On exponential convergence and robustness of least-squares identification

Robustness and convergence properties of exponentially weighted least-squares identification are studied. It is shown that exponential convergence in the noiseless case can be obtained for a class of increasing or decreasing regression vectors. The rate of change of the limits in the regressors affect the convergence rates, which are explicitly given. It is demonstrated that for a sub-class of regressors decreasing-in-the-norm exponential convergence without the noise does not guarantee robustness subject to a bounded noise. Instead, exponential divergence of the estimate is shown in a specific case.     

Correspondence On stochastic identification algorithms

In this paper, an adaptive observer design method based upon the least square approach is presented for an unknown time invariant continuous linear plant. This observer is then implemented in the design of an adaptive pole placement problem for arbitrarily positioning all the poles of the unknown plant. The generated feedback control signal is shown to converge to a desired pole placing state feedback control signal.     

On convergence of the recursive identification algorithms

The paper is concerned with identification of a linear dynamic system through recursive algorithms of the approximate maximum likelihood (AML) method. In all papers on the convergence of the recursive AML procedure, no matter what method of analysis is used, a certain rather restrictive positive real condition is imposed on the model of disturbance. In this work, it is shown that recursive AML algorithms converge with probability one under a fairly broad (also positive real) condition which significantly expands the AML application area. The well-known principle of averaging from physics is used as a tool of analysis. A sketch of the proof of the principle of averaging for stochastic difference equations is given.     

Constrained robustness analysis by randomized algorithms

This paper shows that many robust control problems can be formulated as constrained optimization problems and can be tackled by using randomized algorithms. Two different approaches in searching reliable solutions to robustness analysis problems under constraints are proposed, and the minimum computational efforts for achieving certain reliability and accuracy are investigated and bounds for sample size are derived. Moreover, the existing order statistics distribution theory is extended to the general case in which the distribution of population is not assumed to be continuous and the order statistics is associated with certain constraints     

Stochastic algorithms for robustness of control performances

In recent years, there has been a growing interest in developing statistical learning methods to provide approximate solutions to “difficult” control problems. In particular, randomized algorithms have become a very popular tool used for stability and performance analysis as well as for design of control systems. However, as randomized algorithms provide an efficient solution procedure to the “intractable” problems, stochastic methods bring closer to understanding the properties of the real systems. The topic of this paper is the use of stochastic methods in order to solve the problem of control robustness: the case of parametric stochastic uncertainty is considered. Necessary concepts regarding stochastic control theory and stochastic differential equations are introduced. Then a convergence analysis is provided by means of the Chernoff bounds, which guarantees robustness in mean and in probability. As an illustration, the robustness of control performances of example control systems is computed.     

On strong consistency of least squares identification algorithms

In this paper almost sure convergence results are derived for least squares identification algorithms. The convergence conditions expressed in terms of the measurable signal model states derived for asymptotically stable signal models and possibly nonstationary processes are in essence the same as those previously given, but are derived more directly. Strong consistency results are derived for the case of signal models with unstable modes and exponential rates of convergence to the unstable modes are demonstrated. These latter convergence results are stronger than those earlier ones in which weak consistency conditions are given and there is also less restriction on the noise disturbances than in earlier theories. The derivations in the paper appeal to martingale convergence theorems and the Toeplitz lemma.     

On least squares algorithms for system parameter identification

A new least squares solution for obtaining asymptotically unbiased and consistent estimates of unknown parameters in noisy linear systems is presented. The proposed algorithms are in many ways more advantageous than generalized least squares algorithm. Extensions to on-line and multivariable problems can be easily implemented. Examples are given to illustrate the performance of these new algorithms.     

On robustness in control and LTI identification: Near-linearity and non-conic uncertainty

Robustness issues are studied in the context of linear models in linear controller design and in system identification when the true system is nonlinear. The notion of nearly linear system is generalized to include time-varying and open-loop unstable systems. This class of systems, although it presents the simplest possible (global) generalization of linear systems, is in many ways nontrivial for the purpose of linear controller design and linear model identification from input-output data. This is mainly due to the presence of non-conic uncertainty, which is not included in standard treatments of robust control theory and stochastic system identification theory. Signal distribution theory, a realistic non-stochastic signal analysis tool, is used to study the limiting least squares estimates of linear finite impulse response (FIR) and autoregressive with external input (ARX) model parametrizations for two classes of nonlinear systems. Some connections to worst-case analysis of linear model identification are also discussed.     

