In this paper,we propose a neural network approach to learn the parameters of a class of stochastic Lotka-Volterra systems.Approximations of the mean and covariance matrix of the observational variables are obtained f...In this paper,we propose a neural network approach to learn the parameters of a class of stochastic Lotka-Volterra systems.Approximations of the mean and covariance matrix of the observational variables are obtained from the Euler-Maruyama discretization of the underlying stochastic differential equations(SDEs),based on which the loss function is built.The stochastic gradient descent method is applied in the neural network training.Numerical experiments demonstrate the effectiveness of our method.展开更多
In this paper, we investigate the decentralized stabilization of some time-varying uncertain large-scale stochastic systems with delays under matching conditions. A type of decentralized controllers with guaranteed s...In this paper, we investigate the decentralized stabilization of some time-varying uncertain large-scale stochastic systems with delays under matching conditions. A type of decentralized controllers with guaranteed stabilization and sub-optimality are also given.展开更多
The problem of robust H_∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabil...The problem of robust H_∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method.Then,a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality（BMI）,which ensures a prescribed stochastic robust H_∞ performance level for the resulting closed-loop system with nonzero disturbance input and for all admissible uncertainties.An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.展开更多
The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay. Although the exponential stability of impulsive stochastic delay systems has been discusse...The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay. Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors, few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems. Firstly, the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem. Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive effects. The obtained results show that the system will stable if the impulses＇ frequency and amplitude are suitably related to the increase or decrease of the continuous flows, and impulses may be used as controllers to stabilize the underlying stochastic system. Numerical examples are given to show the effectiveness of the results.展开更多
The mean-square exponential stability problem is investigated for a class of stochastic time-varying delay systems with Markovian jumping parameters. By decomposing the delay interval into multiple equidistant subinte...The mean-square exponential stability problem is investigated for a class of stochastic time-varying delay systems with Markovian jumping parameters. By decomposing the delay interval into multiple equidistant subintervals, a new delay-dependent and decay-rate-dependent criterion is presented based on constructing a novel Lyapunov functional and employing stochastic analysis technique. Besides, the decay rate has no conventional constraint and can be selected according to different practical conditions. Finally, two numerical examples are provided to show that the obtained result has less conservatism than some existing ones in the literature.展开更多
The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen＇s integral inequality and com...The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen＇s integral inequality and combining with the free weighting matrix approach, new delay-dependent stability conditions and delayed state feedback stabilization criteria are obtained in terms of linear matrix inequalities. Meanwhile, the proposed delayed state feedback stabilization criteria are more convenient in application than the existing ones since fewer tuning parameters are involved. Numerical examples are given to illustrate the effectiveness of the proposed methods.展开更多
A new adaptive neural network（NN） output-feedback stabilization controller is investigated for a class of uncertain stochastic nonlinear strict-feedback systems with discrete and distributed time-varying delays and ...A new adaptive neural network（NN） output-feedback stabilization controller is investigated for a class of uncertain stochastic nonlinear strict-feedback systems with discrete and distributed time-varying delays and unknown nonlinear functions in both drift and diffusion terms.First,an extensional stability notion and the related criterion are introduced.Then,a nonlinear observer to estimate the unmeasurable states is designed,and a systematic backstepping procedure to design an adaptive NN output-feedback controller is proposed such that the closed-loop system is stable in probability.The effectiveness of the proposed control scheme is demonstrated via a numerical example.展开更多
A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimiza...A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.展开更多
To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system wi...To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.展开更多
The exponential stability in mean square and stabiliza- tion problems for It＆ stochastic switched systems with multiple time-delays are investigated. The system possesses the norm- bounded uncertainties and Markovian...The exponential stability in mean square and stabiliza- tion problems for It＆ stochastic switched systems with multiple time-delays are investigated. The system possesses the norm- bounded uncertainties and Markovian jumping parameters. By using an effective descriptor model transformation of the system and applying Ito＇s differential formula and Moon＇s inequality for bounding cross terms, a new delay-dependent sufficient condi- tion is derived in terms of linear matrix inequalities, and its states feedback controller is designed. Numerical examples are given to illustrate the efficiency and less conservation of the results.展开更多
This paper is concerned with the global boundedness problem for a class of stochastic nonlinear systems with matched conditions. The uncertainties in the systems are due to parameter variations and external stochastic...This paper is concerned with the global boundedness problem for a class of stochastic nonlinear systems with matched conditions. The uncertainties in the systems are due to parameter variations and external stochastic disturbance. Only the matched conditions and the possible bound of the uncertainties are demanded. Based on the stochastic Lyapunov stability theory, an explicit controller is constructed in the gradient direction, which renders responses of the closed-loop systems be globally bounded in probability. When the systems degrade to linear systems, the controller becomes linear. Illustrative examples are given to show the effectiveness of the proposed method.展开更多
