In this paper, the issues of stochastic stability analysis and fault estimation are investigated for a class of continuoustime Markov jump piecewise-affine(PWA) systems against actuator and sensor faults. Firstly, a n...In this paper, the issues of stochastic stability analysis and fault estimation are investigated for a class of continuoustime Markov jump piecewise-affine(PWA) systems against actuator and sensor faults. Firstly, a novel mode-dependent PWA iterative learning observer with current feedback is designed to estimate the system states and faults, simultaneously, which contains both the previous iteration information and the current feedback mechanism. The auxiliary feedback channel optimizes the response speed of the observer, therefore the estimation error would converge to zero rapidly. Then, sufficient conditions for stochastic stability with guaranteed performance are demonstrated for the estimation error system, and the equivalence relations between the system information and the estimated information can be established via iterative accumulating representation.Finally, two illustrative examples containing a class of tunnel diode circuit systems are presented to fully demonstrate the effectiveness and superiority of the proposed iterative learning observer with current feedback.展开更多
This paper is concerned with finite-time H_(∞) filtering for Markov jump systems with uniform quantization. The objective is to design quantized mode-dependent filters to ensure that the filtering error system is not...This paper is concerned with finite-time H_(∞) filtering for Markov jump systems with uniform quantization. The objective is to design quantized mode-dependent filters to ensure that the filtering error system is not only mean-square finite-time bounded but also has a prescribed finite-time H_(∞) performance. First, the case where the switching modes of the filter align with those of the MJS is considered. A numerically tractable filter design approach is proposed utilizing a mode-dependent Lyapunov function, Schur’s complement, and Dynkin’s formula. Then, the study is extended to a scenario where the switching modes of the filter can differ from those of the MJS. To address this situation, a mode-mismatched filter design approach is developed by leveraging a hidden Markov model to describe the asynchronous mode switching and the double expectation formula. Finally, a spring system model subject to a Markov chain is employed to validate the effectiveness of the quantized filter design approaches.展开更多
In this paper,the distributed stochastic model predictive control(MPC)is proposed for the noncooperative game problem of the discrete-time multi-player systems(MPSs)with the undirected Markov jump graph.To reflect the...In this paper,the distributed stochastic model predictive control(MPC)is proposed for the noncooperative game problem of the discrete-time multi-player systems(MPSs)with the undirected Markov jump graph.To reflect the reality,the state and input constraints have been considered along with the external disturbances.An iterative algorithm is designed such that model predictive noncooperative game could converge to the socalledε-Nash equilibrium in a distributed manner.Sufficient conditions are established to guarantee the convergence of the proposed algorithm.In addition,a set of easy-to-check conditions are provided to ensure the mean-square uniform bounded stability of the underlying MPSs.Finally,a numerical example on a group of spacecrafts is studied to verify the effectiveness of the proposed method.展开更多
We investigate the problem of H_(∞) state estimation for discrete-time Markov jump neural networks. The transition probabilities of the Markov chain are assumed to be piecewise time-varying, and the persistent dwell-...We investigate the problem of H_(∞) state estimation for discrete-time Markov jump neural networks. The transition probabilities of the Markov chain are assumed to be piecewise time-varying, and the persistent dwell-time switching rule,as a more general switching rule, is adopted to describe this variation characteristic. Afterwards, based on the classical Lyapunov stability theory, a Lyapunov function is established, in which the information about the Markov jump feature of the system mode and the persistent dwell-time switching of the transition probabilities is considered simultaneously.Furthermore, via using the stochastic analysis method and some advanced matrix transformation techniques, some sufficient conditions are obtained such that the estimation error system is mean-square exponentially stable with an H_(∞) performance level, from which the specific form of the estimator can be obtained. Finally, the rationality and effectiveness of the obtained results are verified by a numerical example.展开更多
This paper studies the nonstationary filtering problem of Markov jump system under <span style="white-space:nowrap;"><i>l</i><sub>2</sub> - <i>l</i><sub>...This paper studies the nonstationary filtering problem of Markov jump system under <span style="white-space:nowrap;"><i>l</i><sub>2</sub> - <i>l</i><sub>∞</sub> </span>performance. Due to the difference in propagation channels, signal strength and phase will inevitably change randomly and cause the waste of signals resources. In response to this problem, a channel fading model with multiplicative noise is introduced. And then a nonstationary filter, which receives signals more efficiently is designed. Meanwhile Lyapunov function is constructed for error analysis. Finally, the gain matrix for filtering is obtained by solving the matrix inequality, and the results showed that the nonstationary filter converges to the stable point more quickly than the traditional asynchronous filter, the stability of the designed filter is verified.展开更多
