In this paper, a model predictive control(MPC)framework is proposed for finite-time stabilization of linear and nonlinear discrete-time systems subject to state and control constraints. The proposed MPC framework guar...In this paper, a model predictive control(MPC)framework is proposed for finite-time stabilization of linear and nonlinear discrete-time systems subject to state and control constraints. The proposed MPC framework guarantees the finite-time convergence property by assigning the control horizon equal to the dimension of the overall system, and only penalizing the terminal cost in the optimization, where the stage costs are not penalized explicitly. A terminal inequality constraint is added to guarantee the feasibility and stability of the closed-loop system.Initial feasibility can be improved via augmentation. The finite-time convergence of the proposed MPC is proved theoretically,and is supported by simulation examples.展开更多
This paper investigates the problem of global/semi-global finite-time consensus for integrator-type multi-agent sys-tems.New hyperbolic tangent function-based protocols are pro-posed to achieve global and semi-global ...This paper investigates the problem of global/semi-global finite-time consensus for integrator-type multi-agent sys-tems.New hyperbolic tangent function-based protocols are pro-posed to achieve global and semi-global finite-time consensus for both single-integrator and double-integrator multi-agent systems with leaderless undirected and leader-following directed commu-nication topologies.These new protocols not only provide an explicit upper-bound estimate for the settling time,but also have a user-prescribed bounded control level.In addition,compared to some existing results based on the saturation function,the pro-posed approach considerably simplifies the protocol design and the stability analysis.Illustrative examples and an application demonstrate the effectiveness of the proposed protocols.展开更多
This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eli...This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm.展开更多
This paper investigates the adaptive fuzzy finite-time output-feedback fault-tolerant control (FTC) problemfor a class of nonlinear underactuated wheeled mobile robots (UWMRs) system with intermittent actuatorfaults. ...This paper investigates the adaptive fuzzy finite-time output-feedback fault-tolerant control (FTC) problemfor a class of nonlinear underactuated wheeled mobile robots (UWMRs) system with intermittent actuatorfaults. The UWMR system includes unknown nonlinear dynamics and immeasurable states. Fuzzy logic systems(FLSs) are utilized to work out immeasurable functions. Furthermore, with the support of the backsteppingcontrol technique and adaptive fuzzy state observer, a fuzzy adaptive finite-time output-feedback FTC scheme isdeveloped under the intermittent actuator faults. It is testifying the scheme can ensure the controlled nonlinearUWMRs is stable and the estimation errors are convergent. Finally, the comparison results and simulationvalidate the effectiveness of the proposed fuzzy adaptive finite-time FTC approach.展开更多
Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting...Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.展开更多
A time series model is used in this paper to describe the progress of circulating direct condensation heat recovery of the compound condensing process (CCP) which is made of two water cooling condensing processes in s...A time series model is used in this paper to describe the progress of circulating direct condensation heat recovery of the compound condensing process (CCP) which is made of two water cooling condensing processes in series for a centrifugal chiller in the paper. A finite-time thermodynamics method is used to set up the time series simulation model. As a result, an upper bound of recoverable condensation heat for the compound condensing process is obtained which is in good agreement with experimental result. And the result is valuable and useful to optimization design of condensing heat recovery.展开更多
This paper studies a finite-time adaptive fractionalorder fault-tolerant control(FTC)scheme for the slave position tracking of the teleoperating cyber physical system(TCPS)with external disturbances and actuator fault...This paper studies a finite-time adaptive fractionalorder fault-tolerant control(FTC)scheme for the slave position tracking of the teleoperating cyber physical system(TCPS)with external disturbances and actuator faults.Based on the fractional Lyapunov stability theory and the finite-time stability theory,a fractional-order nonsingular fast terminal sliding mode(FONFTSM)control law is proposed to promote the tracking and fault tolerance performance of the considered system.Meanwhile,the adaptive fractional-order update laws are designed to cope with the unknown upper bounds of the unknown actuator faults and external disturbances.Furthermore,the finite-time stability of the closed-loop system is proved.Finally,comparison simulation results are also provided to show the validity and the advantages of the proposed techniques.展开更多