On robustness of B-trees

A method is presented to detect index corruption and pointer corruption in B⁺-trees. The method uses the semantic information of indices and requires no extra pointers to be added to the data structure. Previous research on the robustness on B-trees has considered index corruption and pointer corruption separately and required extra pointers to be added to the data structure to achieve detectability, and correctability. The proposed method can detect and identify a single semantic or structural error     

典型源相机分类算法性能研究

现有文献中的源相机分类算法很少讨论测试图像在受到轻微图像处理后算法性能的变化。利用支持向量机,对源相机分类算法的性能和鲁棒性进行了分析,比较了测试图像遭受处理前后分类算法的检测准确率,并研究了图像特征的鲁棒性。由于基于模式分类的算法通常需要精简特征个数以提高执行效率,因此,还讨论了精简模式下相机分类算法的性能以及特征选择对辨识算法鲁棒性的影响。     

Randomized algorithms for probabilistic robustness with real andcomplex structured uncertainty

There has been a growing interest in developing randomized algorithms for probabilistic robustness of uncertain control systems. Unlike classical worst case methods, these algorithms provide probabilistic estimates assessing, for instance, if a certain design specification is met with a given probability. One of the advantages of this approach is that the robustness margins can be often increased by a considerable amount, at the expense of a small risk. In this sense, randomized algorithms may be used by the control engineer together with standard worst case methods to obtain additional useful information. The applicability of these probabilistic methods to robust control is presently limited by the fact that the sample generation is feasible only in very special cases which include systems affected by real parametric uncertainty bounded in rectangles or spheres. Sampling in more general uncertainty sets is generally performed through overbounding, at the expense of an exponential rejection rate. In the paper, randomized algorithms for stability and performance of linear time invariant uncertain systems described by a general M-Δ configuration are studied. In particular, efficient polynomial-time algorithms for uncertainty structures Δ consisting of an arbitrary number of full complex blocks and uncertain parameters are developed     

Performance and robustness of discrete and finite time average consensus algorithms

In this paper, we review some of the main discrete and finite time average consensus implementations in the literature, discussing their strengths and shortcomings from a theoretical and empirical point of view. In particular, we compare the computational characteristics of the different algorithms, their behaviour considering different underlying network topologies, their ability to withstand packet losses and their robustness to attacks where a malicious node aims to steer the result of the algorithm towards a desired value, without letting the other nodes detect the attack. Specifically, we will discuss synchronous approaches, where the nodes broadcast their messages, and asynchronous approaches, where the nodes need to be able to address their neighbours individually on a point-to-point basis (i.e. by direct communication between a specific sender and a specific receiver). With the aim to overcome some critical aspects of the considered methodologies, in this paper we present an asynchronous consensus algorithm based on a broadcast-only approach. The algorithm is characterised by a good trade-off between the robustness of synchronous approaches and to low computational demands of asynchronous methods.     

Randomized algorithms for stability and robustness analysis of high-speed communication networks

This paper initiates a study toward developing and applying randomized algorithms for stability of high-speed communication networks. The focus is on congestion and delay-based flow controllers for sources, which are "utility maximizers" for individual users. First, we introduce a nonlinear algorithm for such source flow controllers, which uses as feedback aggregate congestion and delay information from bottleneck nodes of the network, and depends on a number of parameters, among which are link capacities, user preference for utility, and pricing. We then linearize this nonlinear model around its unique equilibrium point and perform a robustness analysis for a special symmetric case with a single bottleneck node. The "symmetry" here captures the scenario when certain utility and pricing parameters are the same across all active users, for which we derive closed-form necessary and sufficient conditions for stability and robustness under parameter variations. In addition, the ranges of values for the utility and pricing parameters for which stability is guaranteed are computed exactly. These results also admit counterparts for the case when the pricing parameters vary across users, but the utility parameter values are still the same. In the general nonsymmetric case, when closed-form derivation is not possible, we construct specific randomized algorithms which provide a probabilistic estimate of the local stability of the network. In particular, we use Monte Carlo as well as quasi-Monte Carlo techniques for the linearized model. The results obtained provide a complete analysis of congestion control algorithms for internet style networks with a single bottleneck node as well as for networks with general random topologies.     