This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems (MJSs) with uncertain parameters and multiple time-delays. The delays are respectively considered as constant ...This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems (MJSs) with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities (LMIs), which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.展开更多
The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback me...The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures. The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities (LMIs). A numerical example is also given to illustrate the design procedures and their effectiveness.展开更多
The robust H∞ control problems for stochastic fuzzy neutral Markov jump systems(MJSs) with parameters uncertainties and multiple time-delays are considered.The delays are respectively considered as constant and time ...The robust H∞ control problems for stochastic fuzzy neutral Markov jump systems(MJSs) with parameters uncertainties and multiple time-delays are considered.The delays are respectively considered as constant and time varying,and the uncertain parameters are assumed to be norm bounded.By means of Takagi-Sugeno fuzzy models,the overall closed-loop fuzzy dynamics are constructed through selected membership functions.By selecting the appropriate Lyapunov-Krasovskii functions,the sufficient condition is given such that the uncertain fuzzy neutral MJSs are stochastically stability for all admissible uncertainties and satisfies the given H∞ control index.The stability and H∞ control criteria are formulated in the form of linear matrix inequalities,which can be easily checked in practice.Practical examples illustrate the effectiveness of the developed techniques.展开更多
This study is concerned with the problem of finite-time H∞ filter design for uncertain discrete-time Markov Jump stochastic systems. Our attention is focused on the design of mode-dependent H∞ filter to ensure the f...This study is concerned with the problem of finite-time H∞ filter design for uncertain discrete-time Markov Jump stochastic systems. Our attention is focused on the design of mode-dependent H∞ filter to ensure the finite-time stability of the filtering error system and preserve a prescribed H∞ performance level for all admissible uncertainties. Sufficient conditions of filtering design for the system under consideration are developed and the corresponding filter parameters can be achieved in terms of linear matrix inequalities (LMI). Finally, a numerical example is provided to illustrate the validity of the proposed method.展开更多
This paper investigates the stochastic stability of discrete time positive Markov jump nonlinear systems(PMJNS).Some definitions on stochastic stability for discrete time PMJNS are introduced first.Then,using the mult...This paper investigates the stochastic stability of discrete time positive Markov jump nonlinear systems(PMJNS).Some definitions on stochastic stability for discrete time PMJNS are introduced first.Then,using the multiply max-separable Lyapunov function method,some stochastic stability criterions of discrete time PMJNS are provided,and some corresponding criterions are also provided for discrete time positive Markov jump linear systems(PMJLS).Different from previous conclusions that require subsystems to be stable or marginally stable,the obtained results allow some subsystems to be unstable.Based on the proposed criterions,the stochastic stability behavior of discrete time positive Markov jump systems can be obtained just from the algebraic properties of the system function and the probability characteristics of the Markov chain.To illustrate the main results,two simulation examples are provided at the end.展开更多
This paper investigates the static output feedback secure control problem for discrete-time hidden Markov jump systems against replay attacks. The main purpose is to realise that closed-loopsystems are stochastically ...This paper investigates the static output feedback secure control problem for discrete-time hidden Markov jump systems against replay attacks. The main purpose is to realise that closed-loopsystems are stochastically stable with or without replay attacks. Firstly, the tampered sensorsunder replay attacks can be identified via the proposed detection method. Then, an asynchronousstatic output feedback controller is designed, which can eliminate the negative impactcaused by replay attacks in view of the detection results. Based on the linear matrix inequalitytechnique, some sufficient conditions which ensure the closed-loop systems are stochasticallystable and meet a given H∞ performance are established. Finally, a numerical example and apractical example are given to verify the effectiveness and superiority of the proposed method.展开更多
This paper is concerned with state estimation problem for Markov jump linear systems where the disturbances involved in the systems equations and measurement equations are assumed to be Gaussian noise sequences.Based ...This paper is concerned with state estimation problem for Markov jump linear systems where the disturbances involved in the systems equations and measurement equations are assumed to be Gaussian noise sequences.Based on two properties of conditional expectation,orthogonal projective theorem is applied to the state estimation problem of the considered systems so that a novel suboptimal algorithm is obtained.The novelty of the algorithm lies in using orthogonal projective theorem instead of Kalman filters to estimate the state.A numerical comparison of the algorithm with the interacting multiple model algorithm is given to illustrate the effectiveness of the proposed algorithm.展开更多