Advanced traveler information systems （ATIS） can not only improve drivers＇ accessibility to the more accurate route travel time information, but also can improve drivers＇ adaptability to the stochastic network cap...Advanced traveler information systems （ATIS） can not only improve drivers＇ accessibility to the more accurate route travel time information, but also can improve drivers＇ adaptability to the stochastic network capacity degradations. In this paper, a mixed stochastic user equilibrium model was proposed to describe the interactive route choice behaviors between ATIS equipped and unequipped drivers on a degradable transport network. In the proposed model the information accessibility of equipped drivers was reflected by lower degree of uncertainty in their stochastic equilibrium flow distributions, and their behavioral adaptability was captured by multiple equilibrium behaviors over the stochastic network state set. The mixed equilibrium model was formulated as a fixed point problem defined in the mixed route flows, and its solution was achieved by executing an iterative algorithm. Numerical experiments were provided to verify the properties of the mixed network equilibrium model and the efficiency of the iterative algorithm.展开更多
The problem of track control is studied for a class of strict-feedback stochastic nonlinear systems in which unknown virtual control gain function is the main feature. First, the so-called stochastic LaSalle theory is...The problem of track control is studied for a class of strict-feedback stochastic nonlinear systems in which unknown virtual control gain function is the main feature. First, the so-called stochastic LaSalle theory is extended to some extent, and accordingly, the results of global ultimate boundedness for stochastic nonlinear systems are developed. Next, a new design scheme of fuzzy adaptive control is proposed. The advantage of it is that it does not require priori knowledge of virtual control gain function sign, which is usually demanded in many designs. At the same time, the track performance of closed-loop systems is improved by adaptive modifying the estimated error upper bound. By theoretical analysis, the signals of closed-loop systems are globally ultimately bounded in probability and the track error converges to a small residual set around the origin in 4th-power expectation.展开更多
Compared with the classical Markov repairable system, the Markov repairable system with stochastic regimes switching introduced in the paper provides a more realistic description of the practical system. The system ca...Compared with the classical Markov repairable system, the Markov repairable system with stochastic regimes switching introduced in the paper provides a more realistic description of the practical system. The system can be used to model the dynamics of a repairable system whose performance regimes switch according to the external conditions. For example, to satisfy the demand variation that is typical for the power and communication systems and reduce the cost, these systems usually adjust their operating regimes. The transition rate matrices under distinct operating regimes are assumed to be different and the sojourn times in distinct regimes are governed by a finite state Markov chain. By using the theory of Markov process, Ion channel theory, and Laplace transforms, the up time of the system are studied. A numerical example is given to illustrate the obtained results. The effect of sojourn times in distinct regimes on the availability and the up time are also discussed in the numerical example.展开更多
This paper proposes a predictive compensation strategy to reduce the detrimental effect of stochastic time delays induced by communication networks on control performance. Values of a manipulated variable at the prese...This paper proposes a predictive compensation strategy to reduce the detrimental effect of stochastic time delays induced by communication networks on control performance. Values of a manipulated variable at the present sampling instant and future time instants can be determined by performing a receding horizon optimal procedure only once. When the present value of the manipulated variable does not arrive at a smart actuator, its predictive one is imposed to the corresponding process. Switching of a manipulated variable between its true present value and the predictive one usually results in unsmooth operation of a control system. This paper shows: 1) for a steady process,as long as its input is sufficiently smooth, the smoothness of its output can be guaranteed; 2) a manipulated variable can be switched smoothly by filtering the manipulated variable just using a simple low-pass filter. Thus the control performance can be improved. Finally, the effectiveness of the proposed method is demonstrated by simulation study.展开更多
A robust dissipative control problem for a class of It-type stochastic systems is discussed with Markovian jumping parameters and time-varying delay. A memoryless state feedback dissipative controller is developed bas...A robust dissipative control problem for a class of It-type stochastic systems is discussed with Markovian jumping parameters and time-varying delay. A memoryless state feedback dissipative controller is developed based on Lyapunov-Krasovskii functional approach such that the closed-loop system is robustly stochastically stable and weakly delay-dependent （RSSWDD） and strictly （Q, S, R）-dissipative. The sufficient condition on the existence of state feedback dissipative controller is presented by linear matrix inequality （LMI）. And the desired controller can be concluded as solving a set of LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.展开更多
基金Supported by the National Natural Science Foundation of China(11971458,11471310)。
文摘In this paper,we propose a neural network approach to learn the parameters of a class of stochastic Lotka-Volterra systems.Approximations of the mean and covariance matrix of the observational variables are obtained from the Euler-Maruyama discretization of the underlying stochastic differential equations(SDEs),based on which the loss function is built.The stochastic gradient descent method is applied in the neural network training.Numerical experiments demonstrate the effectiveness of our method.