This paper is concerned with the parabolic-parabolic-elliptic system■in a bounded domainΩ?Rnwith a smooth boundary,where the parametersχ,ζ1,ζ2are positive constants and m≥1.Based on the coupled energy estimates,...This paper is concerned with the parabolic-parabolic-elliptic system■in a bounded domainΩ?Rnwith a smooth boundary,where the parametersχ,ζ1,ζ2are positive constants and m≥1.Based on the coupled energy estimates,the boundedness of the global classical solution is established in any dimensions(n≥1)provided that m>1.展开更多
This paper is concerned with the finite-time dissipative synchronization control problem of semi-Markov switched cyber-physical systems in the presence of packet losses, which is constructed by the Takagi–Sugeno fuzz...This paper is concerned with the finite-time dissipative synchronization control problem of semi-Markov switched cyber-physical systems in the presence of packet losses, which is constructed by the Takagi–Sugeno fuzzy model. To save the network communication burden, a distributed dynamic event-triggered mechanism is developed to restrain the information update. Besides, random packet dropouts following the Bernoulli distribution are assumed to occur in sensor to controller channels, where the triggered control input is analyzed via an equivalent method containing a new stochastic variable. By establishing the mode-dependent Lyapunov–Krasovskii functional with augmented terms, the finite-time boundness of the error system limited to strict dissipativity is studied. As a result of the help of an extended reciprocally convex matrix inequality technique, less conservative criteria in terms of linear matrix inequalities are deduced to calculate the desired control gains. Finally, two examples in regard to practical systems are provided to display the effectiveness of the proposed theory.展开更多
This paper is concerned with finite-time H_(∞) filtering for Markov jump systems with uniform quantization. The objective is to design quantized mode-dependent filters to ensure that the filtering error system is not...This paper is concerned with finite-time H_(∞) filtering for Markov jump systems with uniform quantization. The objective is to design quantized mode-dependent filters to ensure that the filtering error system is not only mean-square finite-time bounded but also has a prescribed finite-time H_(∞) performance. First, the case where the switching modes of the filter align with those of the MJS is considered. A numerically tractable filter design approach is proposed utilizing a mode-dependent Lyapunov function, Schur’s complement, and Dynkin’s formula. Then, the study is extended to a scenario where the switching modes of the filter can differ from those of the MJS. To address this situation, a mode-mismatched filter design approach is developed by leveraging a hidden Markov model to describe the asynchronous mode switching and the double expectation formula. Finally, a spring system model subject to a Markov chain is employed to validate the effectiveness of the quantized filter design approaches.展开更多
This paper deals with the supervisory control problem of discrete event systems modeled by labeled Petri nets. The system is originally unbounded. First, the solvability of the problem is confirmed. A necessary condit...This paper deals with the supervisory control problem of discrete event systems modeled by labeled Petri nets. The system is originally unbounded. First, the solvability of the problem is confirmed. A necessary condition is given and proven for the existence of a feasible priority-based controller based on the notions of liveness and transition invariants. Next, a cyclic behavior graph is constructed, which shows the reachable markings that guarantee the maximum liveness of the system within a given bound vector. Finally, an on-line control strategy is proposed to enforce boundedness and liveness to the given system by appending priority relations to transitions. The dynamic priority relation changes flexibly according to the current state of the system and enforces the system evolving in a bounded and live manner. In addition, numerical examples are studied to verify the validity of the proposed approach that remains the structure of the plant net and is efficient for on-line control.展开更多
This paper presents a finite-time economic model predictive control(MPC)algorithm that can be used for frequency regulation and optimal load dispatch in multi-area power systems.Economic MPC can be used in a power sys...This paper presents a finite-time economic model predictive control(MPC)algorithm that can be used for frequency regulation and optimal load dispatch in multi-area power systems.Economic MPC can be used in a power system to ensure frequency stability,real-time economic optimization,control of the system and optimal load dispatch from it.A generalized terminal penalty term was used,and the finite-time convergence of the system was guaranteed.The effectiveness of the proposed model predictive control algorithm was verified by simulating a power system,which had two areas connected by an AC tie line.The simulation results demonstrated the effectiveness of the algorithm.展开更多
We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the gener...We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the generators of ϕ<sup>j</sup>-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences.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 investigates the finite-time H<sub>∞</sub> control problem of switched nonlinear systems via state-dependent switching and state feedback control. Unlike the existing approach based on time-dep...This paper investigates the finite-time H<sub>∞</sub> control problem of switched nonlinear systems via state-dependent switching and state feedback control. Unlike the existing approach based on time-dependent switching strategy, in which the switching instants must be given in advance, the state-dependent switching strategy is used to design switching signals. Based on multiple Lyapunov-like functions method, several criteria for switched nonlinear systems to be finite-time H<sub>∞</sub> control are derived. Finally, a numerical example with simulation results is provided to show the validity of the conclusions.展开更多
This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers...This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.展开更多
This paper studies the sliding mode controller design problems for a class of nonlinear system. The nonlinear function is considered to satisfy conic-type constraint condition. A novel finite-time boundedness(FTB) bas...This paper studies the sliding mode controller design problems for a class of nonlinear system. The nonlinear function is considered to satisfy conic-type constraint condition. A novel finite-time boundedness(FTB) based sliding mode controller design theory is proposed. And then a sufficient condition is obtained in terms of linear matrix inequalities(LMIs), which guarantees the resulted sliding mode dynamics to be FTB wrt some predefined scalars. Thereafter, a FTB-based sliding mode control(SMC) law is synthesized to ensure the state of the controlled system is driven into a novel desired switching surface s(t) = c(c is a constant) in a finite time. Simulation results illustrate the validity of the proposed FTB-based SMC design theory.展开更多
This article addresses the finite-time boundedness(FTB)problem for nonlinear descriptor systems.Firstly,the nonlinear descriptor system is represented by the Takagi-Sugeno(T-S)model,where fuzzy representation is assum...This article addresses the finite-time boundedness(FTB)problem for nonlinear descriptor systems.Firstly,the nonlinear descriptor system is represented by the Takagi-Sugeno(T-S)model,where fuzzy representation is assumed to be appearing not only in both the state and input matrices but also in the derivative matrix.By using a descriptor redundancy approach,the fuzzy representation in the derivative matrix is reformulated into a linear one.Then,we introduce a fuzzy sliding mode control(FSMC)law,which ensures the finite-time boundedness(FTB)of closed-loop fuzzy control systems over the reaching phase and sliding motion phase.Moreover,by further employing the descriptor redundancy representation,the sufficient condition for designing FSMC law,which ensures the FTB of the closed-loop control systems over the entire finite-time interval,is derived in terms of linear matrix inequalities(LMIs).Finally,a simulation study with control of a photovoltaic(PV)nonlinear system is given to show the effectiveness of the proposed method.展开更多
In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilize...In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.展开更多
Several boundedness criteria for the impulsive integro-differential systems with fixed moments of impulse effects are established, employing the method of Lyapunov functions and Razumikhin technique.
基金supported by the National Natural Science Foundation of China (62073015,62173036,62122014)。
文摘In this paper, a model predictive control(MPC)framework is proposed for finite-time stabilization of linear and nonlinear discrete-time systems subject to state and control constraints. The proposed MPC framework guarantees the finite-time convergence property by assigning the control horizon equal to the dimension of the overall system, and only penalizing the terminal cost in the optimization, where the stage costs are not penalized explicitly. A terminal inequality constraint is added to guarantee the feasibility and stability of the closed-loop system.Initial feasibility can be improved via augmentation. The finite-time convergence of the proposed MPC is proved theoretically,and is supported by simulation examples.
基金supported by the National Natural Science Foundation of China(62073019)。
文摘This paper investigates the problem of global/semi-global finite-time consensus for integrator-type multi-agent sys-tems.New hyperbolic tangent function-based protocols are pro-posed to achieve global and semi-global finite-time consensus for both single-integrator and double-integrator multi-agent systems with leaderless undirected and leader-following directed commu-nication topologies.These new protocols not only provide an explicit upper-bound estimate for the settling time,but also have a user-prescribed bounded control level.In addition,compared to some existing results based on the saturation function,the pro-posed approach considerably simplifies the protocol design and the stability analysis.Illustrative examples and an application demonstrate the effectiveness of the proposed protocols.