This paper investigates Nash games for a class of linear stochastic systems governed by Itô’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon.First,stoc...This paper investigates Nash games for a class of linear stochastic systems governed by Itô’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon.First,stochastic Nash games are formulated by applying the results of indefinite stochastic linear quadratic(LQ)control problems.Second,in order to obtain Nash equilibrium strategies,crosscoupled stochastic Riccati differential(algebraic)equations(CSRDEs and CSRAEs)are derived.Moreover,in order to demonstrate the validity of the obtained results,stochastic H2/H∞control with state-and control-dependent noise is discussed as an immediate application.Finally,a numerical example is provided.展开更多
Identity by descent(IBD)sharing is a very important genomic feature in population genetics which can be used to reconstruct recent demographic history.In this paper we provide a framework to estimate IBD sharing for a...Identity by descent(IBD)sharing is a very important genomic feature in population genetics which can be used to reconstruct recent demographic history.In this paper we provide a framework to estimate IBD sharing for a demographic model called two-population model with migration.We adopt the structured coalescent theory and use a continuous-time Markov jump process{X(t),t≥0}to describe the genealogical process in such model.Then we apply Kolmogorov backward equation to calculate the distribution of coalescence time and develop a formula for estimating the IBD sharing.The simulation studies show that our method to estimate IBD sharing for this demographic model is robust and accurate.展开更多
This paper researches the strict dissipative control problem for uncertain fuzzy neutral Markov jump systems by Takagi-Sugeno fuzzy rules.The asynchronous phenomenon is considered between the uncertain fuzzy neutral M...This paper researches the strict dissipative control problem for uncertain fuzzy neutral Markov jump systems by Takagi-Sugeno fuzzy rules.The asynchronous phenomenon is considered between the uncertain fuzzy neutral Markov jump systems modes and asynchronous fuzzy P-D feedback controller modes,which is described by a hidden Markov model.Via using linear matrix inequalities,the desired asynchronous fuzzy P-D feedback controller is obtained,which can ensure that the closed-loop uncertain fuzzy neutral Markov jump systems satisfies robustly exponential mean square stabilization with strict dissipativity.A numerical example and a single-link robot arm are utilized to demonstrate the effectiveness of the method.展开更多
基金supported in part by the National Natural Science Foundation of China (62222310, U1813201, 61973131, 62033008)the Research Fund for the Taishan Scholar Project of Shandong Province of China+2 种基金the NSFSD(ZR2022ZD34)Japan Society for the Promotion of Science (21K04129)Fujian Outstanding Youth Science Fund (2020J06022)。
文摘In this paper, the issues of stochastic stability analysis and fault estimation are investigated for a class of continuoustime Markov jump piecewise-affine(PWA) systems against actuator and sensor faults. Firstly, a novel mode-dependent PWA iterative learning observer with current feedback is designed to estimate the system states and faults, simultaneously, which contains both the previous iteration information and the current feedback mechanism. The auxiliary feedback channel optimizes the response speed of the observer, therefore the estimation error would converge to zero rapidly. Then, sufficient conditions for stochastic stability with guaranteed performance are demonstrated for the estimation error system, and the equivalence relations between the system information and the estimated information can be established via iterative accumulating representation.Finally, two illustrative examples containing a class of tunnel diode circuit systems are presented to fully demonstrate the effectiveness and superiority of the proposed iterative learning observer with current feedback.
基金Project supported by the Natural Science Foundation of the Anhui Higher Education Institutions (Grant Nos. KJ2020A0248 and 2022AH050310)。
文摘This paper is concerned with finite-time H_(∞) filtering for Markov jump systems with uniform quantization. The objective is to design quantized mode-dependent filters to ensure that the filtering error system is not only mean-square finite-time bounded but also has a prescribed finite-time H_(∞) performance. First, the case where the switching modes of the filter align with those of the MJS is considered. A numerically tractable filter design approach is proposed utilizing a mode-dependent Lyapunov function, Schur’s complement, and Dynkin’s formula. Then, the study is extended to a scenario where the switching modes of the filter can differ from those of the MJS. To address this situation, a mode-mismatched filter design approach is developed by leveraging a hidden Markov model to describe the asynchronous mode switching and the double expectation formula. Finally, a spring system model subject to a Markov chain is employed to validate the effectiveness of the quantized filter design approaches.
