Model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints

Robust predictive control handles constrained systems that are subject to stochastic uncertainty but propagating the effects of uncertainty over a prediction horizon can be computationally expensive and conservative. This paper overcomes these issues through an augmented autonomous prediction formulation, and provides a method of handling probabilistic constraints and ensuring closed loop stability through the use of an extension of the concept of invariance, namely invariance with probability p.     

Suppressing intersample behavior in iterative learning control

Iterative Learning Control (ILC) is a control strategy to improve the performance of digital batch repetitive processes. Due to its digital implementation, discrete time ILC approaches do not guarantee good intersample behavior. In fact, common discrete time ILC approaches may deteriorate the intersample behavior, thereby reducing the performance of the sampled-data system. In this paper, a generally applicable multirate ILC approach is presented that enables to balance the at-sample performance and the intersample behavior. Furthermore, key theoretical issues regarding multirate systems are addressed, including the time-varying nature of the multirate ILC setup. The proposed multirate ILC approach is shown to outperform discrete time ILC in realistic simulation examples.     

Stabilizing switching design for switched linear systems: A state-feedback path-wise switching approach

This paper addresses the problem of switching stabilization for discrete-time switched linear systems. Based on the abstraction-aggregation methodology, we propose a state-feedback path-wise switching law, which is a state-feedback concatenation from a finite set of switching paths each defined over a finite time interval. We prove that the set of state-feedback path-wise switching laws is universal in the sense that any stabilizable switched linear system admits a stabilizing switching law in this set. We further develop a computational procedure to calculate a stabilizing switching law in the set.     

A comment on “Using locally estimated geodesic distance to optimize neighborhood graph for isometric data embedding”

A geodesic distance-based approach to build the neighborhood graph for isometric embedding is proposed to deal with the highly twisted and folded manifold by Wen et al. [Using locally estimated geodesic distance to optimize neighborhood graph for isometric data embedding, Pattern Recognition 41 (2008) 2226-2236]. This comment is to identify the error in their example and the ineffectiveness of their algorithm.     

Combining feature spaces for classification

In this paper we offer a variational Bayes approximation to the multinomial probit model for basis expansion and kernel combination. Our model is well-founded within a hierarchical Bayesian framework and is able to instructively combine available sources of information for multinomial classification. The proposed framework enables informative integration of possibly heterogeneous sources in a multitude of ways, from the simple summation of feature expansions to weighted product of kernels, and it is shown to match and in certain cases outperform the well-known ensemble learning approaches of combining individual classifiers. At the same time the approximation reduces considerably the CPU time and resources required with respect to both the ensemble learning methods and the full Markov chain Monte Carlo, Metropolis-Hastings within Gibbs solution of our model. We present our proposed framework together with extensive experimental studies on synthetic and benchmark datasets and also for the first time report a comparison between summation and product of individual kernels as possible different methods for constructing the composite kernel matrix.     

Stable local dimensionality reduction approaches

Dimensionality reduction is a big challenge in many areas. A large number of local approaches, stemming from statistics or geometry, have been developed. However, in practice these local approaches are often in lack of robustness, since in contrast to maximum variance unfolding (MVU), which explicitly unfolds the manifold, they merely characterize local geometry structure. Moreover, the eigenproblems that they encounter, are hard to solve. We propose a unified framework that explicitly unfolds the manifold and reformulate local approaches as the semi-definite programs instead of the above-mentioned eigenproblems. Three well-known algorithms, locally linear embedding (LLE), laplacian eigenmaps (LE) and local tangent space alignment (LTSA) are reinterpreted and improved within this framework. Several experiments are presented to demonstrate the potential of our framework and the improvements of these local algorithms.     

A unifying criterion for unsupervised clustering and feature selection

Exploratory data analysis methods are essential for getting insight into data. Identifying the most important variables and detecting quasi-homogenous groups of data are problems of interest in this context. Solving such problems is a difficult task, mainly due to the unsupervised nature of the underlying learning process. Unsupervised feature selection and unsupervised clustering can be successfully approached as optimization problems by means of global optimization heuristics if an appropriate objective function is considered. This paper introduces an objective function capable of efficiently guiding the search for significant features and simultaneously for the respective optimal partitions. Experiments conducted on complex synthetic data suggest that the function we propose is unbiased with respect to both the number of clusters and the number of features.     

On the estimation of adequate test set size using fault failure rates

Test set size in terms of the number of test cases is an important consideration when testing software systems. Using too few test cases might result in poor fault detection and using too many might be very expensive and suffer from redundancy. We define the failure rate of a program as the fraction of test cases in an available test pool that result in execution failure on that program. This paper investigates the relationship between failure rates and the number of test cases required to detect the faults. Our experiments based on 11 sets of C programs suggest that an accurate estimation of failure rates of potential fault(s) in a program can provide a reliable estimate of adequate test set size with respect to fault detection and should therefore be one of the factors kept in mind during test set construction. Furthermore, the model proposed herein is fairly robust to incorrect estimations in failure rates and can still provide good predictive quality. Experiments are also performed to observe the relationship between multiple faults present in the same program using the concept of a failure rate. When predicting the effectiveness against a program with multiple faults, results indicate that not knowing the number of faults in the program is not a significant concern, as the predictive quality is typically not affected adversely.     

Approximate steady-state analysis of large Markov models based on the structure of their decision diagram encoding

We propose a new approximate numerical algorithm for the steady-state solution of general structured ergodic Markov models. The approximation uses a state-space encoding based on multiway decision diagrams and a transition rate encoding based on a new class of edge-valued decision diagrams. The new method retains the favorable properties of a previously proposed Kronecker-based approximation, while eliminating the need for a Kronecker-consistent model decomposition. Removing this restriction allows for a greater utilization of event locality, which facilitates the generation of both the state-space and the transition rate matrix, thus extends the applicability of this algorithm to larger and more complex models.