基金This project was supported by the National Natural Science Foundation of China (No. 69874015) and Natural Science Foundation of
文摘In this paper, we investigate the decentralized stabilization of some time-varying uncertain large-scale stochastic systems with delays under matching conditions. A type of decentralized controllers with guaranteed stabilization and sub-optimality are also given.
基金supported by the National Natural Science Foundation of China(607404306646087403160904060)
文摘The problem of robust H_∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method.Then,a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality（BMI）,which ensures a prescribed stochastic robust H_∞ performance level for the resulting closed-loop system with nonzero disturbance input and for all admissible uncertainties.An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.
基金supported by the National Natural Science Foundation of China (60874114)the Fundamental Research Funds for the Central Universities, South China University of Technology (SCUT)(2009ZM0140)
文摘The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay. Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors, few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems. Firstly, the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem. Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive effects. The obtained results show that the system will stable if the impulses＇ frequency and amplitude are suitably related to the increase or decrease of the continuous flows, and impulses may be used as controllers to stabilize the underlying stochastic system. Numerical examples are given to show the effectiveness of the results.
基金Supported by National Natural Science Foundation of China （60425310, 60574014）, the Doctor Subject Foundation of China （20050533015, 200805330004）, the Program for New Century Excellent Talents in University （NCET-06-0679）, and the Natural Science Foundation of Hunan Province （08JJ1010）
基金supported by the Program for New Century Excellent Talents in University, the Graduate Innovation Program of Jiangsu Province (CX06B-051Z)the Scientific Research Foundation of Graduate School of Southeast University (YBJJ0929)
文摘The mean-square exponential stability problem is investigated for a class of stochastic time-varying delay systems with Markovian jumping parameters. By decomposing the delay interval into multiple equidistant subintervals, a new delay-dependent and decay-rate-dependent criterion is presented based on constructing a novel Lyapunov functional and employing stochastic analysis technique. Besides, the decay rate has no conventional constraint and can be selected according to different practical conditions. Finally, two numerical examples are provided to show that the obtained result has less conservatism than some existing ones in the literature.
基金supported by the National Natural Science Foundation of China(10971232)the Natural Science Foundation of Guangdong Province(101510090010000398351009001000002)
文摘The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen＇s integral inequality and combining with the free weighting matrix approach, new delay-dependent stability conditions and delayed state feedback stabilization criteria are obtained in terms of linear matrix inequalities. Meanwhile, the proposed delayed state feedback stabilization criteria are more convenient in application than the existing ones since fewer tuning parameters are involved. Numerical examples are given to illustrate the effectiveness of the proposed methods.
基金supported by the National Natural Science Fundation of China (6080402160974139+3 种基金61075117)the Fundamental Research Funds for the Central Universities (JY10000970001K5051070000272103676)
文摘A new adaptive neural network（NN） output-feedback stabilization controller is investigated for a class of uncertain stochastic nonlinear strict-feedback systems with discrete and distributed time-varying delays and unknown nonlinear functions in both drift and diffusion terms.First,an extensional stability notion and the related criterion are introduced.Then,a nonlinear observer to estimate the unmeasurable states is designed,and a systematic backstepping procedure to design an adaptive NN output-feedback controller is proposed such that the closed-loop system is stable in probability.The effectiveness of the proposed control scheme is demonstrated via a numerical example.
基金supported by the National Natural Science Fundation of China(61273127)the Specialized Research Fund of the Doctoral Program in Higher Education(20106118110009+2 种基金20116118110008)the Scientific Research Plan Projects of Shaanxi Education Department(12JK0524)the Young Teachers Scientific Research Fund of Xi’an University of Posts and Telecommunications(1100434)
文摘A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.
基金the National Natural Science Foundation of China (60574088,60274014).
文摘To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.
文摘The exponential stability in mean square and stabiliza- tion problems for It＆ stochastic switched systems with multiple time-delays are investigated. The system possesses the norm- bounded uncertainties and Markovian jumping parameters. By using an effective descriptor model transformation of the system and applying Ito＇s differential formula and Moon＇s inequality for bounding cross terms, a new delay-dependent sufficient condi- tion is derived in terms of linear matrix inequalities, and its states feedback controller is designed. Numerical examples are given to illustrate the efficiency and less conservation of the results.
基金supported by the National Natural Science Foundation of China(61304020)
文摘This paper is concerned with the global boundedness problem for a class of stochastic nonlinear systems with matched conditions. The uncertainties in the systems are due to parameter variations and external stochastic disturbance. Only the matched conditions and the possible bound of the uncertainties are demanded. Based on the stochastic Lyapunov stability theory, an explicit controller is constructed in the gradient direction, which renders responses of the closed-loop systems be globally bounded in probability. When the systems degrade to linear systems, the controller becomes linear. Illustrative examples are given to show the effectiveness of the proposed method.
