Small Parameter Limit for Ergodic, Discrete-Time, Partially Observed, Risk-Sensitive Control Problems

We show that discrete-time, partially observed, risk-sensitive control problems over an infinite time horizon converge, in the small noise limit, to deterministic dynamic games, in the sense of uniform convergence of the value function on compact subsets of its domain. We make use of new results concerning large deviations and existence of value functions. Date received: May 21, 1999. Date revised: April 7, 2000.     

离散随机线性系统最优滤波,预报和平滑估计的一种统一方法

基于射影理论及新息分析方法，讨论离散随机线性系统最优化状态估计问题。提出了一种统一处理最优滤波、预报和平滑估计的的新方法，证明了新算法的渐近稳定性。     

对称位相型滤波器及其在边缘检测中的应用

该文从概率的角度提出了两类新的滤波器：对称位相型滤波器和对称梯阶滤波器;证明了对任意给定的非负对称滤波器可用这两类滤波器的序列在（－∞,＋∞）内一致逼近;这种序列有着统一的结构形式：L（x）＝^s∑i＝1e^λi│x－μ│^Ni∑k＝0ak^（i）│x－μ│^ k。对于L（x）,文中给出了选择L（x）一些最优准则的解析表达。从而表明L（x）既具有一般性,又易进行解析处理和数值计算。对于已有文献中相关于对称指数滤波器的两类不同形式,例如Li等和Ma等,该文从理论上进一步刻画了它们的内在一致性。     

Vector Median Filters, Inf-Sup Operations, and Coupled PDE's: Theoretical Connections

In this paper, we formally connect between vector median filters, inf-sup morphological operations, and geometric partial differential equations. Considering a lexicographic order, which permits to define an order between vectors in R^N, we first show that the vector median filter of a vector-valued image is equivalent to a collection of infimum-supremum morphological operations. We then proceed and study the asymptotic behavior of this filter. We also provide an interpretation of the infinitesimal iteration of this vectorial median filter in terms of systems of coupled geometric partial differential equations. The main component of the vector evolves according to curvature motion, while, intuitively, the others regularly deform their level-sets toward those of this main component. These results extend to the vector case classical connections between scalar median filters, mathematical morphology, and mean curvature motion.     

Removing Noise and Preserving Details with Relaxed Median Filters

In this paper, a median based filter called relaxed median filter is proposed. The filter is obtained by relaxing the order statistic for pixel substitution. Noise attenuation properties as well as edge and line preservation are analyzed statistically. The trade-off between noise elimination and detail preservation is widely analyzed. It is shown that relaxed median filters preserve details better than the standard median filter, and remove noise better than other median type filters.     

初始状态为正交的二维线性正系统的渐近稳定性

本文分析了初始状态为正交的二维线性正系统的渐近稳定性. 与一维系统不同, 初始状态为正交的二维系统的稳定性严格依赖于合适的初始条件. 首先, 当初始状态 绝对收敛时, 二维正FM I 模型的渐近稳定性判据被提出. 然后, 针对二维正Rosser模型, 在初始状态 绝对收敛时, 相似的结论被给出. 最后, 两个数字实例证实了这些判据的有效性.     

Stable and optimal controls of a proton exchange membrane fuel cell

In this paper, the trajectory tracking problem of a proton exchange membrane (PEM) fuel cell is considered. To solve this problem, stable and optimal controllers are proposed. The stable and optimal techniques have the objective that the system states should reach the desired trajectories while in the first, the tracking error is minimised, and in the second, the tracking error and inputs are minimised. The effectiveness of the proposed techniques is verified by simulations.     

A Stable Analytical Solution Method for Car-Like Robot Trajectory Tracking and Optimization

In this paper, the car-like robot kinematic model trajectory tracking and control problem is revisited by exploring an optimal analytical solution which guarantees the global exponential stability of the tracking error. The problem is formulated in the form of tracking error optimization in which the quadratic errors of the position, velocity, and acceleration are minimized subject to the rear-wheel car-like robot kinematic model. The input-output linearization technique is employed to transform the nonlinear problem into a linear formulation. By using the variational approach, the analytical solution is obtained, which is guaranteed to be globally exponentially stable and is also appropriate for real-time applications. The simulation results demonstrate the validity of the proposed mechanism in generating an optimal trajectory and control inputs by evaluating the proposed method in an eight-shape tracking scenario.     