基金This work was supported by the National Natural Science Foundation of China(62122063,62073268,U22B2036,11931015)the Young Star of Science and Technology in Shaanxi Province(2020KJXX-078)+1 种基金the National Science Fund for Distinguished Young Scholars(62025602)the XPLORER PRIZE。
文摘In this paper,the distributed stochastic model predictive control(MPC)is proposed for the noncooperative game problem of the discrete-time multi-player systems(MPSs)with the undirected Markov jump graph.To reflect the reality,the state and input constraints have been considered along with the external disturbances.An iterative algorithm is designed such that model predictive noncooperative game could converge to the socalledε-Nash equilibrium in a distributed manner.Sufficient conditions are established to guarantee the convergence of the proposed algorithm.In addition,a set of easy-to-check conditions are provided to ensure the mean-square uniform bounded stability of the underlying MPSs.Finally,a numerical example on a group of spacecrafts is studied to verify the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China (Grant Nos. 61873002, 61703004, 61973199, 61573008, and 61973200)。
文摘We investigate the problem of H_(∞) state estimation for discrete-time Markov jump neural networks. The transition probabilities of the Markov chain are assumed to be piecewise time-varying, and the persistent dwell-time switching rule,as a more general switching rule, is adopted to describe this variation characteristic. Afterwards, based on the classical Lyapunov stability theory, a Lyapunov function is established, in which the information about the Markov jump feature of the system mode and the persistent dwell-time switching of the transition probabilities is considered simultaneously.Furthermore, via using the stochastic analysis method and some advanced matrix transformation techniques, some sufficient conditions are obtained such that the estimation error system is mean-square exponentially stable with an H_(∞) performance level, from which the specific form of the estimator can be obtained. Finally, the rationality and effectiveness of the obtained results are verified by a numerical example.
文摘This paper studies the nonstationary filtering problem of Markov jump system under <span style="white-space:nowrap;"><i>l</i><sub>2</sub> - <i>l</i><sub>∞</sub> </span>performance. Due to the difference in propagation channels, signal strength and phase will inevitably change randomly and cause the waste of signals resources. In response to this problem, a channel fading model with multiplicative noise is introduced. And then a nonstationary filter, which receives signals more efficiently is designed. Meanwhile Lyapunov function is constructed for error analysis. Finally, the gain matrix for filtering is obtained by solving the matrix inequality, and the results showed that the nonstationary filter converges to the stable point more quickly than the traditional asynchronous filter, the stability of the designed filter is verified.
基金supported by the National Natural Science Foundation of China (No.60574001)Program for New Century Excellent Talents in University (No.050485)Program for Innovative Research Team of Jiangnan University
文摘This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems (MJSs) with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities (LMIs), which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.
基金the National Natural Science Foundation of China (60574001)Program for New Century Excellent Talents in University (05-0485)Program for Innovative Research Team of Jiangnan University
文摘The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures. The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities (LMIs). A numerical example is also given to illustrate the design procedures and their effectiveness.
基金supported by the National Natural Science Foundation of China (6097400160904045)+2 种基金the National Natural Science Foundation of Jiangsu Province (BK2009068)the Six Projects Sponsoring Talent Summits of Jiangsu Provincethe Program for Postgraduate Scientific Research and Innovation of Jiangsu Province
文摘The robust H∞ control problems for stochastic fuzzy neutral Markov jump systems(MJSs) with parameters uncertainties and multiple time-delays are considered.The delays are respectively considered as constant and time varying,and the uncertain parameters are assumed to be norm bounded.By means of Takagi-Sugeno fuzzy models,the overall closed-loop fuzzy dynamics are constructed through selected membership functions.By selecting the appropriate Lyapunov-Krasovskii functions,the sufficient condition is given such that the uncertain fuzzy neutral MJSs are stochastically stability for all admissible uncertainties and satisfies the given H∞ control index.The stability and H∞ control criteria are formulated in the form of linear matrix inequalities,which can be easily checked in practice.Practical examples illustrate the effectiveness of the developed techniques.
文摘This study is concerned with the problem of finite-time H∞ filter design for uncertain discrete-time Markov Jump stochastic systems. Our attention is focused on the design of mode-dependent H∞ filter to ensure the finite-time stability of the filtering error system and preserve a prescribed H∞ performance level for all admissible uncertainties. Sufficient conditions of filtering design for the system under consideration are developed and the corresponding filter parameters can be achieved in terms of linear matrix inequalities (LMI). Finally, a numerical example is provided to illustrate the validity of the proposed method.
基金supported by the Shandong Provincial Natural Science Foundation,China under Grant No.ZR2017JL028。
文摘This paper investigates the stochastic stability of discrete time positive Markov jump nonlinear systems(PMJNS).Some definitions on stochastic stability for discrete time PMJNS are introduced first.Then,using the multiply max-separable Lyapunov function method,some stochastic stability criterions of discrete time PMJNS are provided,and some corresponding criterions are also provided for discrete time positive Markov jump linear systems(PMJLS).Different from previous conclusions that require subsystems to be stable or marginally stable,the obtained results allow some subsystems to be unstable.Based on the proposed criterions,the stochastic stability behavior of discrete time positive Markov jump systems can be obtained just from the algebraic properties of the system function and the probability characteristics of the Markov chain.To illustrate the main results,two simulation examples are provided at the end.