基金the National Natural Science Foundation of China(62203356)Fundamental Research Funds for the Central Universities of China(31020210502002)。
文摘This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm.
基金the National Natural Science Foundation of China under Grant U22A2043.
文摘This paper investigates the adaptive fuzzy finite-time output-feedback fault-tolerant control (FTC) problemfor a class of nonlinear underactuated wheeled mobile robots (UWMRs) system with intermittent actuatorfaults. The UWMR system includes unknown nonlinear dynamics and immeasurable states. Fuzzy logic systems(FLSs) are utilized to work out immeasurable functions. Furthermore, with the support of the backsteppingcontrol technique and adaptive fuzzy state observer, a fuzzy adaptive finite-time output-feedback FTC scheme isdeveloped under the intermittent actuator faults. It is testifying the scheme can ensure the controlled nonlinearUWMRs is stable and the estimation errors are convergent. Finally, the comparison results and simulationvalidate the effectiveness of the proposed fuzzy adaptive finite-time FTC approach.
文摘Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.
文摘A time series model is used in this paper to describe the progress of circulating direct condensation heat recovery of the compound condensing process (CCP) which is made of two water cooling condensing processes in series for a centrifugal chiller in the paper. A finite-time thermodynamics method is used to set up the time series simulation model. As a result, an upper bound of recoverable condensation heat for the compound condensing process is obtained which is in good agreement with experimental result. And the result is valuable and useful to optimization design of condensing heat recovery.
基金supported by the National Natural Science Foundation of China(61973331,61973257)the National Key Research and Development Plan Programs of China(2018YFB0106101).
文摘This paper studies a finite-time adaptive fractionalorder fault-tolerant control(FTC)scheme for the slave position tracking of the teleoperating cyber physical system(TCPS)with external disturbances and actuator faults.Based on the fractional Lyapunov stability theory and the finite-time stability theory,a fractional-order nonsingular fast terminal sliding mode(FONFTSM)control law is proposed to promote the tracking and fault tolerance performance of the considered system.Meanwhile,the adaptive fractional-order update laws are designed to cope with the unknown upper bounds of the unknown actuator faults and external disturbances.Furthermore,the finite-time stability of the closed-loop system is proved.Finally,comparison simulation results are also provided to show the validity and the advantages of the proposed techniques.
基金supported by the NSF of China(11871226)Guangdong Basic and Applied Basic Research Foundation(2020A1515010140 and 2022B1515020032)Guangzhou Science and Technology Program(202002030363)。
文摘This paper is concerned with the parabolic-parabolic-elliptic system■in a bounded domainΩ?Rnwith a smooth boundary,where the parametersχ,ζ1,ζ2are positive constants and m≥1.Based on the coupled energy estimates,the boundedness of the global classical solution is established in any dimensions(n≥1)provided that m>1.
基金Project supported by the National Natural Science Foundation of China (Grant No. 62263005)Guangxi Natural Science Foundation (Grant No. 2020GXNSFDA238029)+2 种基金Laboratory of AI and Information Processing (Hechi University), Education Department of Guangxi Zhuang Autonomous Region (Grant No. 2022GXZDSY004)Innovation Project of Guangxi Graduate Education (Grant No. YCSW2023298)Innovation Project of GUET Graduate Education (Grant Nos. 2022YCXS149 and 2022YCXS155)。
文摘This paper is concerned with the finite-time dissipative synchronization control problem of semi-Markov switched cyber-physical systems in the presence of packet losses, which is constructed by the Takagi–Sugeno fuzzy model. To save the network communication burden, a distributed dynamic event-triggered mechanism is developed to restrain the information update. Besides, random packet dropouts following the Bernoulli distribution are assumed to occur in sensor to controller channels, where the triggered control input is analyzed via an equivalent method containing a new stochastic variable. By establishing the mode-dependent Lyapunov–Krasovskii functional with augmented terms, the finite-time boundness of the error system limited to strict dissipativity is studied. As a result of the help of an extended reciprocally convex matrix inequality technique, less conservative criteria in terms of linear matrix inequalities are deduced to calculate the desired control gains. Finally, two examples in regard to practical systems are provided to display the effectiveness of the proposed theory.