Exponential Periodicity of Continuous-time and Discrete-Time Neural Networks with Delays

Exponential periodicity of continuous-time neural networks with delays is investigated. Without assuming the boundedness and differentiability of the activation functions, some new sufficient conditions ensuring existence and uniqueness of periodic solution for a general class of neural systems are obtained. Discrete-time analogue of the continuous-time system with periodic input is formulated and we study their dynamical characteristics. The exponential periodicity of the continuous-time system is preserved by the discrete-time analogue without any restriction imposed on the uniform discretization step-size.     

含噪声驱动阵的相关噪声卡尔曼滤波及稳定性

探讨相关噪声下离散时变线性系统的卡尔曼滤波模型。借助广义逆和最小模最小二乘解的思想,在Frobenius范数意义下,获得基于偏差最优估计的转换系数矩阵,将相关噪声系统转化为不相关噪声系统,获得相应的卡尔曼滤波模型。理论上,在误差协方差矩阵有界前提下,获证该滤波模型是全局渐近稳定的,数值实验获该模型的合理性。理论和实验结果表明,该模型是稳定的,且可有效解决含相关噪声和时变量测噪声驱动阵的离散时变系统的状态估计问题。     

Properties of optimal stochastic control systems with dead-time

Structural, stability and sensitivity properties of optimal stochastic control systems for dead-time, stable minimum phase as well as non-minimum phase processes are presented. The processes are described by rational transfer functions plus dead-times and the disturbances by rational spectral densities. It is shown that although the frequency domain design techniques guarantee asymptotically stable systems for given process and disturbance models, many of the designs might be practically unstable. Necessary and sufficient conditions that must be imposed on the design to assure practically stable optimal systems are derived. The uncertainties in the parameters and in the structure of the process model are measured by means of an ignorance function. Sufficient conditions in terms of the ignorance function, which guarantee stable design and by means of which the bounds of the uncertainties for a given design may be estimated, are stated. Conditions under which the optimal designs possess attractive relative stability properties, namely gain and phase margins of at least 2 and 60°, respectively, are stated, too. It is further shown that any optimal controller, for the type of processes discussed in this paper, may be separated into a primary controller and into a dead-time compensator where the latter is completely independent of the cost and the disturbance properties. Such a decomposition gives excellent insight into the role of the cost and the disturbance in the design. When low order process and disturbance models are used, the conventional PI and PID control laws coupled with the dead-time compensator emerge.     

Optimal filtering for linear systems with state and observation delays

In this paper, the optimal filtering problem for linear systems with state and observation delays is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate, error variance, and various error covariances. As a result, the optimal estimate equation similar to the traditional Kalman–Bucy one is derived; however, it is impossible to obtain a system of the filtering equations, that is closed with respect to the only two variables, the optimal estimate and the error variance, as in the Kalman–Bucy filter. The resulting system of equations for determining the filter gain matrix consists, in the general case, of an infinite set of equations. It is however demonstrated that a finite set of the filtering equations, whose number is specified by the ratio between the current filtering horizon and the delay values, can be obtained in the particular case of equal or commensurable (τ=qh, q is natural) delays in the observation and state equations. In the example, performance of the designed optimal filter for linear systems with state and observation delays is verified against the best Kalman–Bucy filter available for linear systems without delays and two versions of the extended Kalman–Bucy filter for time delay systems. Copyright © 2005 John Wiley & Sons, Ltd.     

Simultaneous External and Internal Stabilization for Continuous and Discrete-Time Critically Unstable Linear Systems with Saturating Actuators

The issues arising in hybrid or simultaneous external as well as internal stabilization of linear systems with saturating actuators are considered. Four different stabilization problems are studied. Roughly, these problems are (1) simultaneous semi-global external as well as semi-global internal stabilization, (2) simultaneous semi-global external as well as global internal stabilization, (3) simultaneous global external as well as semi-global internal stabilization, and (4) simultaneous global external as well as global internal stabilization. As evident from the literature, the requirement of internal stabilization alone either in the global or semi-global sense demands that the linear part of the given system be (a) stabilizable, and (b) has all its poles in the closed left half complex plane for continuous-time systems while it has all its poles inside and/or on the unit circle for discrete-time systems. This implies that the posed simultaneous stabilization problems are solvable at best only under the conditions (a) and (b). Under such conditions, we construct here explicit state as well as measurement feedback controllers for all the four problems in the case of continuous-time systems, and for the problems (1), (2) and (4) in the case of discrete-time systems. The design methodologies used to construct appropriate feedback laws are based on by now familiar low-gain and low-and-high gain design concepts or certain scheduled versions of them.     

