On nonlinear H∞ filtering for discrete-time stochastic systems with missing measurements

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the H∞ filtering problem is investigated for a general class of nonlinear discrete-time stochastic systems with missing measurements. The system under study is not only corrupted by state-dependent white noises but also disturbed by exogenous inputs. The measurement output contains randomly missing data that is modeled by a Bernoulli distributed white sequence with a known conditional probability. A filter of very general form is first designed such that the filtering process is stochastically stable and the filtering error satisfies H infin performance constraint for all admissible missing observations and nonzero exogenous disturbances under the zero-initial condition. The existence conditions of the desired filter are described in terms of a second-order nonlinear inequality. Such an inequality can be decoupled into some auxiliary ones that can be solved independently by taking special form of the Lyapunov functionals. As a consequence, a linear time-invariant filter design problem is discussed for the benefit of practical applications, and some simplified conditions are obtained. Finally, two numerical simulation examples are given to illustrate the main results of this paper

Background derivation and image flattening: getimages

Modern high-resolution images obtained with space observatories display extremely strong intensity variations across images on all spatial scales. Source extraction in such images with methods based on global thresholding may bring unacceptably large numbers of spurious sources in bright areas while failing to detect sources in low-background or low-noise areas. It would be highly beneficial to subtract background and equalize the levels of small-scale fluctuations in the images before extracting sources or filaments. This paper describes getimages, a new method of background derivation and image flattening. It is based on median filtering with sliding windows that correspond to a range of spatial scales from the observational beam size up to a maximum structure width $X_{\lambda}$. The latter is a single free parameter of getimages that can be evaluated manually from the observed image $\mathcal{I}_{\lambda}$. The median filtering algorithm provides a background image $\tilde{\mathcal{B}}_{\lambda}$ for structures of all widths below $X_{\lambda}$. The same median filtering procedure applied to an image of standard deviations $\mathcal{D}_{\lambda}$ derived from a background-subtracted image $\tilde{\mathcal{S}}_{\lambda}$ results in a flattening image $\tilde{\mathcal{F}}_{\lambda}$. Finally, a flattened detection image $\mathcal{I}_{{\lambda}\mathrm{D}}{\,=\,}\tilde{\mathcal{S}}_{\lambda}{/}\tilde{\mathcal{F}}_{\lambda}$ is computed, whose standard deviations are uniform outside sources and filaments. Detecting sources in such greatly simplified images results in much cleaner extractions that are more complete and reliable. As a bonus, getimages reduces various observational and map-making artifacts and equalizes noise levels between independent tiles of mosaicked images.Comment: 14 pages, 11 figures (main text + 3 appendices), accepted by Astronomy & Astrophysics; fixed Metadata abstract (typesetting

Musical recommendations and personalization in a social network

This paper presents a set of algorithms used for music recommendations and personalization in a general purpose social network www.ok.ru, the second largest social network in the CIS visited by more then 40 millions users per day. In addition to classical recommendation features like "recommend a sequence" and "find similar items" the paper describes novel algorithms for construction of context aware recommendations, personalization of the service, handling of the cold-start problem, and more. All algorithms described in the paper are working on-line and are able to detect and address changes in the user's behavior and needs in the real time. The core component of the algorithms is a taste graph containing information about different entities (users, tracks, artists, etc.) and relations between them (for example, user A likes song B with certainty X, track B created by artist C, artist C is similar to artist D with certainty Y and so on). Using the graph it is possible to select tracks a user would most probably like, to arrange them in a way that they match each other well, to estimate which items from a fixed list are most relevant for the user, and more. In addition, the paper describes the approach used to estimate algorithms efficiency and analyze the impact of different recommendation related features on the users' behavior and overall activity at the service.Comment: This is a full version of a 4 pages article published at ACM RecSys 201

Robust H∞ control for networked systems with random packet losses

Copyright [2007] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the robust Hinfin control problem Is considered for a class of networked systems with random communication packet losses. Because of the limited bandwidth of the channels, such random packet losses could occur, simultaneously, in the communication channels from the sensor to the controller and from the controller to the actuator. The random packet loss is assumed to obey the Bernoulli random binary distribution, and the parameter uncertainties are norm-bounded and enter into both the system and output matrices. In the presence of random packet losses, an observer-based feedback controller is designed to robustly exponentially stabilize the networked system in the sense of mean square and also achieve the prescribed Hinfin disturbance-rejection-attenuation level. Both the stability-analysis and controller-synthesis problems are thoroughly investigated. It is shown that the controller-design problem under consideration is solvable if certain linear matrix inequalities (LMIs) are feasible. A simulation example is exploited to demonstrate the effectiveness of the proposed LMI approach

Variance-constrained control for uncertain stochastic systems with missing measurements

Copyright [2005] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we are concerned with a new control problem for uncertain discrete-time stochastic systems with missing measurements. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The system measurements may be unavailable (i.e., missing data) at any sample time, and the probability of the occurrence of missing data is assumed to be known. The purpose of this problem is to design an output feedback controller such that, for all admissible parameter uncertainties and all possible incomplete observations, the system state of the closed-loop system is mean square bounded, and the steady-state variance of each state is not more than the individual prescribed upper bound. We show that the addressed problem can be solved by means of algebraic matrix inequalities. The explicit expression of the desired robust controllers is derived in terms of some free parameters, which may be exploited to achieve further performance requirements. An illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach