用于图像去噪的改进型非线性扩散方程

修改一类图像处理用的非线性扩散方程模型的扩散系数函数,使所获得的新模型能够在考虑到图像梯度以及二阶导数的情况下,用于去除图像高梯度噪声并保持图像边缘细节。实验表明,该新模型能够在保持图像中有意义的尖峰和窄边缘的同时,消除高梯度噪声。     

Decentralized output-feedback control of large-scale nonlinear systems with sensor noise

This paper presents a new tool for decentralized output-feedback control design of large-scale nonlinear systems in the presence of non-smooth sensor noise. Through a recursive control design approach, the closed-loop decentralized system is transformed into a network of input-to-state stable (ISS) systems and the influences of the sensor noise are represented by ISS gains. The decentralized control objective is achieved by applying the cyclic-small-gain theorem to the closed-loop decentralized system. Moreover, the outputs of the closed-loop decentralized system can be driven arbitrarily close to the levels of their corresponding sensor noise.     

On some finite dimensional nonlinear filters for certain diffusions observed in correlated noise

An extension of the one dimensional Bene nonlinear filter to the case of correlated process and observation noises is presented. Conditions are derived so that the optimal nonlinear filter is finite dimensional.     

Truncation nonlinear filters for state estimation with nonlinear inequality constraints

The paper focuses on the state estimation problem of nonlinear non-Gaussian systems with state subject to a nonlinear inequality constraint. Taking into account the available additional information about the state given by the constraint increases the estimate quality compared to classical state estimation methods which cannot utilize the information. Considering the constraint in the form of an inequality involving a nonlinear function of the state makes the state estimation problem difficult and hence treated only marginally. In this paper, a generic local filter for the inequality constrained estimation problem is proposed. It covers the extended Kalman filter, unscented Kalman filter, and divided difference filter as special cases and enforces the constraint by truncating the conditional density of the state. The truncation is computationally cheap, yet it provides high estimate quality of the constrained estimate. The same idea is then utilized in a truncation Gaussian mixture filter which is also proposed in the paper to increase the estimate quality further by providing a global constrained estimate. Superior estimate quality and computational efficiency of the proposed filters are illustrated in two numerical examples.     

Fractional-order Kalman filters for continuous-time linear and nonlinear fractional-order systems using Tustin generating function

This paper presents the fractional-order Kalman filters using Tustin generating function for linear and nonlinear fractional-order systems involving process noise and measurement noise. By using the Tustin generating function, the differential equation model is obtained by discretising the investigated continuous-time fractional-order system. The two kinds of fractional-order Kalman filters are given for the correlated and uncorrelated cases in terms of the process noise and measurement noise for linear fractional-order system, respectively. In addition, based on the first-order Taylor expansion formula, the extended fractional-order Kalman filter using Tustin generating function is proposed to improve the accuracy of state estimation. Finally, three examples are illustrated to verify the effectiveness of the Tustion fractional-order Kalman filters for linear and nonlinear fractional-order systems.     

Ultimate boundedness control of linear systems with band-bounded nonlinear actuators and additive measurement noise

For linear systems driven by band-bounded nonlinear actuators, a set of linear matrix inequality (LMI) based sufficient conditions are derived for finding state feedback controllers which assure ultimate boundedness of state trajectories. Besides actuator nonlinearity, it is assumed that additive noise exists when state variables are measured for feedback. The purpose is to minimize the ultimate boundedness region while tolerating noise of the largest magnitude. When a state feedback controller is determined for a given system by solving the LMI conditions or by any other means, a less conservative LMI condition is given for further examination of the resultant ultimate boundedness region and tolerable noise magnitude.     