基金supported by the National Natural Science Foundation of China [grant number 62103005]the Major NaturalScience Foundation of Higher Education Institutionsof Anhui Province [grant number KJ2020ZD28]+3 种基金the MajorTechnologies Research and Development Special Program ofAnhui Province under Grant 202003a05020001the NaturalScience Foundation of Anhui Provincial Natural ScienceFoundation [grant number 2108085QF276]the Key researchand development projects of Anhui Province [grant number202104a05020015]the Opening Project of Key Laboratoryof Power Electronics and Motion Control of Anhui HigherEducation Institutions [grant number OP14100135].
文摘This paper investigates the static output feedback secure control problem for discrete-time hidden Markov jump systems against replay attacks. The main purpose is to realise that closed-loopsystems are stochastically stable with or without replay attacks. Firstly, the tampered sensorsunder replay attacks can be identified via the proposed detection method. Then, an asynchronousstatic output feedback controller is designed, which can eliminate the negative impactcaused by replay attacks in view of the detection results. Based on the linear matrix inequalitytechnique, some sufficient conditions which ensure the closed-loop systems are stochasticallystable and meet a given H∞ performance are established. Finally, a numerical example and apractical example are given to verify the effectiveness and superiority of the proposed method.
基金supported by the National Natural Science Foundation of China (No. 50977008,60521003,60774048)
文摘This paper is concerned with state estimation problem for Markov jump linear systems where the disturbances involved in the systems equations and measurement equations are assumed to be Gaussian noise sequences.Based on two properties of conditional expectation,orthogonal projective theorem is applied to the state estimation problem of the considered systems so that a novel suboptimal algorithm is obtained.The novelty of the algorithm lies in using orthogonal projective theorem instead of Kalman filters to estimate the state.A numerical comparison of the algorithm with the interacting multiple model algorithm is given to illustrate the effectiveness of the proposed algorithm.
基金supported by the National Natural Science Foundation of China(No.71171061)China Postdoctoral Science Foundation(No.2014M552177)+2 种基金the Natural Science Foundation of Guangdong Province(No.S2011010004970)the Doctors Start-up Project of Guangdong University of Technology(No.13ZS0031)the 2014 Guangzhou Philosophy and Social Science Project(No.14Q21).
文摘This paper investigates Nash games for a class of linear stochastic systems governed by Itô’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon.First,stochastic Nash games are formulated by applying the results of indefinite stochastic linear quadratic(LQ)control problems.Second,in order to obtain Nash equilibrium strategies,crosscoupled stochastic Riccati differential(algebraic)equations(CSRDEs and CSRAEs)are derived.Moreover,in order to demonstrate the validity of the obtained results,stochastic H2/H∞control with state-and control-dependent noise is discussed as an immediate application.Finally,a numerical example is provided.
基金supported by the Fundamental Research Funds for the Central Universities(2020RC001)。
文摘Identity by descent(IBD)sharing is a very important genomic feature in population genetics which can be used to reconstruct recent demographic history.In this paper we provide a framework to estimate IBD sharing for a demographic model called two-population model with migration.We adopt the structured coalescent theory and use a continuous-time Markov jump process{X(t),t≥0}to describe the genealogical process in such model.Then we apply Kolmogorov backward equation to calculate the distribution of coalescence time and develop a formula for estimating the IBD sharing.The simulation studies show that our method to estimate IBD sharing for this demographic model is robust and accurate.
基金supported by the National Natural Science Foundation of China under Grant Nos.62173174,61773191,61973148,62003154Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions under Grant No.2019KJI010+2 种基金the Natural Science Foundation of Shandong Province for Outstanding Young Talents in Provincial Universities under Grant No.ZR2016JL025Undergraduate Education Reform Project of higher Education in Shandong Province under Grant No.M2018X047Liaocheng University Education Reform Project Foundation under Grant Nos.G201811,26322170267。
文摘This paper researches the strict dissipative control problem for uncertain fuzzy neutral Markov jump systems by Takagi-Sugeno fuzzy rules.The asynchronous phenomenon is considered between the uncertain fuzzy neutral Markov jump systems modes and asynchronous fuzzy P-D feedback controller modes,which is described by a hidden Markov model.Via using linear matrix inequalities,the desired asynchronous fuzzy P-D feedback controller is obtained,which can ensure that the closed-loop uncertain fuzzy neutral Markov jump systems satisfies robustly exponential mean square stabilization with strict dissipativity.A numerical example and a single-link robot arm are utilized to demonstrate the effectiveness of the method.