基金Projects(51378119,51578150)supported by the National Natural Science Foundation of China
文摘Advanced traveler information systems （ATIS） can not only improve drivers＇ accessibility to the more accurate route travel time information, but also can improve drivers＇ adaptability to the stochastic network capacity degradations. In this paper, a mixed stochastic user equilibrium model was proposed to describe the interactive route choice behaviors between ATIS equipped and unequipped drivers on a degradable transport network. In the proposed model the information accessibility of equipped drivers was reflected by lower degree of uncertainty in their stochastic equilibrium flow distributions, and their behavioral adaptability was captured by multiple equilibrium behaviors over the stochastic network state set. The mixed equilibrium model was formulated as a fixed point problem defined in the mixed route flows, and its solution was achieved by executing an iterative algorithm. Numerical experiments were provided to verify the properties of the mixed network equilibrium model and the efficiency of the iterative algorithm.
基金Supported by National Natural Science Foundation of P. R. China (60572070, 60325311, 60534010) Natural Science Foundation of Liaoning Province (20022030)
文摘The problem of track control is studied for a class of strict-feedback stochastic nonlinear systems in which unknown virtual control gain function is the main feature. First, the so-called stochastic LaSalle theory is extended to some extent, and accordingly, the results of global ultimate boundedness for stochastic nonlinear systems are developed. Next, a new design scheme of fuzzy adaptive control is proposed. The advantage of it is that it does not require priori knowledge of virtual control gain function sign, which is usually demanded in many designs. At the same time, the track performance of closed-loop systems is improved by adaptive modifying the estimated error upper bound. By theoretical analysis, the signals of closed-loop systems are globally ultimately bounded in probability and the track error converges to a small residual set around the origin in 4th-power expectation.
基金supported by the National Natural Science Foundation of China (71071020 60705036)Beijing Excellent Doctoral Dissertation Instructor Project of Humanities and Social Sciences(yb20091000701)
文摘Compared with the classical Markov repairable system, the Markov repairable system with stochastic regimes switching introduced in the paper provides a more realistic description of the practical system. The system can be used to model the dynamics of a repairable system whose performance regimes switch according to the external conditions. For example, to satisfy the demand variation that is typical for the power and communication systems and reduce the cost, these systems usually adjust their operating regimes. The transition rate matrices under distinct operating regimes are assumed to be different and the sojourn times in distinct regimes are governed by a finite state Markov chain. By using the theory of Markov process, Ion channel theory, and Laplace transforms, the up time of the system are studied. A numerical example is given to illustrate the obtained results. The effect of sojourn times in distinct regimes on the availability and the up time are also discussed in the numerical example.
基金Supported by National Natural Science Foundation of China （60774010）, Program for New Century Excellent Talents in University of China （NCET-05-0607）, Program for Summit of Six Types of Talents of Jiangsu Province （07-A-020）, and Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province （07KJB510114）
文摘适应州反馈的稳定为在的高顺序的随机的非线性的系统的一个类被调查函数 fi 的上面的界限(?? 铄吗？？
基金Supported by National Natural Science Foundation of China （10571036） the Key Discipline Development Program of Beijing Municipal Commission （XK100080537）
基金Supported by National High Technology Research and Development Program of P. R. China (2002AA412510)National Natural Science Foundation of P. R. China (60274034)
文摘This paper proposes a predictive compensation strategy to reduce the detrimental effect of stochastic time delays induced by communication networks on control performance. Values of a manipulated variable at the present sampling instant and future time instants can be determined by performing a receding horizon optimal procedure only once. When the present value of the manipulated variable does not arrive at a smart actuator, its predictive one is imposed to the corresponding process. Switching of a manipulated variable between its true present value and the predictive one usually results in unsmooth operation of a control system. This paper shows: 1) for a steady process,as long as its input is sufficiently smooth, the smoothness of its output can be guaranteed; 2) a manipulated variable can be switched smoothly by filtering the manipulated variable just using a simple low-pass filter. Thus the control performance can be improved. Finally, the effectiveness of the proposed method is demonstrated by simulation study.
基金supported in part by the National Natural Science Foundation of China (60874045 60904030)+1 种基金the Foundation of the Education Bureau of Jiangsu Province (09KJB510019)the Natural Science Foundation of Jiangsu Province (BK2009184)
文摘A robust dissipative control problem for a class of It-type stochastic systems is discussed with Markovian jumping parameters and time-varying delay. A memoryless state feedback dissipative controller is developed based on Lyapunov-Krasovskii functional approach such that the closed-loop system is robustly stochastically stable and weakly delay-dependent （RSSWDD） and strictly （Q, S, R）-dissipative. The sufficient condition on the existence of state feedback dissipative controller is presented by linear matrix inequality （LMI）. And the desired controller can be concluded as solving a set of LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.
