Robust Η∞Control for a Class of Discrete Time-Delay Stochastic Systems with Randomly Occurring Nonlinearities

Copyright © 2014 Yamin Wang 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 this paper, we consider the robust Η∞ control problem for a class of discrete time-delay stochastic systems with randomly occurring nonlinearities. The parameter uncertainties enter all the system matrices; the stochastic disturbances are both state and control dependent, and the randomly occurring nonlinearities obey the sector boundedness conditions. The purpose of the problem addressed is to design a state feedback controller such that, for all admissible uncertainties, nonlinearities, and time delays, the closed-loop system is robustly asymptotically stable in the mean square, and a prescribed Η∞ disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and stochastic analysis tools, a linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the existence of the desired controllers, where the conditions are dependent on the lower and upper bounds of the time-varying delays. The explicit parameterization of the desired controller gains is also given. Finally, a numerical example is exploited to show the usefulness of the results obtained.This work was supported in part by the National Natural Science Foundation of China under Grants 61374010, 61074129, and 61175111, the Natural Science Foundation of Jiangsu Province of China under Grant BK2012682, the Qing Lan Project of Jiangsu Province (2010), the 333 Project of Jiangsu Province (2011), and the Six Talents Peak Project of Jiangsu Province (2012)

Existence of random attractors for a class of second order lattice dynamical systems with Brownian motions

Copyright © 2014 Yamin Wang 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.For abstract, see attached file.The National Natural Science Foundation of China under Grant nos. 61374010, 61074129, and 61175111, the Natural Science Foundation of Jiangsu Province of China under Grant BK2012682, the Qing Lan Project of Jiangsu Province (2010), the 333 Project of Jiangsu Province (2011), and the Six Talents Peak Project of Jiangsu Province (DZXX-047)

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

Analysis, filtering, and control for Takagi-Sugeno fuzzy models in networked systems

Copyright © 2015 Sunjie Zhang 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.The fuzzy logic theory has been proven to be effective in dealing with various nonlinear systems and has a great success in industry applications. Among different kinds of models for fuzzy systems, the so-called Takagi-Sugeno (T-S) fuzzy model has been quite popular due to its convenient and simple dynamic structure as well as its capability of approximating any smooth nonlinear function to any specified accuracy within any compact set. In terms of such a model, the performance analysis and the design of controllers and filters play important roles in the research of fuzzy systems. In this paper, we aim to survey some recent advances on the T-S fuzzy control and filtering problems with various network-induced phenomena. The network-induced phenomena under consideration mainly include communication delays, packet dropouts, signal quantization, and randomly occurring uncertainties (ROUs). With such network-induced phenomena, the developments on T-S fuzzy control and filtering issues are reviewed in detail. In addition, some latest results on this topic are highlighted. In the end, conclusions are drawn and some possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 11301118 and 61174136, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the Fundamental Research Funds for the Central Universities of China under Grant CUSF-DH-D-2013061, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

An integrated approach to global synchronization and state estimation for nonlinear singularly perturbed complex networks

This paper aims to establish a unified framework to handle both the exponential synchronization and state estimation problems for a class of nonlinear singularly perturbed complex networks (SPCNs). Each node in the SPCN comprises both 'slow' and 'fast' dynamics that reflects the singular perturbation behavior. General sector-like nonlinear function is employed to describe the nonlinearities existing in the network. All nodes in the SPCN have the same structures and properties. By utilizing a novel Lyapunov functional and the Kronecker product, it is shown that the addressed SPCN is synchronized if certain matrix inequalities are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that dynamics (both slow and fast) of the estimation error is guaranteed to be globally asymptotically stable. Again, a matrix inequality approach is developed for the state estimation problem. Two numerical examples are presented to verify the effectiveness and merits of the proposed synchronization scheme and state estimation formulation. It is worth mentioning that our main results are still valid even if the slow subsystems within the network are unstable

Mobile optical wireless system using fast beam Angle, delay and power adaptation with angle diversity receivers

In this paper, we introduce a novel fast angle and power adaptation method in optical wireless (OW) systems. The fast angle and power adaptive line strip multibeam system (FAPA-LSMS) can identify the optimum spots distribution based on a divide and conquer (D&C) algorithm and can achieve a signal-to-noise ratio (SNR) performance comparable to that obtained using the normal APA-LSMS. This results in a significant reduction in the system adaptation time by a factor of 20. The proposed FAPA system makes use of delay adaptation to minimize the delay spread at the receiver. A significant reduction in the delay spread by a factor of 50 can be achieved compared to the non-adaptive LSMS. The proposed system improves the SNR by 50 dB over a conventional diffuse system

