Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous sta...Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous state monitoring. In contrast to the existing self-triggered control method, novel self-triggered mechanism(STM) is proposed by incorporating a waiting time for stabilizing impulses. This allows for direct prediction of the next impulsive instant.展开更多
The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear st...The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear stochastic systems. Firstly, we derive and prove the form of the controller by investigating the Fokker-PlanckKolmogorov(FPK) equation arising from the stochastic system. Secondly, an approach for getting approximate solution of the FPK equation is provided. A special function including some parameters is taken as the approximate stationary solution of the FPK equation. We use nonlinear least square method to solve the parameters in the function, and capture the approximate solution of the FPK equation. Substituting the approximate solution into the form of the controller, we can acquire the PDF shape controller. Lastly, some example simulations are conducted to verify the algorithm.展开更多
This paper deals with the robust control problem for a class of uncertain nonlinear networked systems with stochastic communication delays via sliding mode conception （SMC）. A sequence of variables obeying Bernoulli...This paper deals with the robust control problem for a class of uncertain nonlinear networked systems with stochastic communication delays via sliding mode conception （SMC）. A sequence of variables obeying Bernoulli distribution are employed to model the randomly occurring communication delays which could be different for different state variables. A discrete switching function that is different from those in the existing literature is first proposed. Then, expressed as the feasibility of a linear matrix inequality （LMI） with an equality constraint, sufficient conditions are derived in order to ensure the globally mean-square asymptotic stability of the system dynamics on the sliding surface. A discrete-time SMC controller is then synthesized to guarantee the discrete-time sliding mode reaching condition with the specified sliding surface. Finally, a simulation example is given to show the effectiveness of the proposed method.展开更多
The extended state observer(ESO)is the most important part of an emerging control technology known as active disturbance rejection control to this day,aiming at estimating"total disturbance"from observable m...The extended state observer(ESO)is the most important part of an emerging control technology known as active disturbance rejection control to this day,aiming at estimating"total disturbance"from observable measured output.In this paper,we construct a nonlinear ESO for a class of uncertain lower triangular nonlinear systems with stochastic disturbance and show its convergence,where the total disturbance includes internal uncertain nonlinear part and external stochastic disturbance.The numerical experiments are carried out to illustrate effectiveness of the proposed approach.展开更多
This paper investigates the fixed-time stability theorem and state-feedback controller design for stochastic nonlinear systems.We propose an improved fixed-time Lyapunov theorem with a more rigorous and reasonable pro...This paper investigates the fixed-time stability theorem and state-feedback controller design for stochastic nonlinear systems.We propose an improved fixed-time Lyapunov theorem with a more rigorous and reasonable proof procedure.In particular,an important corollary is obtained,which can give a less conservative upper-bound estimate of the settling time.Based on the backstepping technique and the addition of a power integrator method,a state-feedback controller is skillfully designed for a class of stochastic nonlinear systems.It is proved that the proposed controller can render the closed-loop system fixed-time stable in probability with the help of the proposed fixed-time stability criteria.Finally,the effectiveness of the proposed controller is demonstrated by simulation examples and comparisons.展开更多
This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new...This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.展开更多
In this work,a novel shape control approach of the probability density function(PDF)for nonlinear stochastic systems is presented.First,we provide the formula for the PDF shape controller without devising the control ...In this work,a novel shape control approach of the probability density function(PDF)for nonlinear stochastic systems is presented.First,we provide the formula for the PDF shape controller without devising the control law of the controller.Then,based on the exact analytical solution of the Fokker-PlanckKolmogorov(FPK)equation,the product function of the polynomial and the exponential polynomial is regarded as the stationary PDF of the state response.To validate the performance of the proposed control approach,we compared it with the exponential polynomial method and the multi-Gaussian closure method by implementing comparative simulation experiments.The results show that the novel PDF shape control approach is effective and feasible.Using an equal number of parameters,our method can achieve a similar or better control effect as the exponential polynomial method.By comparison with the multiGaussian closure method,our method has clear advantages in PDF shape control performance.For all cases,the integral of squared error and the errors of first four moments of our proposed method were very small,indicating superior performance and promising good overall control effects of our method.The approach presented in this study provides an alternative for PDF shape control in nonlinear stochastic systems.展开更多
This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix i...This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.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