A coupled nonlinear spacecraft attitude controller and observer with an unknown constant gyro bias and gyro noise

We propose a new algorithm for estimating constant biases in gyro measurements of angular velocity, and demonstrate that the resulting estimates converge to the true bias values exponentially fast. The new observer is then combined with a nonlinear attitude tracking control strategy in a certainty equivalence fashion, and the combination shown via Lyapunov analysis to produce globally stable closed-loop dynamics, with asymptotically perfect tracking of any commanded attitude sequence. The analysis is then extended to consider the effects of stochastic measurement noise in the gyro in addition to the bias. A simulation is given for a rigid spacecraft tracking a specified, time-varying attitude sequence to illustrate the theoretical claims.     

Approximate models for continuous-time linear systems with sampling jitter

The behaviour of single input, single output, continuous time systems sampled with various types of jitter in both measurement and control action is investigated. It is shown that the effects of jitter can be modelled by approximations for the plant dynamics, and additive noise constructed by the modulation of plant signals with the jitter. These approximations give useful insights for digital controller design.     

MPI implementation of parallel subdomain methods for linear and nonlinear convection–diffusion problems

The solution of linear and nonlinear convection–diffusion problems via parallel subdomain methods is considered. MPI implementation of parallel Schwarz alternating methods on distributed memory multiprocessors is discussed. Parallel synchronous and asynchronous iterative schemes of computation are studied. Experimental results obtained from IBM-SP series machines are displayed and analyzed. The benefits of using parallel asynchronous Schwarz alternating methods are clearly shown.     

Approximate linear programming for networks: Average cost bounds

This paper uses approximate linear programming (ALP) to compute average cost bounds for queueing network control problems. Like most approximate dynamic programming (ADP) methods, ALP approximates the differential cost by a linear form. New types of approximating functions are identified that offer more accuracy than previous ALP studies or other performance bound methods. The structure of the infinite constraint set is exploited to reduce it to a more manageable set. When needed, constraint sampling and truncation methods are also developed. Numerical experiments show that the LPs using quadratic approximating functions can be easily solved on examples with up to 17 buffers. Using additional functions reduced the error to 1–5% at the cost of larger LPs. These ALPs were solved for systems with up to 6–11 buffers, depending on the functions used. The method computes bounds much faster than value iteration. It also gives some insights into policies. The ALPs do not scale to very large problems, but they offer more accurate bounds than other methods and the simplicity of just solving an LP.     

Simple method for solving the constant gains of Kalman filters with single output

A simple method is described for the calculation of the optimal gains for steady-state Kalman filters in continuous- and discrete-time systems with single output. The procedure consists of comparing the optimal closed-loop characteristic polynomial with a determinant expansion containing the unknown constant gains. It is then shown that for the case when a computer program is not used for finding the roots of a polynomial, the optimal closed-loop characteristic polynomial in the discretetime problem is not as readily obtainable as that in the continuous-time problem, even though the system under consideration is of lower order. This drawback, however, is shown to be overcome by invoking the bilinear transformation.     

New explicit filters and smoothers for diffusions with nonlinear drift and measurements

The optimal least-squares filtering of a diffusion x(t) from its noisy measurements {y(τ); 0 τ t} is given by the conditional mean E[x(t)|y(τ); 0 τ t]. When x(t) satisfies the stochastic diffusion equation dx(t) = f(x(t)) dt + dw(t) and y(t) = ∫₀^tx(s) ds + b(t), where f(·) is a global solution of the Riccati equation /xf(x) + f(x)² = f(x)² = αx² + βx + γ, for some , and w(·), b(·) are independent Brownian motions, Benes gave an explicit formula for computing the conditional mean. This paper extends Benes results to measurements y(t) = ∫₀^tx(s) ds + ∫₀^t dx(s) + b(t) (and its multidimensional version) without imposing additional conditions on f(·). Analogous results are also derived for the optimal least-squares smoothed estimate E[x(s)|y(τ); 0 τ t], s < t. The methodology relies on Girsanov's measure transformations, gauge transformations, function space integrations, Lie algebras, and the Duncan-Mortensen-Zakai equation.     

