The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are de...The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.展开更多
This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems（DFBS）.Based on the parallel distributed compensation（PDC） approach,the sufficient co...This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems（DFBS）.Based on the parallel distributed compensation（PDC） approach,the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations.The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities（BMIs）.The Van de Vusse model is utilized to demonstrate the validity and effectiveness of the proposed approach.展开更多
The memory state feedback control problem for a class of discrete-time systems with input delay and unknown state delay is addressed based on LMIs and Lyapunov-Krasovskii functional method. Under the action of our des...The memory state feedback control problem for a class of discrete-time systems with input delay and unknown state delay is addressed based on LMIs and Lyapunov-Krasovskii functional method. Under the action of our designed adaptive control law, the unknown time-delay parameter is included in memory state feedback controller. Using LMI technique, delay-dependent sufficient conditions for the existence of the feedback controller are obtained. Finally, the effectiveness of the proposed design method is demonstrated by a numerical example.展开更多
An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membe...An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membership functions in fuzzy logic systems are adjusted according to adaptive laws for the purpose of controlling the plant to track a reference trajectory. It is proved that the scheme can not only guarantee the boundedness of the input and output of the closed-loop system, but also make the tracking error converge to a small neighborhood of the origin. Simulation results indicate the effectiveness of this scheme.展开更多
The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, prop...The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, property of matrix inverse and S-procedure, a new sufficient condition independent of the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is established. With Schur complement, another equivalent sufficient condition for robust stability of discrete-time nonlinear systems with time-delay is given. Finally, a sufficient condition dependent on the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is obtained. A unified approach is used to cast the robust stability problem into a convex optimization involving linear matrix inequalities.展开更多
This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi- Sugeno （T-S） fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate n...This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi- Sugeno （T-S） fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate nonlinear uncertain systems at any precision. A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory. With the help of linear matrix inequality （LMI） method, robust passive controllers are designed so that the closed-loop system is robust stable and strictly passive. Furthermore, a convex optimization problem with LMI constraints is formulated to design robust passive controllers with the maximum dissipation rate. A numerical example illustrates the validity of the proposed method.展开更多
To alleviate the conservativeness of the stability criterion for Takagi-Sugeno （T-S） fuzzy time-delay systems, a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function ...To alleviate the conservativeness of the stability criterion for Takagi-Sugeno （T-S） fuzzy time-delay systems, a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with an additional triple-integral term, which was firstly u3ed to derive the stability criterion for T-S fuzzy time-delay systems. By the same approach, the robust stability issue for fuzzy time-delay systems with uncertain parameters was also considered. On the other hand, in order to enhance the design flexibility, a new design approach for uncertain fuzzy time-delay systems under imperfect premise matching was also proposed, which allows the fuzzy controller to employ different membership functions from the fuzzy time-delay model. By the numerical examples, the proposed stability conditions are less conservative in the sense of getting larger allowable time-delay and obtaining smaller feedback control gains. For instance, when the allowable time-delay increases from 7.3 s to 12 s for an uncertain T-S fuzzy control system with time-delay, the norm of the feedback gains decreases from （34.299 2, 38.560 3） to （10.073 3, 11.349 0）, respectively. Meanwhile, the effectiveness of the proposed design method was illustrated by the last example with the robustly stable curves of system state under the initial condition of x（0） = [3 -1].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 problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed.By using the linear matrix inequality（LMI） method, the problem of fuzzy r...The problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed.By using the linear matrix inequality（LMI） method, the problem of fuzzy robust H ∞ controller design for the system is studied.Assuming that the nonlinear uncertain functions in the model considered are gain-bounded, a sufficient condition for the robustly asymptotic stability of the closed-loop system is obtained via Lyapunov stability theory.By solving the LMI, a feedback control law which guarantees the robustly asymptotic stability of the closed-loop system is constructed and the effect of the disturbance input on the controlled output is ruduced to a prescribed level.展开更多
The goethite iron precipitation process consists of several continuous reactors and involves a series of complex chemical reactions,such as oxidation reaction,hydrolysis reaction and neutralization reaction.It is hard...The goethite iron precipitation process consists of several continuous reactors and involves a series of complex chemical reactions,such as oxidation reaction,hydrolysis reaction and neutralization reaction.It is hard to accurately establish a mathematical model of the process featured by strong nonlinearity,uncertainty and time-delay.A modeling method based on time-delay fuzzy gray cognitive network(T-FGCN)for the goethite iron precipitation process was proposed in this paper.On the basis of the process mechanism,experts’practical experience and historical data,the T-FGCN model of the goethite iron precipitation system was established and the weights were studied by using the nonlinear hebbian learning(NHL)algorithm with terminal constraints.By analyzing the system in uncertain environment of varying degrees,in the environment of high uncertainty,the T-FGCN can accurately simulate industrial systems with large time-delay and uncertainty and the simulated system can converge to steady state with zero gray scale or a small one.展开更多
The problems of stability and stabilization for the discrete Takagi-Sugeno（T-S） fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function（PLKF） in each maximal over...The problems of stability and stabilization for the discrete Takagi-Sugeno（T-S） fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function（PLKF） in each maximal overlapped-rules group（MORG）,a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function（CLKF） approach and the fuzzy Lyapunov-Krasovskii function（FLKF） approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.展开更多
A robust decentralized H∞ control problem was considered for uncertain multi-channel discrete-time systems with time-delay. The uncertainties were assumed to be time-invariant, norm-bounded, and exist in the system, ...A robust decentralized H∞ control problem was considered for uncertain multi-channel discrete-time systems with time-delay. The uncertainties were assumed to be time-invariant, norm-bounded, and exist in the system, the time-delay and the output matrices. Dynamic output feedback was focused on. A sufficient condition for the multi-channel uncertain discrete time-delay system to be robustly stabilizable with a specified disturbance attenuation level was derived based on the theorem of Lyapunov stability theory. By setting the Lyapunov matrix as block diagonal appropriately according to the desired order of the controller, the problem was reduced to a linear matrix inequality (LMI) which is sufficient to existence condition but much more tractable. An example was given to show the efficiency of this method.展开更多
Security and reliability must be focused on control sys- tems firstly, and fault detection and diagnosis （FDD） is the main theory and technology. Now, there are many positive results in FDD for linear networked cont...Security and reliability must be focused on control sys- tems firstly, and fault detection and diagnosis （FDD） is the main theory and technology. Now, there are many positive results in FDD for linear networked control systems （LNCSs）, but nonlinear networked control systems （NNCSs） are less involved. Based on the T-S fuzzy-modeling theory, NNCSs are modeled and network random time-delays are changed into the unknown bounded uncertain part without changing its structure. Then a fuzzy state observer is designed and an observer-based fault detection approach for an NNCS is presented. The main results are given and the relative theories are proved in detail. Finally, some simulation results are given and demonstrate the proposed method is effective.展开更多
The problem of robust H ∞ fuzzy state feedback control for uncertain fuzzy descriptor systems with state delay is solved. In the case that time-varying uncertainties are in all parameter matrices, sufficient conditi...The problem of robust H ∞ fuzzy state feedback control for uncertain fuzzy descriptor systems with state delay is solved. In the case that time-varying uncertainties are in all parameter matrices, sufficient conditions for the existence of fuzzy state feedback controller are presented in terms of linear matrix inequality (LMI). The proposed robust H ∞ control laws guarantee that the resulting closed-loop system is regular, impulse free, and stable with prescribed H ∞ norm bounded constraint for all admissible uncertainties. Finally, a numerical example is provided to demonstrate the validity of the proposed method.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 tim...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
文摘The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.
基金supported by the National Natural Science Foundation of China(60374015)
文摘This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems（DFBS）.Based on the parallel distributed compensation（PDC） approach,the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations.The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities（BMIs）.The Van de Vusse model is utilized to demonstrate the validity and effectiveness of the proposed approach.
基金supported by the National Natural Science Foundation of China (60574006 60804017+2 种基金 608350017)the Foundation of Doctor(20060286039)the Jiangsu Provincal Sustentation Fund of Recruiting Post Doctor(1660631171)
文摘The memory state feedback control problem for a class of discrete-time systems with input delay and unknown state delay is addressed based on LMIs and Lyapunov-Krasovskii functional method. Under the action of our designed adaptive control law, the unknown time-delay parameter is included in memory state feedback controller. Using LMI technique, delay-dependent sufficient conditions for the existence of the feedback controller are obtained. Finally, the effectiveness of the proposed design method is demonstrated by a numerical example.
基金surported by Tianjin Science and Technology Development for Higher Education(20051206).
文摘An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membership functions in fuzzy logic systems are adjusted according to adaptive laws for the purpose of controlling the plant to track a reference trajectory. It is proved that the scheme can not only guarantee the boundedness of the input and output of the closed-loop system, but also make the tracking error converge to a small neighborhood of the origin. Simulation results indicate the effectiveness of this scheme.
基金Project (60425310) supported by the National Natural Science Foundation of China project (2001AA4422200) supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China
文摘The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, property of matrix inverse and S-procedure, a new sufficient condition independent of the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is established. With Schur complement, another equivalent sufficient condition for robust stability of discrete-time nonlinear systems with time-delay is given. Finally, a sufficient condition dependent on the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is obtained. A unified approach is used to cast the robust stability problem into a convex optimization involving linear matrix inequalities.
基金supported by the National Natural Science Foundation of China(60710002)Self-Planned Task of State Key Laboratory of Robotics and System(SKLRS200801A03).
文摘This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi- Sugeno （T-S） fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate nonlinear uncertain systems at any precision. A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory. With the help of linear matrix inequality （LMI） method, robust passive controllers are designed so that the closed-loop system is robust stable and strictly passive. Furthermore, a convex optimization problem with LMI constraints is formulated to design robust passive controllers with the maximum dissipation rate. A numerical example illustrates the validity of the proposed method.
基金Project(61273095)supported by the National Natural Science Foundation of ChinaProject(135225)supported by the Academy of Finland
文摘To alleviate the conservativeness of the stability criterion for Takagi-Sugeno （T-S） fuzzy time-delay systems, a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with an additional triple-integral term, which was firstly u3ed to derive the stability criterion for T-S fuzzy time-delay systems. By the same approach, the robust stability issue for fuzzy time-delay systems with uncertain parameters was also considered. On the other hand, in order to enhance the design flexibility, a new design approach for uncertain fuzzy time-delay systems under imperfect premise matching was also proposed, which allows the fuzzy controller to employ different membership functions from the fuzzy time-delay model. By the numerical examples, the proposed stability conditions are less conservative in the sense of getting larger allowable time-delay and obtaining smaller feedback control gains. For instance, when the allowable time-delay increases from 7.3 s to 12 s for an uncertain T-S fuzzy control system with time-delay, the norm of the feedback gains decreases from （34.299 2, 38.560 3） to （10.073 3, 11.349 0）, respectively. Meanwhile, the effectiveness of the proposed design method was illustrated by the last example with the robustly stable curves of system state under the initial condition of x（0） = [3 -1].
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 Program for Natural Science Foundation of Beijing (4062030)Young Teacher Research Foundation of North China Electric Power University
文摘The problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed.By using the linear matrix inequality（LMI） method, the problem of fuzzy robust H ∞ controller design for the system is studied.Assuming that the nonlinear uncertain functions in the model considered are gain-bounded, a sufficient condition for the robustly asymptotic stability of the closed-loop system is obtained via Lyapunov stability theory.By solving the LMI, a feedback control law which guarantees the robustly asymptotic stability of the closed-loop system is constructed and the effect of the disturbance input on the controlled output is ruduced to a prescribed level.
基金Project(61673399)supported by the National Natural Science Foundation of ChinaProject(2017JJ2329)supported by the Natural Science Foundation of Hunan Province,ChinaProject(2018zzts550)supported by the Fundamental Research Funds for Central Universities,China
文摘The goethite iron precipitation process consists of several continuous reactors and involves a series of complex chemical reactions,such as oxidation reaction,hydrolysis reaction and neutralization reaction.It is hard to accurately establish a mathematical model of the process featured by strong nonlinearity,uncertainty and time-delay.A modeling method based on time-delay fuzzy gray cognitive network(T-FGCN)for the goethite iron precipitation process was proposed in this paper.On the basis of the process mechanism,experts’practical experience and historical data,the T-FGCN model of the goethite iron precipitation system was established and the weights were studied by using the nonlinear hebbian learning(NHL)algorithm with terminal constraints.By analyzing the system in uncertain environment of varying degrees,in the environment of high uncertainty,the T-FGCN can accurately simulate industrial systems with large time-delay and uncertainty and the simulated system can converge to steady state with zero gray scale or a small one.
基金supported in part by the Scientific Research Project of Heilongjiang Province Education Bureau(12541200)
文摘The problems of stability and stabilization for the discrete Takagi-Sugeno（T-S） fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function（PLKF） in each maximal overlapped-rules group（MORG）,a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function（CLKF） approach and the fuzzy Lyapunov-Krasovskii function（FLKF） approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.
基金Project(60634020) supported by the National Natural Science Foundation of ChinaProject(07JJ6138) supported by Natural Science Foundation of Hunan Province, ChinaProject(20060390883) supported by the Postdoctoral Science Foundation of China
文摘A robust decentralized H∞ control problem was considered for uncertain multi-channel discrete-time systems with time-delay. The uncertainties were assumed to be time-invariant, norm-bounded, and exist in the system, the time-delay and the output matrices. Dynamic output feedback was focused on. A sufficient condition for the multi-channel uncertain discrete time-delay system to be robustly stabilizable with a specified disturbance attenuation level was derived based on the theorem of Lyapunov stability theory. By setting the Lyapunov matrix as block diagonal appropriately according to the desired order of the controller, the problem was reduced to a linear matrix inequality (LMI) which is sufficient to existence condition but much more tractable. An example was given to show the efficiency of this method.
文摘Security and reliability must be focused on control sys- tems firstly, and fault detection and diagnosis （FDD） is the main theory and technology. Now, there are many positive results in FDD for linear networked control systems （LNCSs）, but nonlinear networked control systems （NNCSs） are less involved. Based on the T-S fuzzy-modeling theory, NNCSs are modeled and network random time-delays are changed into the unknown bounded uncertain part without changing its structure. Then a fuzzy state observer is designed and an observer-based fault detection approach for an NNCS is presented. The main results are given and the relative theories are proved in detail. Finally, some simulation results are given and demonstrate the proposed method is effective.
文摘The problem of robust H ∞ fuzzy state feedback control for uncertain fuzzy descriptor systems with state delay is solved. In the case that time-varying uncertainties are in all parameter matrices, sufficient conditions for the existence of fuzzy state feedback controller are presented in terms of linear matrix inequality (LMI). The proposed robust H ∞ control laws guarantee that the resulting closed-loop system is regular, impulse free, and stable with prescribed H ∞ norm bounded constraint for all admissible uncertainties. Finally, a numerical example is provided to demonstrate the validity of the proposed method.
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.