Recursive State Estimation for Stochastic Complex Networks under Round-Robin Communication Protocol: Handling Packet Disorders

This paper investigates the recursive state estimation problem for a class of discrete-time stochastic complex networks with packet disorders under Round-Robin (RR) communication protocols. The phenomenon of packet disorders results from the random transmission delays during the signal propagation process due to the unpredictable fluctuations of the network load, and such random delays are modeled by a set of random variables satisfying certain known probability distributions. For the sake of lessening the communication burden and abating the data collisions, the RR protocol is introduced to govern the order of the nodes for data transmission. Under the scheduling of the RR protocol, only one node is allowed to gain the access to the network at each time instant. Then, a recursive estimator is devised to guarantee an upper bound for the estimation error covariance, and then the obtained upper bound is locally minimized by adequately choosing the estimator parameters. Furthermore, the boundedness of estimation error is analyzed in the sense of mean square with the help of stochastic analysis techniques. At last, a simulation example is presented to show the applicability of the proposed estimator design scheme.10.13039/501100004054-King Abdulaziz University (Grant Number: RG-19-611-42); 10.13039/501100001809-National Natural Science Foundation of China (Grant Number: 61773017, 61873148, 61873230 and 61933007); Royal Society of the U.K.; Alexander Von Humboldt Foundation of German

Non-fragile state estimation for discrete Markovian jumping neural networks

In this paper, the non-fragile state estimation problem is investigated for a class of discrete-time neural networks subject to Markovian jumping parameters and time delays. In terms of a Markov chain, the mode switching phenomenon at different times is considered in both the parameters and the discrete delays of the neural networks. To account for the possible gain variations occurring in the implementation, the gain of the estimator is assumed to be perturbed by multiplicative norm-bounded uncertainties. We aim to design a non-fragile state estimator such that, in the presence of all admissible gain variations, the estimation error converges to zero exponentially. By adopting the Lyapunov–Krasovskii functional and the stochastic analysis theory, sufficient conditions are established to ensure the existence of the desired state estimator that guarantees the stability of the overall estimation error dynamics. The explicit expression of such estimators is parameterized by solving a convex optimization problem via the semi-definite programming method. A numerical simulation example is provided to verify the usefulness of the proposed methods

Almost sure H∞ filtering for nonlinear hybrid stochastic systems with mode-dependent interval delays

In this paper, the problem of almost sure H∞ filtering is studied for a class of nonlinear hybrid stochastic systems. In the system under investigation, Markovian jumping parameters, mode-dependent interval delays, nonzero exogenous disturbances as well as white noises are simultaneously taken into consideration to better model the real-world systems. Intensive stochastic analysis is carried out to obtain sufficient conditions for ensuring the almost surely exponential stability and the prescribed H∞ performance for the overall filtering error dynamics. Furthermore, the obtained results are applied to two classes of special hybrid stochastic systems with mode-dependent interval delays, where the desired filter gain is obtained in terms of the solutions to a set of linear matrix inequalities. Finally, two numerical examples are provided to show the effectiveness of the proposed filter design scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009 and 61329301, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Nonfragile H∞Fuzzy filtering with randomly occurring gain variations and channel fadings

This paper is concerned with the nonfragile filtering problem for a class of discrete-Time Takagi-Sugeno (T-S) fuzzy systems with both randomly occurring gain variations (ROGVs) and channel fadings.The phenomenon of the ROGVs is introduced into the system model so as to account for the parameter fluctuations occurring during the filter implementation. Two sequences of random variables obeying the Bernoulli distribution are employed to describe the phenomenon of the ROGVs bounded by prescribed norms. In addition, the Rice fading model is utilized to describe the phenomena of channel fadings, where the occurrence probabilities of the random channel coefficients are allowed to time varying. Through stochastic analysis and Lyapunov functional approach, sufficient conditions are established under which the filtering error dynamics is exponentially mean-square stable with a prespecified ∞ performance. The set of the desired nonfragile ∞ filters is characterized by solving a convex optimization problem via the semidefinite programming method. An illustrative example is given to show the usefulness and effectiveness of the proposed design method in this paper.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 61203139, 61374127 and 61422301, the Hujiang Foundation of China under Grant C14002, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany