Analysis and Design of Singular Markovian Jump Systems

This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H? control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat’s Lemma, among other techniques. Features of the book include: · study of the stability problem for SMJSs with general transition rate matrices (TRMs); · stabilization for SMJSs by TRM design, noise control, proportional-derivative and partially mode-dependent control, in terms of LMIs with and without equation constraints; · mode-dependent and mode-independent H? control solutions with development of a type of disordered controller; · observer-based controllers of SMJSs in which both the designed observer and controller are either mode-dependent or mode-independent; · consideration of robust H? filtering in terms of uncertain TRM or filter parameters leading to a method for totally mode-independent filtering · development of LMI-based conditions for a class of adaptive state feedback controllers with almost-certainly-bounded estimated error and almost-certainly-asymptotically-stable corresponding closed-loop system states · applications of Markov process on singular systems with norm bounded uncertainties and time-varying delays Analysis and Design of Singular Markovian Jump Systems contains valuable reference material for academic researchers wishing to explore the area. The contents are also suitable for a one-semester graduate course

Metric sparsification and operator norm localization

We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. A metric space X is said to have operator norm localization property if there exists a positive number c such that for every r>0, there is R>0 for which, if m is a positive locally finite Borel measure on X, H is a separable infinite dimensional Hilbert space and T is a bounded linear operator acting on L^2(X,m) with propagation r, then there exists an unit vector v satisfying with support of diameter at most R and such that |Tv| is larger or equal than c|T|. If X has finite asymptotic dimension, then X has operator norm localization property. In this paper, we introduce a sufficient geometric condition for the operator norm localization property. This is used to give many examples of finitely generated groups with infinite asymptotic dimension and the operator norm localization property. We also show that any sequence of expanding graphs does not possess the operator norm localization property

Adversarial Sample Detection for Deep Neural Network through Model Mutation Testing

Deep neural networks (DNN) have been shown to be useful in a wide range of applications. However, they are also known to be vulnerable to adversarial samples. By transforming a normal sample with some carefully crafted human imperceptible perturbations, even highly accurate DNN make wrong decisions. Multiple defense mechanisms have been proposed which aim to hinder the generation of such adversarial samples. However, a recent work show that most of them are ineffective. In this work, we propose an alternative approach to detect adversarial samples at runtime. Our main observation is that adversarial samples are much more sensitive than normal samples if we impose random mutations on the DNN. We thus first propose a measure of `sensitivity' and show empirically that normal samples and adversarial samples have distinguishable sensitivity. We then integrate statistical hypothesis testing and model mutation testing to check whether an input sample is likely to be normal or adversarial at runtime by measuring its sensitivity. We evaluated our approach on the MNIST and CIFAR10 datasets. The results show that our approach detects adversarial samples generated by state-of-the-art attacking methods efficiently and accurately.Comment: Accepted by ICSE 201