Using graph theory, matrix theory, adaptive control, fuzzy logic systems and other tools, this paper studies the leader-follower global consensus of two kinds of stochastic uncertain nonlinear multi-agent systems(MAS)...Using graph theory, matrix theory, adaptive control, fuzzy logic systems and other tools, this paper studies the leader-follower global consensus of two kinds of stochastic uncertain nonlinear multi-agent systems(MAS). Firstly, the fuzzy logic systems replaces the feedback compensator as the feedforward compensator to describe the uncertain nonlinear dynamics. Secondly, based on the network topology, all followers are divided into two categories: One is the followers who can obtain the leader signal, and the other is the follower who cannot obtain the leader signal. Thirdly, based on the adaptive control method, distributed control protocols are designed for the two types of followers. Fourthly, based on matrix theory and stochastic Lyapunov stability theory, the stability of the closed-loop systems is analyzed. Finally, three simulation examples are given to verify the effectiveness of the proposed control algorithms.展开更多
This paper is concerned with the problem of global output feedback stabilization in probability for a class of switched stochastic nonlinear systems under arbitrary switchings. The subsystems are assumed to be in outp...This paper is concerned with the problem of global output feedback stabilization in probability for a class of switched stochastic nonlinear systems under arbitrary switchings. The subsystems are assumed to be in output feedback form and driven by white noise. By introducing a common Lyapunov function, the common output feedback controller independent of switching signals is constructed based on the backstepping approach. It is proved that the zero solution of the closed-loop system is fourth-moment exponentially stable. An example is given to show the effectiveness of the proposed method.展开更多
A bounded optimal control strategy for strongly non-linear systems under non-white wide-band random excitation with actuator saturation is proposed. First, the stochastic averaging method is introduced for controlled ...A bounded optimal control strategy for strongly non-linear systems under non-white wide-band random excitation with actuator saturation is proposed. First, the stochastic averaging method is introduced for controlled strongly non-linear systems under wide-band random excitation using generalized harmonic functions. Then, the dynamical programming equation for the saturated control problem is formulated from the partially averaged Itō equation based on the dynamical programming principle. The optimal control consisting of the unbounded optimal control and the bounded bang-bang control is determined by solving the dynamical programming equation. Finally, the response of the optimally controlled system is predicted by solving the reduced Fokker-Planck-Kolmogorov （FPK） equation associated with the completed averaged Itō equation. An example is given to illustrate the proposed control strategy. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and the chattering is reduced significantly comparing with the bang-bang control strategy.展开更多
This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic...This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.展开更多
In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization...In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated for the first time. Under some weaker assumptions, a smooth state feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0,∞）, the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.展开更多
This paper considers the output tracking problem for more general classes of stochastic nonlinear systems with unknown control coefficients and driven by noise of unknown covariance. By utilizing the radial basis func...This paper considers the output tracking problem for more general classes of stochastic nonlinear systems with unknown control coefficients and driven by noise of unknown covariance. By utilizing the radial basis function neural network approximation method and backstepping technique, we successfully construct a controller to guarantee the solution process to be bounded in probability.The tracking error signal is 4th-moment semi-globally uniformly ultimately bounded（SGUUB） and can be regulated into a small neighborhood of the origin in probability. A simulation example is given to demonstrate the effectiveness of the control scheme.展开更多
This paper addresses the problem of event-triggered finite-time H<sub>∞</sub> filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-K...This paper addresses the problem of event-triggered finite-time H<sub>∞</sub> filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H<sub>∞</sub> filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H<sub>∞</sub> filter gain matrices can be expressed in an explicit form.展开更多
This paper gives a mathematical definition for the "caution" and "probing", and presents a decomposition theorem for nonlinear discrete-time stochastic systems. Under some assumptions, the problem ...This paper gives a mathematical definition for the "caution" and "probing", and presents a decomposition theorem for nonlinear discrete-time stochastic systems. Under some assumptions, the problem of finding the closed-loop optimal control can be decomposed into three problems: the deterministic optimal feedback, cautious optimal and probing optimal control problems.展开更多
The problem of adaptive stabilization is addressed for a class of uncertain stochastic nonlinear strict-feedback systems with both unknown dead-zone and unknown gain functions.By using the backstepping method and neur...The problem of adaptive stabilization is addressed for a class of uncertain stochastic nonlinear strict-feedback systems with both unknown dead-zone and unknown gain functions.By using the backstepping method and neural network（NN） parameterization,a novel adaptive neural control scheme which contains fewer learning parameters is developed to solve the stabilization problem of such systems.Meanwhile,stability analysis is presented to guarantee that all the error variables are semi-globally uniformly ultimately bounded with desired probability in a compact set.The effectiveness of the proposed design is illustrated by simulation results.展开更多
基金supported by the National Natural Science Foundation of China(62403393,12202058,62103118)the China Postdoctoral Science Foundation(2021T140160,2023 T160051)the Natural Science Foundation of Chongqing(CSTB 2023NSCQ-MSX0152)
文摘Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous state monitoring. In contrast to the existing self-triggered control method, novel self-triggered mechanism(STM) is proposed by incorporating a waiting time for stabilizing impulses. This allows for direct prediction of the next impulsive instant.