不确定噪声方差定常系统保性能鲁棒Kalman滤波器

对带不确定噪声方差线性定常系统鲁棒Kalman滤波,提出一般的统一的保性能鲁棒性概念.用Lyapunov方程方法,提出两类保性能极大极小鲁棒稳态Kalman滤波器.一类是寻求不确定噪声方差最大扰动域(鲁棒域),使得对于扰动域内的所有扰动,确保系统滤波精度偏差的最大下界是零,最小上界是所预置的精度偏差指标;另一类是在预置噪声方差有界扰动域内,寻求滤波精度偏差的最大下界和最小上界.通过引入不确定噪声方差扰动的参数化表示,问题转化为相应的非线性与线性最优化问题,可分别用Lagrange乘数法和线性规划(LP)方法求解.应用于跟踪系统的仿真例子验证了所提结果的正确性和有效性.     

A novel radial basis function method for 3D linear and nonlinear advection diffusion reaction equations with variable coefficients

The radial basis function method for 3D advection diffusion reaction equations with variable coefficients is presented. The proposed method implements the linear combination of radial basis functions which impose boundary conditions in advance, and thus such a combination with weighted parameters can be used to construct the final approximation. Furthermore, the weighted parameters are solved by substituting the approximation into governing equations. This method leads to crucial improvements in the feasibility and accuracy which can now be easily applied to general 3D nonlinear problems through linearized techniques. Finally, accuracy and efficiency of the proposed method are verified by several examples.

     

Decentralized observers with consensus filters for distributed discrete-time linear systems

This paper presents a decentralized observer with a consensus filter for the state observation of discrete-time linear distributed systems. Each agent in the distributed system has an observer with a model of the plant that utilizes the set of locally available measurements, which may not make the full plant state detectable. This lack of detectability is overcome by utilizing a consensus filter that blends the state estimate of each agent with its neighbors’ estimates. It is proven that the state estimates of the proposed observer exponentially converge to the actual plant states under arbitrarily changing, but connected, communication and pseudo-connected sensing graph topologies. Except these connectivity properties, full knowledge of the sensing and communication graphs is not needed at the design time. As a byproduct, we obtained a result on the location of eigenvalues, i.e., the spectrum, of the Laplacian for a family of graphs with self-loops.     

受正弦扰动时滞非线性系统的近似最优减振控制

研究时滞非线性系统在正弦扰动作用下的最优减振控制问题,给出一种无时滞近似最优减振控制律的迭代方法．通过假设Lagrange算子,将由原系统最优控制问题得到的既含时滞项又含有超前项的非线性两点边值问题转换为新的有利于求解的形式,再通过构造序列将其转化为不舍时滞项和超前项的线性非齐次两点边值问题序列．证明了该序列的收敛性．通过交替迭代序列得到了系统最优减振控制律．仿真结果表明,该方法在不同时滞下对扰动都具有很好的鲁棒性．     

一种求解线性约束的非线性规划神经网络方法

针对线性约束的非线性规划的求解问题,利用罚函数求解优化问题的思想将其转化为二次凸规划,基于神经网络的结构特性,定义所需的能量函数,从而使网络收敛于唯一稳定点最终实现线性约束的非线性规划的求解。实验仿真结果表明,该方法是有效和正确的,且能推广到含参的非线性规划和多目标规划中去。     

带有乘性噪声的线性时滞系统固定步长平滑估计

研究带有乘性噪声的线性时滞系统的固定步长平滑估计问题.通过虚拟噪声补偿技术,将该问题转化为一类带有未知时变噪声的随机系统的估计问题;基于等价系统的新息重组分析及投影定理,通过求解与原系统同维的Riccati方程,得到系统的最优平滑估计器.该方法无需扩维,具有较大的计算优势.仿真实验表明了该算法的有效性.     

Dual adaptive controls for linear system with unknown constant parameters

The semi-explicit solution of a dual adaptive control problem driven by a linear system with unknown constant parameters is given. The controls are tested in the simulation experiment and analysed in contrast to the certainty equivalent controls and cautious controls. The probing feature of dual controls is discussed and accomplished with data. The probing signal generation mechanism is investigated.