Bounded H∞ synchronization and state estimation for discrete time-varying stochastic complex for discrete time-varying stochastic complex networks over a finite horizon

Copyright [2011] 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, new synchronization and state estimation problems are considered for an array of coupled discrete time-varying stochastic complex networks over a finite horizon. A novel concept of bounded H∞ synchronization is proposed to handle the time-varying nature of the complex networks. Such a concept captures the transient behavior of the time-varying complex network over a finite horizon, where the degree of bounded synchronization is quantified in terms of the H∞-norm. A general sector-like nonlinear function is employed to describe the nonlinearities existing in the network. By utilizing a timevarying real-valued function and the Kronecker product, criteria are established that ensure the bounded H∞ synchronization in terms of a set of recursive linear matrix inequalities (RLMIs), where the RLMIs can be computed recursively by employing available MATLAB toolboxes. The bounded H∞ 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, over a finite horizon, the dynamics of the estimation error is guaranteed to be bounded with a given disturbance attenuation level. Again, an RLMI approach is developed for the state estimation problem. Finally, two simulation examples are exploited to show the effectiveness of the results derived in this paper.This work was supported in part by the Engineering and Physical Sciences Research Council of U.K. under Grant GR/S27658/01, the National Natural Science Foundation of China under Grant 61028008 and Grant 60974030, the National 973 Program of China under Grant 2009CB320600, the International Science and Technology Cooperation Project of China under Grant 2009DFA32050, and the Alexander von Humboldt Foundation of Germany

Error-constrained filtering for a class of nonlinear time-varying delay systems with non-gaussian noises

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 technical note, the quadratic error-constrained filtering problem is formulated and investigated for discrete time-varying nonlinear systems with state delays and non-Gaussian noises. Both the Lipschitz-like and ellipsoid-bounded nonlinearities are considered. The non-Gaussian noises are assumed to be unknown, bounded, and confined to specified ellipsoidal sets. The aim of the addressed filtering problem is to develop a recursive algorithm based on the semi-definite programme method such that, for the admissible time-delays, nonlinear parameters and external bounded noise disturbances, the quadratic estimation error is not more than a certain optimized upper bound at every time step. The filter parameters are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programme method. A simulation example is exploited to illustrate the effectiveness of the proposed design procedures.This work was supported in part by the Leverhulme Trust of the U.K., the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grant 61028008 and Grant 61074016, the Shanghai Natural Science Foundation of China under Grant 10ZR1421200, and the Alexander von Humboldt Foundation of Germany. Recommended by Associate Editor E. Fabre

Sampled-data synchronization control of dynamical networks with stochastic sampling

Copyright @ 2012 IEEEThis technical note is concerned with the sampled-data synchronization control problem for a class of dynamical networks. The sampling period considered here is assumed to be time-varying that switches between two different values in a random way with given probability. The addressed synchronization control problem is first formulated as an exponentially mean-square stabilization problem for a new class of dynamical networks that involve both the multiple probabilistic interval delays (MPIDs) and the sector-bounded nonlinearities (SBNs). Then, a novel Lyapunov functional is constructed to obtain sufficient conditions under which the dynamical network is exponentially mean-square stable. Both Gronwall's inequality and Jenson integral inequality are utilized to substantially simplify the derivation of the main results. Subsequently, a set of sampled-data synchronization controllers is designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software. Finally, a numerical simulation example is employed to show the effectiveness of the proposed sampled-data synchronization control scheme.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Natural Science Foundation of China under Grants 61028008, 60974030, 61134009 and 61104125, the National 973 Program of China under Grant 2009CB320600, and the Alexander von Humboldt Foundation of Germany

Probability-dependent gain-scheduled control for discrete stochastic delayed systems with randomly occurring nonlinearities

This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 John Wiley & Sons, Ltd.In this paper, the gain-scheduled control problem is addressed by using probability-dependent Lyapunov functions for a class of discrete-time stochastic delayed systems with randomly occurring sector nonlinearities. The sector nonlinearities are assumed to occur according to a time-varying Bernoulli distribution with measurable probability in real time. The multiplicative noises are given by means of a scalar Gaussian white noise sequence with known variances. The aim of the addressed gain-scheduled control problem is to design a controller with scheduled gains such that, for the admissible randomly occurring nonlinearities, time delays and external noise disturbances, the closed-loop system is exponentially mean-square stable. Note that the designed gain-scheduled controller is based on the measured time-varying probability and is therefore less conservative than the conventional controller with constant gains. It is shown that the time-varying controller gains can be derived in terms of the measurable probability by solving a convex optimization problem via the semi-definite programme method. A simulation example is exploited to illustrate the effectiveness of the proposed design procedures.This work was supported in part by the Leverhulme Trust of the UK, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the National Natural Science Foundation of China under Grants 61028008, 61134009, 61074016, 61104125 and 60974030, the Shanghai Natural Science Foundation of China under Grant 10ZR1421200, and the Alexander von Humboldt Foundation of Germany