On asymptotic properties of real-time identification algorithms based on dynamic stochastic approximation

The algorithms of dynamic stochastic approximation type are proposed for real-time identification of multivariable linear dynamic discrete-time systems with stochastic parameters. These algorithms can be considered as the general representatives of a class of gradient-type equation-error recursive identification methods. The analysis of their asymptotic properties is presented. It is proved that the algorithms converge either in the mean-square sense, or in the sense of keeping the mean-square error bounded, depending on system parameter properties. Convergence conditions are expressed in terms of inherent system characteristics, e.g., properties of the impulse response matrices and their realizations. A large class of input random processes is supposed.     

A reality check for radiometric camera response recovery algorithms

The radiometric response of a camera governs the relationship between the incident light on the camera sensor and the output pixel values that are produced. This relationship, which is typically unknown and nonlinear, needs to be estimated for applications that require accurate measurement of scene radiance. Until now, various camera response recovery algorithms have been proposed each with different merits and drawbacks. However, an evaluation study that compares these algorithms has not been presented. In this work, we aim to fill this gap by conducting a rigorous experiment that evaluates the selected algorithms with respect to three metrics: consistency, accuracy, and robustness. In particular, we seek the answer of the following four questions: (1) Which camera response recovery algorithm gives the most accurate results? (2) Which algorithm produces the camera response most consistently for different scenes? (3) Which algorithm performs better under varying degrees of noise? (4) Does the sRGB assumption hold in practice? Our findings indicate that Grossberg and Nayar's (GN) algorithm (2004 [1]) is the most accurate; Mitsunaga and Nayar's (MN) algorithm (1999 [2]) is the most consistent; and Debevec and Malik's (DM) algorithm (1997 [3]) is the most resistant to noise together with MN. We also find that the studied algorithms are not statistically better than each other in terms of accuracy although all of them statistically outperform the sRGB assumption. By answering these questions, we aim to help the researchers and practitioners in the high dynamic range (HDR) imaging community to make better choices when choosing an algorithm for camera response recovery.     

Digital camera identification from sensor pattern noise

In this paper, we propose a new method for the problem of digital camera identification from its images based on the sensor's pattern noise. For each camera under investigation, we first determine its reference pattern noise, which serves as a unique identification fingerprint. This is achieved by averaging the noise obtained from multiple images using a denoising filter. To identify the camera from a given image, we consider the reference pattern noise as a spread-spectrum watermark, whose presence in the image is established by using a correlation detector. Experiments on approximately 320 images taken with nine consumer digital cameras are used to estimate false alarm rates and false rejection rates. Additionally, we study how the error rates change with common image processing, such as JPEG compression or gamma correction.     

On the robustness of symmetric systems

This note concerns the robustness of LTI symmetric systems under symmetric or diagonal perturbations. It is shown that for symmetric systems the robust stability condition for dynamic perturbations given by the small gain theorem is also necessary if the perturbation matrix is assumed to be diagonal, but the robust stability condition for parametric perturbations given by the real stability radius is no longer necessary if the perturbation matrix is merely assumed to be symmetric.     

Worst-case properties of the uniform distribution and randomized algorithms for robustness analysis

In this paper we study aprobabilistic approach which is an alternative to the classical worst-case algorithms for robustness analysis and design of uncertain control systems. That is, we aim to estimate the probability that a control system with uncertain parametersq restricted to a boxQ attains a given level of performance γ. Since this probability depends on the underlying distribution, we address the following question: What is a “reasonable” distribution so that the estimated probability makes sense? To answer this question, we define two worstcase criteria and prove that the uniform distribution is optimal in both cases. In the second part of the paper we turn our attention to a subsequent problem. That is, we estimate the sizes of both the so-called “good” and “bad” sets via sampling. Roughly speaking, the good set contains the parametersq∈Q with a performance level better than or equal to γ while the bad set is the set of parametersq∈Q with a performance level worse than γ. We give bounds on the minimum sample size to attain a good estimate of these sets in a certain probabilistic sense.     

Achieving efficient source camera identification on Hadoop

Multimedia Tools and Applications - Hadoop is a software framework allowing for the possibility of coding distributed applications starting from a MapReduce algorithm with very low programming...     

On the robustness of LQ regulators

It is shown that in spite of its large gain and phase margins the linear quadratic state feedback regulator may suffer from poor robustness where small changes in the parameters of the system may lead to fast unstable closed-loop modes.