基金the National Natural Science Foundation of China(No.61273127)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20116118110008)the Scientific Research Plan Projects of Shaanxi Education Department(No.12JK0524)
文摘The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear stochastic systems. Firstly, we derive and prove the form of the controller by investigating the Fokker-PlanckKolmogorov(FPK) equation arising from the stochastic system. Secondly, an approach for getting approximate solution of the FPK equation is provided. A special function including some parameters is taken as the approximate stationary solution of the FPK equation. We use nonlinear least square method to solve the parameters in the function, and capture the approximate solution of the FPK equation. Substituting the approximate solution into the form of the controller, we can acquire the PDF shape controller. Lastly, some example simulations are conducted to verify the algorithm.
基金supported by the Engineering and Physical Sciences Research Council(EPSRC)of the UK(No.GR/S27658/01)the Royal Society of the UK and the Alexander von Humboldt Foundation of Germany
文摘This paper deals with the robust control problem for a class of uncertain nonlinear networked systems with stochastic communication delays via sliding mode conception （SMC）. A sequence of variables obeying Bernoulli distribution are employed to model the randomly occurring communication delays which could be different for different state variables. A discrete switching function that is different from those in the existing literature is first proposed. Then, expressed as the feasibility of a linear matrix inequality （LMI） with an equality constraint, sufficient conditions are derived in order to ensure the globally mean-square asymptotic stability of the system dynamics on the sliding surface. A discrete-time SMC controller is then synthesized to guarantee the discrete-time sliding mode reaching condition with the specified sliding surface. Finally, a simulation example is given to show the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(No.61273129).
文摘The extended state observer(ESO)is the most important part of an emerging control technology known as active disturbance rejection control to this day,aiming at estimating"total disturbance"from observable measured output.In this paper,we construct a nonlinear ESO for a class of uncertain lower triangular nonlinear systems with stochastic disturbance and show its convergence,where the total disturbance includes internal uncertain nonlinear part and external stochastic disturbance.The numerical experiments are carried out to illustrate effectiveness of the proposed approach.
基金supported in part by the National Natural Science Foundation of China(62073166,61673215)the Key Laboratory of Jiangsu Province。
文摘This paper investigates the fixed-time stability theorem and state-feedback controller design for stochastic nonlinear systems.We propose an improved fixed-time Lyapunov theorem with a more rigorous and reasonable proof procedure.In particular,an important corollary is obtained,which can give a less conservative upper-bound estimate of the settling time.Based on the backstepping technique and the addition of a power integrator method,a state-feedback controller is skillfully designed for a class of stochastic nonlinear systems.It is proved that the proposed controller can render the closed-loop system fixed-time stable in probability with the help of the proposed fixed-time stability criteria.Finally,the effectiveness of the proposed controller is demonstrated by simulation examples and comparisons.
基金This work was partially supported by the National Science Foundation （Nos. ECCS-1230040, ECCS-1501044）.
文摘This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.
基金supported in part by the National Natural Science Foundation of China(61903298,62073259,61773016)。
文摘In this work,a novel shape control approach of the probability density function(PDF)for nonlinear stochastic systems is presented.First,we provide the formula for the PDF shape controller without devising the control law of the controller.Then,based on the exact analytical solution of the Fokker-PlanckKolmogorov(FPK)equation,the product function of the polynomial and the exponential polynomial is regarded as the stationary PDF of the state response.To validate the performance of the proposed control approach,we compared it with the exponential polynomial method and the multi-Gaussian closure method by implementing comparative simulation experiments.The results show that the novel PDF shape control approach is effective and feasible.Using an equal number of parameters,our method can achieve a similar or better control effect as the exponential polynomial method.By comparison with the multiGaussian closure method,our method has clear advantages in PDF shape control performance.For all cases,the integral of squared error and the errors of first four moments of our proposed method were very small,indicating superior performance and promising good overall control effects of our method.The approach presented in this study provides an alternative for PDF shape control in nonlinear stochastic systems.
基金This work was supported by the National Natural Science Foundation of China(No.60474013)Specialized Research Fund for the Doctoral Program of Higher Education (No. 20050424002)the Doctoral Foundation of Shandong Province (No. 2004BS01010)
文摘This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.
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supported by Natural Science Foundation of China(No.61573013)。
文摘Using graph theory, matrix theory, adaptive control, fuzzy logic systems and other tools, this paper studies the leader-follower global consensus of two kinds of stochastic uncertain nonlinear multi-agent systems(MAS). Firstly, the fuzzy logic systems replaces the feedback compensator as the feedforward compensator to describe the uncertain nonlinear dynamics. Secondly, based on the network topology, all followers are divided into two categories: One is the followers who can obtain the leader signal, and the other is the follower who cannot obtain the leader signal. Thirdly, based on the adaptive control method, distributed control protocols are designed for the two types of followers. Fourthly, based on matrix theory and stochastic Lyapunov stability theory, the stability of the closed-loop systems is analyzed. Finally, three simulation examples are given to verify the effectiveness of the proposed control algorithms.
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 Basic Research Program of China(973 Program)(No.2012CB821205)National Natural Science Foundation of China(Nos.61021002 and 61203125)Fundamental Research Funds for the Central Universities(No.HIT.NSRIF.2013039)
文摘This paper is concerned with the problem of global output feedback stabilization in probability for a class of switched stochastic nonlinear systems under arbitrary switchings. The subsystems are assumed to be in output feedback form and driven by white noise. By introducing a common Lyapunov function, the common output feedback controller independent of switching signals is constructed based on the backstepping approach. It is proved that the zero solution of the closed-loop system is fourth-moment exponentially stable. An example is given to show the effectiveness of the proposed method.
基金the National Natural Science Foundation of China(Nos.10332030 and 10772159)Research Fund for Doctoral Program of Higher Education of China(No.20060335125).
文摘A bounded optimal control strategy for strongly non-linear systems under non-white wide-band random excitation with actuator saturation is proposed. First, the stochastic averaging method is introduced for controlled strongly non-linear systems under wide-band random excitation using generalized harmonic functions. Then, the dynamical programming equation for the saturated control problem is formulated from the partially averaged Itō equation based on the dynamical programming principle. The optimal control consisting of the unbounded optimal control and the bounded bang-bang control is determined by solving the dynamical programming equation. Finally, the response of the optimally controlled system is predicted by solving the reduced Fokker-Planck-Kolmogorov （FPK） equation associated with the completed averaged Itō equation. An example is given to illustrate the proposed control strategy. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and the chattering is reduced significantly comparing with the bang-bang control strategy.
基金Supported by National Natural Science Foundation of China（60774010 10971256） Natural Science Foundation of Jiangsu Province（BK2009083）+1 种基金 Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province（07KJB510114） Shandong Provincial Natural Science Foundation of China（ZR2009GM008 ZR2009AL014）
基金supported by National Natural Science Foundation of China (No. 60774010, 10971256, and 60974028)Jiangsu"Six Top Talents" (No. 07-A-020)+2 种基金Natural Science Foundation of Jiangsu Province (No. BK2009083)Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province(No.07KJB510114)Natural Science Foundation of Xuzhou Normal University (No. 08XLB20)
文摘This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.
基金Program for New Century Excellent Talents in University of China (NCET-05-0607)National Natural Science Fou-ndation of China (No.60774010)Project for Fundamental Research of Natural Sciences in Universities of Jingsu Province (No.07KJB510114)
文摘In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated for the first time. Under some weaker assumptions, a smooth state feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0,∞）, the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.
基金supported by National Natural Science Foundation of China(Nos.61573172,61305149 and 61403174)333 High-level Talents Training Program in Jiangsu Province(No.BRA2015352)Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province(No.15KJB510011)
文摘This paper considers the output tracking problem for more general classes of stochastic nonlinear systems with unknown control coefficients and driven by noise of unknown covariance. By utilizing the radial basis function neural network approximation method and backstepping technique, we successfully construct a controller to guarantee the solution process to be bounded in probability.The tracking error signal is 4th-moment semi-globally uniformly ultimately bounded（SGUUB） and can be regulated into a small neighborhood of the origin in probability. A simulation example is given to demonstrate the effectiveness of the control scheme.
文摘This paper addresses the problem of event-triggered finite-time H<sub>∞</sub> filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H<sub>∞</sub> filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H<sub>∞</sub> filter gain matrices can be expressed in an explicit form.
文摘This paper gives a mathematical definition for the "caution" and "probing", and presents a decomposition theorem for nonlinear discrete-time stochastic systems. Under some assumptions, the problem of finding the closed-loop optimal control can be decomposed into three problems: the deterministic optimal feedback, cautious optimal and probing optimal control problems.
基金supported by the National Natural Science Foundation of China (60704013)the Special Foundation of East China University of Science and Technology for Youth Teacher (YH0157134)
文摘The problem of adaptive stabilization is addressed for a class of uncertain stochastic nonlinear strict-feedback systems with both unknown dead-zone and unknown gain functions.By using the backstepping method and neural network（NN） parameterization,a novel adaptive neural control scheme which contains fewer learning parameters is developed to solve the stabilization problem of such systems.Meanwhile,stability analysis is presented to guarantee that all the error variables are semi-globally uniformly ultimately bounded with desired probability in a compact set.The effectiveness of the proposed design is illustrated by simulation results.
