H∞ filtering for nonlinear discrete-time stochastic systems with randomly varying sensor delays

This is the post print version of the article. The official published version can be obained from the link - Copyright 2009 Elsevier LtdThis paper is concerned with the H∞ filtering problem for a general class of nonlinear discrete-time stochastic systems with randomly varying sensor delays, where the delayed sensor measurement is governed by a stochastic variable satisfying the Bernoulli random binary distribution law. In terms of the Hamilton–Jacobi–Isaacs inequalities, preliminary results are first obtained that ensure the addressed system to possess an l2-gain less than a given positive scalar γ. Next, a sufficient condition is established under which the filtering process is asymptotically stable in the mean square and the filtering error satisfies the H∞ performance constraint for all nonzero exogenous disturbances under the zero-initial condition. Such a sufficient condition is then decoupled into four inequalities for the purpose of easy implementation. Furthermore, it is shown that our main results can be readily specialized to the case of linear stochastic systems. Finally, a numerical simulation example is used to demonstrate the effectiveness of the results derived.This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor James Lam under the direction of Editor Ian R. Petersen. This work was supported by the Shanghai Natural Science Foundation under Grant 07ZR14002, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK and the Alexander von Humboldt Foundation of Germany

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

Probability-guaranteed H∞ finite-horizon filtering for a class of nonlinear time-varying systems with sensor saturations

This is the Post-Print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 ElsevierIn this paper, the probability-guaranteed H∞ finite-horizon filtering problem is investigated for a class of nonlinear time-varying systems with uncertain parameters and sensor saturations. The system matrices are functions of mutually independent stochastic variables that obey uniform distributions over known finite ranges. Attention is focused on the construction of a time-varying filter such that the prescribed H∞ performance requirement can be guaranteed with probability constraint. By using the difference linear matrix inequalities (DLMIs) approach, sufficient conditions are established to guarantee the desired performance of the designed finite-horizon filter. The time-varying filter gains can be obtained in terms of the feasible solutions of a set of DLMIs that can be recursively solved by using the semi-definite programming method. A computational algorithm is specifically developed for the addressed probability-guaranteed H∞ finite-horizon filtering problem. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008, 60825303 and 60834003, National 973 Project under Grant 2009CB320600, the Fok Ying Tung Education Fund under Grant 111064, the Special Fund for the Author of National Excellent Doctoral Dissertation of China under Grant 2007B4, the Key Laboratory of Integrated Automation for the Process Industry (Northeastern University) from the Ministry of Education of China, 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

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

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