Robust H∞ fuzzy output-feedback control with multiple probabilistic delays and multiple missing measurements

Copyright [2010] 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 H∞-control problem is investigated for a class of uncertain discrete-time fuzzy systems with both multiple probabilistic delays and multiple missing measurements. A sequence of random variables, all of which are mutually independent but obey the Bernoulli distribution, is introduced to account for the probabilistic communication delays. The measurement-missing phenomenon occurs in a random way. The missing probability for each sensor satisfies a certain probabilistic distribution in the interval. Here, the attention is focused on the analysis and design of H∞ fuzzy output-feedback controllers such that the closed-loop Takagi-Sugeno (T-S) fuzzy-control system is exponentially stable in the mean square. The disturbance-rejection attenuation is constrained to a given level by means of the H∞-performance index. Intensive analysis is carried out to obtain sufficient conditions for the existence of admissible output feedback controllers, which ensures the exponential stability as well as the prescribed H∞ performance. The cone-complementarity-linearization procedure is employed to cast the controller-design problem into a sequential minimization one that is solved by the semi-definite program method. Simulation results are utilized to demonstrate the effectiveness of the proposed design technique in this paper.This work was supported in part by the Engineering and Physical Sciences Research Council, U.K., under Grant GR/S27658/01, in part by the Royal Society, U.K., in part by the National Natural Science Foundation of China under Grant 60825303, in part by the National 973 Project of China under Grant 2009CB320600, in part by the Heilongjiang Outstanding Youth Science Fund of China under Grant JC200809, in part by the Youth Science Fund of Heilongjiang Province of China under Grant QC2009C63, and in part by the Alexander von Humboldt Foundation of Germany

A note on the robust stability of uncertain stochastic fuzzy systems with time-delays

Copyright [2004] 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.Takagi-Sugeno (T-S) fuzzy models are now often used to describe complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear submodels. In this note, the T-S fuzzy model approach is exploited to establish stability criteria for a class of nonlinear stochastic systems with time delay. Sufficient conditions are derived in the format of linear matrix inequalities (LMIs), such that for all admissible parameter uncertainties, the overall fuzzy system is stochastically exponentially stable in the mean square, independent of the time delay. Therefore, with the numerically attractive Matlab LMI toolbox, the robust stability of the uncertain stochastic fuzzy systems with time delays can be easily checked

H ? filtering for stochastic singular fuzzy systems with time-varying delay

This paper considers the H? filtering problem for stochastic singular fuzzy systems with timevarying delay. We assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by Ito-type stochastic differential equations. Based on an auxiliary vector and an integral inequality, a set of delay-dependent sufficient conditions is established, which ensures that the filtering error system is e?t - weighted integral input-to-state stable in mean (iISSiM). A fuzzy filter is designed such that the filtering error system is impulse-free, e?t -weighted iISSiM and the H? attenuation level from disturbance to estimation error is belowa prescribed scalar.Aset of sufficient conditions for the solvability of the H? filtering problem is obtained in terms of a new type of Lyapunov function and a set of linear matrix inequalities. Simulation examples are provided to illustrate the effectiveness of the proposed filtering approach developed in this paper

On passivity and passification of stochastic fuzzy systems with delays: The discrete-time case

Copyright [2010] 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.Takagi–Sugeno (T-S) fuzzy models, which are usually represented by a set of linear submodels, can be used to describe or approximate any complex nonlinear systems by fuzzily blending these subsystems, and so, significant research efforts have been devoted to the analysis of such models. This paper is concerned with the passivity and passification problems of the stochastic discrete-time T-S fuzzy systems with delay. We first propose the definition of passivity in the sense of expectation. Then, by utilizing the Lyapunov functional method, the stochastic analysis combined with the matrix inequality techniques, a sufficient condition in terms of linear matrix inequalities is presented, ensuring the passivity performance of the T-S fuzzy models. Finally, based on this criterion, state feedback controller is designed, and several criteria are obtained to make the closed-loop system passive in the sense of expectation. The results acquired in this paper are delay dependent in the sense that they depend on not only the lower bound but also the upper bound of the time-varying delay. Numerical examples are also provided to demonstrate the effectiveness and feasibility of our criteria.This work was supported in part by the Royal Society Sino–British Fellowship Trust Award of the U.K., by the National Natural Science Foundation of China under Grant 60804028, by the Specialized Research Fund for the Doctoral Program of Higher Education for New Teachers in China under Grant 200802861044, and by the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China

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

Stability analysis and stabilization for discrete-time fuzzy systems with time-varying delay

This paper is concerned with the problems of stability analysis and stabilization for discrete-time Takagi-Sugeno fuzzy systems with time-varying state delay. By constructing a new fuzzy Lyapunov function and by making use of novel techniques, an improved delay-dependent stability condition is obtained, which is dependent on the lower and upper delay bounds. The merit of the proposed stability condition lies in its reduced conservatism, which is achieved by avoiding the utilization of some bounding inequalities for the cross products between two vectors. Then, delay-dependent stabilization approach based on a parallel distributed compensation scheme is developed for both state feedback and observer-based output feedback cases. The proposed stability and stabilization conditions are formulated in terms of linear matrix inequalities, which can be solved efficiently by using existing optimization techniques. Two illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper. © 2008 IEEE.published_or_final_versio

Time-and event-driven communication process for networked control systems: A survey

Copyright © 2014 Lei Zou 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 recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time-and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Stability and stabilization of delayed T-S fuzzy systems: A delay partitioning approach

This paper proposes a new approach, namely, the delay partitioning approach, to solving the problems of stability analysis and stabilization for continuous time-delay Takagi-Sugeno fuzzy systems. Based on the idea of delay fractioning, a new method is proposed for the delay-dependent stability analysis of fuzzy time-delay systems. Due to the instrumental idea of delay partitioning, the proposed stability condition is much less conservative than most of the existing results. The conservatism reduction becomes more obvious with the partitioning getting thinner. Based on this, the problem of stabilization via the so-called parallel distributed compensation scheme is also solved. Both the stability and stabilization results are further extended to time-delay fuzzy systems with time-varying parameter uncertainties. All the results are formulated in the form of linear matrix inequalities (LMIs), which can be readily solved via standard numerical software. The advantage of the results proposed in this paper lies in their reduced conservatism, as shown via detailed illustrative examples. The idea of delay partitioning is well demonstrated to be efficient for conservatism reduction and could be extended to solving other problems related to fuzzy delay systems. © 2009 IEEE.published_or_final_versio

Fuzzy control turns 50: 10 years later

In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.Guerra, T.; Sala, A.; Tanaka, K. (2015). Fuzzy control turns 50: 10 years later. Fuzzy Sets and Systems. 281:162-182. doi:10.1016/j.fss.2015.05.005S16218228