H∞ inferential filtering, prediction and smoothing problems

A new type of H_∞ optimal linear estimation problem is considered where no direct measurement of the output to be estimated is available. The optimal filter, predictor and smoother are derived for this case where outputs must be inferred from available measurements. The results cover the usual discrete time filtering problems and also optimal deconvolution estimation problems. They also apply to the situation, often found in industry, where estimates of signals are required which can only be determined from secondary measurements. An equalizing solution to the H_∞ problem is obtained, ensuring that the estimation error spectrum is determined directly by the choice of the dynamic cost-weighting function.     

High-gain robust adaptive controllers for multivariable systems

This paper extends the switching free high-gain stabilizing adaptive control rules of Byrnes and Willems to a wide class of adaptive schemes capable of tolerating nonlinear state feedback perturbations.     

用于音乐作品版权保护的数字音频水印算法

提出了一种用于音乐作品版权保护的数字音频水印嵌入算法，该算法首先将视觉可辨的二值水印图像降维成一维水印序列并进行随机置乱，再从原始数字音频信号中随机选取采样数据并进行快速傅立叶变换(FFT)，最后结合人类听觉系统(HAS)掩蔽特性选取绝对值较大的FFT系数嵌入水印信息。仿真实验表明：该数字音频水印嵌入算法不仅具有较好的透明性，而且对诸如叠加噪声、有损压缩、低通滤波、重新采样、重新量化等攻击均具有较好的鲁棒性。     

Near optimal solutions to least-squares problems with stochastic uncertainty

In this paper, we consider least-squares (LS) problems where the regression data is affected by parametric stochastic uncertainty. In this setting, we study the problem of minimizing the expected value with respect to the uncertainty of the LS residual. For general nonlinear dependence of the data on the uncertain parameters, determining an exact solution to this problem is known to be computationally prohibitive. Here, we follow a probabilistic approach, and determine a probable near optimal solution by minimizing the empirical mean of the residual. Finite sample convergence of the proposed method is assessed using statistical learning methods. In particular, we prove that if one constructs the empirical approximation of the mean using a finite number N of samples, then the minimizer of this empirical approximation is, with high probability, an ε-suboptimal solution for the original problem. Moreover, this approximate solution can be efficiently determined numerically by a standard recursive algorithm. Comparisons with gradient algorithms for stochastic optimization are also discussed in the paper and several numerical examples illustrate the proposed methodology.     

Robustness analysis of responses of vibration control structures with uncertain parameters using interval algorithm

Variations in system parameters due to uncertainties may result in system performance deterioration. Uncertainties in modeling of structures are often considered to ensure that control system is robust with respect to response errors. Hence, the uncertain concept plays an important role in vibration control of the engineering structures. The paper discusses the robustness of responses of vibration control systems with the uncertain parameters. The vibration control problem of an uncertain system is approximated by a deterministic one. The uncertain parameters are described by interval variables. The uncertain state matrix is constructed directly using system physical parameters and avoided to use bounds in Euclidean norm. The feedback gain matrix is determined based on the deterministic systems, and then it is applied to the actual uncertain systems. A method to calculate the upper and lower bounds of responses of the closed-loop system with uncertain parameters is presented. The upper bounds of responses can be used to estimate the robustness of responses of the controlled system with uncertain parameters. Two numerical examples are given to illustrate the applications of the present approach.     

Robustness issues in optimal control of unstable plants

This paper presents a robustness analysis of the optimal solution of the step tracking problem in a one-degree of freedom control architecture, for the discrete-time multivariable (MIMO) case. It is shown that the resulting closed loop becomes arbitrarily fragile, i.e. the sensitivity peak becomes arbitrarily large, for certain reference directions. The cause of this problem is that the optimal controller depends on the reference direction. The paper shows that this dependence can be eliminated with an alternative formulation of the optimal problem where the cost is averaged over all reference directions.     

Info-gap robustness for the correlation of tests and simulations of a non-linear transient

An alternative to the theory of probability is applied to the problem of assessing the robustness, to uncertainty in model parameters, of the correlation between measurements and computer simulations. The analysis is based on the theory of information-gap uncertainty, which models the clustering of uncertain events in families of nested sets instead of assuming a probability structure. The system investigated is the propagation of a transient impact through a layer of hyper-elastic material. The two sources of non-linearity are (1) the softening of the constitutive law representing the hyper-elastic material and (2) the contact dynamics at the interface between metallic and crushable materials. The robustness of the correlation between test and simulation, to sources of parameter variability, is first studied to identify the parameters of the model that significantly influence the agreement between measurements and predictions. Model updating under non-probabilistic uncertainty is then illustrated, based on two complementary immunity functions: the robustness to uncertainty and the opportunity from uncertainty. Finally an info-gap model is embedded within a probability density function to represent uncertainty in the knowledge of the model's parameters and their correlation structure. Although computationally expensive, it is demonstrated that info-gap reasoning can greatly enhance our understanding of a moderately complex system when the theory of probability cannot be applied due to insufficient information.     

On the relationship between parity space and approaches to fault detection

Parity space approach and H₂ approach are two important fault detection approaches. This paper studies the relationship between these two approaches, which reveals frequency domain characteristics of the optimal solution of the parity space approach on the one side and provides a numerical solution of the H₂-optimal design of residual generators on the other side.     

Tuning of PIλDμ controllers based on sensitivity constraint

A graphical tuning method for fractional-order PID (PI^λD^μ) controllers is proposed based on the sensitivity function constraint of the closed-loop, which provides the information on robustness to plant uncertainties. The stabilizing regions in integral-derivative plane of the controller are first identified using a graphical stability criterion applicable to fractional-delay systems. Then, via Leibniz Sector Formula, the stabilizing region is optimized with respect to the two fractional orders of the controller to expect bigger stabilizing regions. Finally, the sensitivity function constraint of the closed-loop is mapped into stabilizing region by means of the explicit algebraic equations which can be solved efficiently. Numerical examples of a second-order integrating delay process are followed in each design procedure to show the effectiveness of the method.     

航空发动机鲁棒残差设计故障诊断研究

针对航空发动机的故障,设计了基于观测器的鲁棒故障诊断器。介绍了故障诊断中残差生成的一般形式和干扰解耦的基本原理。针对建模中存在的模型不确定性问题,在假定干扰分布已知的前提下,设计了鲁棒残差生成器,实现了残差对干扰解耦的目标,最后仿真模拟了燃油计量活门和尾喷管作动筒故障的情形。仿真结果表明,所设计的鲁棒残差生成器产生的残差具有对干扰低敏感而对故障高敏感的特性,实现了残差对干扰解耦的目标。