A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information

Copyright q 2012 Hongli Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German

A survey on gain-scheduled control and filtering for parameter-varying systems

Copyright © 2014 Guoliang Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.This paper presents an overview of the recent developments in the gain-scheduled control and filtering problems for the parameter-varying systems. First of all, we recall several important algorithms suitable for gain-scheduling method including gain-scheduled proportional-integral derivative (PID) control, H 2, H ∞ and mixed H 2 / H ∞ gain-scheduling methods as well as fuzzy gain-scheduling techniques. Secondly, various important parameter-varying system models are reviewed, for which gain-scheduled control and filtering issues are usually dealt with. In particular, in view of the randomly occurring phenomena with time-varying probability distributions, some results of our recent work based on the probability-dependent gain-scheduling methods are reviewed. Furthermore, some latest progress in this area is discussed. Finally, conclusions are drawn and several potential future research directions are outlined.The National Natural Science Foundation of China under Grants 61074016, 61374039, 61304010, and 61329301; the Natural Science Foundation of Jiangsu Province of China under Grant BK20130766; the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning; the Program for New Century Excellent Talents in University under Grant NCET-11-1051, the Leverhulme Trust of the U.K., the Alexander von Humboldt Foundation of Germany

Fault detection for markovian jump systems with sensor saturations and randomly varying nonlinearities

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEE.This paper addresses the fault detection problem for discrete-time Markovian jump systems with incomplete knowledge of transition probabilities, randomly varying nonlinearities and sensor saturations. For the Markovian mode jumping, the transition probability matrix is allowed to have partially unknown entries, while the cases with completely known or completely unknown transition probabilities are also investigated as two special cases. The randomly varying nonlinearities and the sensor saturations are introduced to reflect the limited capacity of the communication networks resulting from the noisy environment, probabilistic communication failures, measurements of limited amplitudes, etc. Two energy norm indices are used for the fault detection problem in order to account for, respectively, the restraint of disturbance and the sensitivity of faults. The purpose of the problem addressed is to design an optimized fault detection filter such that 1) the fault detection dynamics is stochastically stable; 2) the effect from the exogenous disturbance on the residual is attenuated with respect to a minimized H∞-norm; and 3) the sensitivity of the residual to the fault is enhanced by means of a maximized H∞-norm. The characterization of the gains of the desired fault detection filters is derived in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programme method. Finally, a simulation example is employed to show the effectiveness of the fault detection filtering scheme proposed in this paper.This work was supported in part by the National 973 Project under Grant 2009CB320600, the National Natural Science Foundation of China under Grants 61028008, 61134009, 60825303, 90916005 and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Stability Analysis for Markovian Jump Neutral Systems with Mixed Delays and Partially Known Transition Rates

The delay-dependent stability problem is studied for Markovian jump neutral systems with partial information on transition probabilities, and the considered delays are mixed and model dependent. By constructing the new stochastic Lyapunov-Krasovskii functional, which combined the introduced free matrices with the analysis technique of matrix inequalities, a sufficient condition for the systems with fully known transition rates is firstly established. Then, making full use of the transition rate matrix, the results are obtained for the other case, and the uncertain neutral Markovian jump system with incomplete transition rates is also considered. Finally, to show the validity of the obtained results, three numerical examples are provided

Stability Analysis of Continuous-Time Switched Systems with a Random Switching Signal

This paper is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part and a random part. The stochastic stability of such switched systems is studied using a Lyapunov approach. A necessary and sufficient condition is established in terms of linear matrix inequalities. The effect of the random switching signal on system stability is illustrated by a numerical example and the results coincide with our intuition.Comment: 6 pages, 6 figures, accepted by IEEE-TA

H∞ model reduction for discrete-time Markovian jump systems with deficient mode information

This paper investigates the problem of H∞ model reduction for a class of discrete-time Markovian jump linear systems (MJLSs) with deficient mode information, which simultaneously involves the exactly known, partially unknown, and uncertain transition probabilities. By fully utilizing the properties of the transition probability matrices, together with the convexification of uncertain domains, a new H∞ performance analysis criterion for the underlying MJLSs is first derived, and then two approaches, namely, the convex linearisation approach and iterative approach, for the H∞ model reduction synthesis are proposed. Finally, a simulation example is provided to illustrate the effectiveness of the proposed design methods

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Reliable H ∞ filtering for stochastic spatial–temporal systems with sensor saturations and failures

This study is concerned with the reliable H∞ filtering problem for a class of stochastic spatial–temporal systems with sensor saturations and failures. Different from the continuous spatial–temporal systems, the dynamic behaviour of the system under consideration evolves in a discrete rectangular region. The aim of this study is to estimate the system states through the measurements received from a set of sensors located at some specified points. In order to cater for more realistic signal transmission process, the phenomena of sensor saturations and sensor failures are taken into account. By using the vector reorganisation approach, the spatial–temporal system is first transformed into an equivalent ordinary differential dynamic system. Then, a filter is constructed and a sufficient condition is obtained under which the filtering error dynamics is asymptotically stable in probability and the H∞ performance requirement is met. On the basis of the analysis results, the desired reliable H∞ filter is designed. Finally, an illustrative example is given to show the effectiveness of the proposed filtering scheme.Deanship of Scientific Research (DSR) at King Abdulaziz University in Saudi Arabia under Grant 16-135-35-HiCi, the National Natural Science Foundation of China under Grants 61329301, 61134009 and 61473076, the Shanghai Rising-Star Program of China under Grant 13QA1400100, the Shu Guang project of Shanghai Municipal Education Commission and Shanghai Education Development Foundation under Grant 13SG34, the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, the Fundamental Research Funds for the Central Universities, the DHU Distinguished Young Professor Program, and the Alexander von Humboldt Foundation of German