(16Mn和Q235B钢)动态拉伸和动态断裂韧度试验。试验结果表明，材料在动载下无论是屈服强度还是抗拉强度均有一定的提高，塑性有了一定的降低；由于缺口尖端区域温度的升高，常温下动载对于16Mn钢母材和焊缝的断裂韧度是有利的；Q235B钢常温下，焊缝的断裂韧度值较低，且动载对母材的断裂韧度影响较大，和静载相比动载下断裂韧度值降低了4倍有余，可以看出，Q235B钢的抗震性能较差。通过研究发现，对于低韧度水平的材料，研究动载下结构的断裂行为时．材料的强度也应该作为一个考虑因素。     

Maximum principle for mean-field jump–diffusion stochastic delay differential equations and its application to finance

This paper investigates a stochastic optimal control problem with delay and of mean-field type, where the controlled state process is governed by a mean-field jump–diffusion stochastic delay differential equation. Two sufficient maximum principles and one necessary maximum principle are established for the underlying system. As an application, a bicriteria mean–variance portfolio selection problem with delay is studied to demonstrate the effectiveness and potential of the proposed techniques. Under certain conditions, explicit expressions are provided for the efficient portfolio and the efficient frontier, which are as elegant as those in the classical mean–variance problem without delays.     

Unscented Kalman filter with advanced adaptation of scaling parameter

The paper deals with state estimation of the nonlinear stochastic systems by means of the unscented Kalman filter with a focus on specification of the σ$\sigma$-points. Their position is influenced by two design parameters—the scaling parameter determining the spread of the σ$\sigma$-points and a covariance matrix decomposition determining rotation of the σ$\sigma$-points. In this paper, a choice of the scaling parameter is analyzed. It is shown that considering other values than the standard choice may lead to increased quality of the estimate, especially if the scaling parameter is adapted. Several different criteria for the adaptation are proposed and techniques to reduce computational costs of the adaptation are developed. The proposed algorithm of the unscented Kalman filter with advanced adaptation of the scaling parameter is illustrated in a numerical example.     

A stochastic controller for a scalar linear system with additive Cauchy noise

A stochastic control scheme is developed for scalar, discrete-time, and linear-dynamic systems driven by Cauchy distributed process and measurement noises. When addressing the optimal control problem for such systems, the standard quadratic cost criteria cannot be used. In this study we introduce a new objective function that is functionally similar to the Cauchy probability density function. The performance index, defined as the expectation of this objective function with respect to the Cauchy densities, exists. The dynamic programming solution to the fixed and finite horizon optimal control problem that uses this performance index appears to be intractable. Therefore, a moving horizon optimal model predictive control problem is implemented, for which the conditional expected value of the objective function and its gradients can be computed in closed   form and without assumptions such as certainty equivalence. Numerical results are shown for this m$m$-step model predictive optimal controller and compared to a similar, Linear-Exponential-Gaussian model predictive controller. An essential difference between the Cauchy and Gaussian controllers when applied to a system with Cauchy noises is that, while the Gaussian controller is linear and reacts strongly to all noise pulses, the Cauchy controller can differentiate between measurement and process noise pulses by ignoring the former while responding to the latter. This property of the Cauchy controller occurs when an impulsive measurement noise is more likely than an impulsive process noise. The Cauchy and Gaussian controllers react similarly when applied to a system with Gaussian noises, demonstrating the robustness of the proposed control scheme.     

Trapping Brownian ensemble optimally using Broadcast Stochastic Receding Horizon Control

Collision of suspended entities with surrounding molecules in a fluid environment leads to random movements of these entities, known as Brownian motion. Suppression of this motion in a Brownian ensemble has recently become essential for facilitating emerging applications in biology and in micro and nano scale self-assembled systems. How optimally this suppression can be performed remains an open question of great interest to both the natural science and the control engineering communities. In this paper, we address this question theoretically by introducing a novel “Broadcast Stochastic Receding Horizon Control” strategy for trapping an ensemble of non-interacting Brownian particles. The strategy designs a control input, independent of the number of particles, using measurements from a single particle as the only available feedback information and broadcasts it to all particles in the ensemble. We show the existence of a minimum region in which all particles can be driven and trapped indefinitely using the proposed control action. Under specific conditions, we guarantee the trapping of all particles in this region with probability 1. Finally, we demonstrate the efficacy of our control design in a simulation environment by trapping 100 Brownian particles in one, two and three dimensional homogeneous medium.     

A stochastic Kaczmarz algorithm for network tomography

We develop a stochastic approximation version of the classical Kaczmarz algorithm that is incremental in nature and takes as input noisy real time data. Our analysis shows that with probability one it mimics the behavior of the original scheme: starting from the same initial point, our algorithm and the corresponding deterministic Kaczmarz algorithm converge to precisely the same point. The motivation for this work comes from network tomography where network parameters are to be estimated based upon end-to-end measurements. Numerical examples via Matlab based simulations demonstrate the efficacy of the algorithm.     

Quadratic control of stochastic hybrid systems with renewal transitions

We study the quadratic control of a class of stochastic hybrid systems with linear continuous dynamics for which the lengths of time that the system stays in each mode are independent random variables with given probability distribution functions. We derive a condition for finding the optimal feedback policy that minimizes a discounted infinite horizon cost. We show that the optimal cost is the solution to a set of differential equations with unknown boundary conditions. Furthermore, we provide a recursive algorithm for computing the optimal cost and the optimal feedback policy. The applicability of our result is illustrated through a numerical example, motivated by stochastic gene regulation in biology.     

Explicit numerical simulation of suspension flow with deposition in porous media: influence of local flow field variation on deposition processes predicted by trajectory methods

A new explicit numerical simulation (ENS) method based on lattice-gas automata (LGA) is introduced here for the flow of solid/fluid suspensions with deposition in porous media. The ENS method explicitly resolves the dynamics of the individual solid particles and the suspending fluid in the domain defined by the pore walls and solid particle surfaces. After describing the new method, it is applied to the study of solid/fluid suspension flow with deposition in a constriction and in a model random porous solid. This study clearly demonstrates that the deposits strongly influence the local flow fields, which in turn affect the deposition process indicating that this interplay should be modelled if accurate results are desired from trajectory methods.