拖尾Rayleigh 分布: 基本性质及其应用

针对使用拖尾Rayleigh分布对合成孔径雷达(Synthetic aperture radar, SAR)幅值图像建模时遇到的问题, 本文讨论了拖尾Rayleigh分布的相关性质及其应用. 首先, 基于负数阶矩理论, 本文提出了拖尾Rayleigh分布的比值估计、对数矩估计和迭代对数矩估计三种参数估计方法, 并通过Monte Carlo仿真实验比较了它们的估计性能. 其次, 本文使用渐近级数计算拖尾Rayleigh分布的概率密度函数, 基于插值多项式拟合, 提出了高效计算密度函数的三步方法. 最后, 本文给出了SAR幅值图像基于拖尾Rayleigh分布的建模实例. 结果表明, 和一般的Rayleigh分布相比, 拖尾Rayleigh分布可以精确反映SAR幅值图像尖峰厚尾的统计特征, 因此它是SAR幅值图像建模的有效工具.     

Understanding the Difference Between Robust Control and Optimal Control in a Linear Discrete-Time System with Time-Varying Parameters

Robust control has been a very popular area of research in the last two decades. The goal of this paper is to investigate the assumptions implicit in the “nonprobabilistic nature” of the a priori information used to derive the linear-quadratic robust control in discrete-time. This is done by comparing robust control with the optimal control for a linear system with time-varying parameters. First the theoretical differences between the two approaches are discussed. Then they are used in two numerical examples: a simple model with one control, one state and a time horizon of two periods, which is suitable for hand calculations, and the permanent income model. The main conclusion is that the decision maker applying robust control is indeed assuming a very restricted class of true, unknown models. JEL classification: C61     

Stability of linear switched differential algebraic equations with stable and unstable subsystems

This article studies linear switched differential algebraic equations (DAEs), which contains stable and unstable subsystems. We prove sufficient conditions for stability of switched DAEs based on the existence of suitable Lyapunov functions. The result shows that stability is preserved under switching with an average dwell time and an additional condition involving consistency projectors holds. Furthermore, we also give an example to illustrate the result.     

基于状态观测的量化系统稳定性分析

针对基于状态观测和信号量化的线性系统,进行了稳定性分析与研究.首先对状态观测误差系统在量化作用下的渐近稳定性进行了分析,接着研究了对象系统本身在量化效应下的渐近稳定性,得到了相应的稳定性条件,同时针对对数型量化器,给出了两个系统稳定性之间的关联.最后,给出了在时变量化作用下基于状态观测的控制策略和仿真例子.     

More Relaxed Non‐Quadratic Stabilization Conditions Using Ts Open Loop System and Control Law Properties

This paper proposes more relaxed stabilization conditions based on a non‐quadratic Lyapunov function (NQLF) and parallel distributed compensator (PDC) controller. The conditions are derived in terms of linear matrix inequalities (LMIs) by introducing three slack matrices based on the properties of TS membership functions, an open loop system and a PDC controller. These slack matrices are utilized to decouple the LMI variables from the TS system and the input matrices. Therefore, the proposed approach greatly reduces the number of LMI conditions and improves feasibility by providing more degrees of freedom compared to recently published studies. Moreover, local stability and stabilization conditions are considered to handle the time derivatives of membership functions appearing in the stabilization synthesis of the TS closed‐loop system with PDC controller. Finally, several examples are presented to demonstrate the advantages of the proposed approaches.     

Stabilization of a chemostat model with Haldane growth functions and a delay in the measurements

The stabilization of equilibria in chemostats with measurement delays is a complex and challenging problem, and is of significant ongoing interest in bioengineering and population dynamics. In this paper, we solve an output feedback stabilization problem for chemostat models having two species, one limiting substrate, and either Haldane or Monod growth functions. Our feedback stabilizers depend on a given linear combination of the species concentrations, which are both measured with a constant time delay. The values of the delays are unknown. Instead, one only knows an upper bound on the delays, and we allow the upper bound to be arbitrarily large. The stabilizing feedback depends on the known upper bound for the delays as well. Our work is based on a Lyapunov-Krasovskii argument.