Gain-constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays

This is the post-print of the Article. The official published version can be accessed from the link below - Copyright @ 2013 IEEE.This paper is concerned with the gain-constrained recursive filtering problem for a class of time-varying nonlinear stochastic systems with probabilistic sensor delays and correlated noises. The stochastic nonlinearities are described by statistical means that cover the multiplicative stochastic disturbances as a special case. The phenomenon of probabilistic sensor delays is modeled by introducing a diagonal matrix composed of Bernoulli distributed random variables taking values of 1 or 0, which means that the sensors may experience randomly occurring delays with individual delay characteristics. The process noise is finite-step autocorrelated. The purpose of the addressed gain-constrained filtering problem is to design a filter such that, for all probabilistic sensor delays, stochastic nonlinearities, gain constraint as well as correlated noises, the cost function concerning the filtering error is minimized at each sampling instant, where the filter gain satisfies a certain equality constraint. A new recursive filtering algorithm is developed that ensures both the local optimality and the unbiasedness of the designed filter at each sampling instant which achieving the pre-specified filter gain constraint. A simulation example is provided to illustrate the effectiveness of the proposed filter design approach.This work was supported in part by the National Natural Science Foundation of China by Grants 61273156, 61028008, 60825303, 61104125, and 11271103, National 973 Project by Grant 2009CB320600, the Fok Ying Tung Education Fund by Grant 111064, the Special Fund for the Author of National Excellent Doctoral Dissertation of China by Grant 2007B4, the State Key Laboratory of Integrated Automation for the Process Industry (Northeastern University) of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. by Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Probability-dependent gain-scheduled filtering for stochastic systems with missing measurements

Copyright @ 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.This brief addresses the gain-scheduled filtering problem for a class of discrete-time systems with missing measurements, nonlinear disturbances, and external stochastic noise. The missing-measurement phenomenon is assumed to occur in a random way, and the missing probability is time-varying with securable upper and lower bounds that can be measured in real time. The multiplicative noise is a state-dependent scalar Gaussian white-noise sequence with known variance. The addressed gain-scheduled filtering problem is concerned with the design of a filter such that, for the admissible random missing measurements, nonlinear parameters, and external noise disturbances, the error dynamics is exponentially mean-square stable. The desired filter is equipped with time-varying gains based primarily on the time-varying missing probability and is therefore less conservative than the traditional filter with fixed gains. It is shown that the filter parameters can be derived in terms of the measurable probability via the semidefinite program method.This work was supported in part by the Leverhulme Trust of the U.K., the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the National Natural Science Foundation of China under Grants 61028008, 61074016 and 60974030, the Shanghai Natural Science Foundation of China under Grant 10ZR1421200, and the Alexander von Humboldt Foundation of Germany

Finite-horizon H∞ control for discrete time-varying systems with randomly occurring nonlinearities and fading measurements

This technical note deals with the H∞ control problem for a class of discrete time-varying nonlinear systems with both randomly occurring nonlinearities and fading measurements over a finite-horizon. The system measurements are transmitted through fading channels described by a modified stochastic Rice fading model. The purpose of the addressed problem is to design a set of time-varying controllers such that, in the presence of channel fading and randomly occurring nonlinearities, the H∞ performance is guaranteed over a given finite-horizon. The model transformation technique is first employed to simplify the addressed problem, and then the stochastic analysis in combination with the completing squares method are carried out to obtain necessary and sufficient conditions of an auxiliary index which is closely related to the finite-horizon H∞ performance. Moreover, the time-varying controller parameters are characterized via solving coupled backward recursive Riccati difference equations (RDEs). A simulation example is utilized to illustrate the usefulness of the proposed controller design scheme

Distributed H-infinity filtering for polynomial nonlinear stochastic systems in sensor networks

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 distributed H1 filtering problem is addressed for a class of polynomial nonlinear stochastic systems in sensor networks. For a Lyapunov function candidate whose entries are polynomials, we calculate its first- and second-order derivatives in order to facilitate the use of Itos differential role. Then, a sufficient condition for the existence of a feasible solution to the addressed distributed H1 filtering problem is derived in terms of parameter-dependent linear matrix inequalities (PDLMIs). For computational convenience, these PDLMIs are further converted into a set of sums of squares (SOSs) that can be solved effectively by using the semidefinite programming technique. Finally, a numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National 973 Program of China under Grant 2009CB320600, the National Natural Science Foundation of China under Grant 60974030 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

Recent advances on filtering and control for nonlinear stochastic complex systems with incomplete information: A survey

This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2012 Hindawi PublishingSome recent advances on the filtering and control problems for nonlinear stochastic complex systems with incomplete information are surveyed. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61104125, 61028008, 61174136, 60974030, and 61074129, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, 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