基金Project supported by the Natural Science Foundation of the Anhui Higher Education Institutions (Grant Nos. KJ2020A0248 and 2022AH050310)。
文摘This paper is concerned with finite-time H_(∞) filtering for Markov jump systems with uniform quantization. The objective is to design quantized mode-dependent filters to ensure that the filtering error system is not only mean-square finite-time bounded but also has a prescribed finite-time H_(∞) performance. First, the case where the switching modes of the filter align with those of the MJS is considered. A numerically tractable filter design approach is proposed utilizing a mode-dependent Lyapunov function, Schur’s complement, and Dynkin’s formula. Then, the study is extended to a scenario where the switching modes of the filter can differ from those of the MJS. To address this situation, a mode-mismatched filter design approach is developed by leveraging a hidden Markov model to describe the asynchronous mode switching and the double expectation formula. Finally, a spring system model subject to a Markov chain is employed to validate the effectiveness of the quantized filter design approaches.
基金the Project of Industrial Internet and Integration of Industrialization and Industrialization of Guangxi,China under Grant No.Guigong2021-37.
文摘This paper deals with the supervisory control problem of discrete event systems modeled by labeled Petri nets. The system is originally unbounded. First, the solvability of the problem is confirmed. A necessary condition is given and proven for the existence of a feasible priority-based controller based on the notions of liveness and transition invariants. Next, a cyclic behavior graph is constructed, which shows the reachable markings that guarantee the maximum liveness of the system within a given bound vector. Finally, an on-line control strategy is proposed to enforce boundedness and liveness to the given system by appending priority relations to transitions. The dynamic priority relation changes flexibly according to the current state of the system and enforces the system evolving in a bounded and live manner. In addition, numerical examples are studied to verify the validity of the proposed approach that remains the structure of the plant net and is efficient for on-line control.
基金supported by the National Natural Science Foundation of China(Grant 62103101)the Natural Science Foundation of Jiangsu Province of China(Grant BK20210217)+5 种基金the China Postdoctoral Science Foundation(Grant 2022M710680)the National Natural Science Foundation of China(Grant 62273094)the"Zhishan"Scholars Programs of Southeast Universitythe Fundamental Science(Natural Science)General Program of Jiangsu Higher Education Institutions(No.21KJB470020)the Open Research Fund of Jiangsu Collaborative Innovation Center for Smart Distribution Network,Nanjing Institute of Technology(No.XTCX202102)the Introduced Talents Scientific Research Start-up Fund Project,Nanjing Institute of Technology(No.YKJ202133).
文摘This paper presents a finite-time economic model predictive control(MPC)algorithm that can be used for frequency regulation and optimal load dispatch in multi-area power systems.Economic MPC can be used in a power system to ensure frequency stability,real-time economic optimization,control of the system and optimal load dispatch from it.A generalized terminal penalty term was used,and the finite-time convergence of the system was guaranteed.The effectiveness of the proposed model predictive control algorithm was verified by simulating a power system,which had two areas connected by an AC tie line.The simulation results demonstrated the effectiveness of the algorithm.
文摘We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the generators of ϕ<sup>j</sup>-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences.
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 investigates the finite-time H<sub>∞</sub> control problem of switched nonlinear systems via state-dependent switching and state feedback control. Unlike the existing approach based on time-dependent switching strategy, in which the switching instants must be given in advance, the state-dependent switching strategy is used to design switching signals. Based on multiple Lyapunov-like functions method, several criteria for switched nonlinear systems to be finite-time H<sub>∞</sub> control are derived. Finally, a numerical example with simulation results is provided to show the validity of the conclusions.
基金supported by the Graduate Education Innovation Funds(2022CXZZ088)at Central China Normal University in Chinasupported by the NSFC(12225106,11931012)the Fundamental Research Funds(CCNU22LJ002)for the Central Universities in China。
文摘This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.
基金supported in part by the National Natural Science Foundation of China(61673001,61203051)the Foundation for Distinguished Young Scholars of Anhui Province(1608085J05)the Key Support Program of University Outstanding Youth Talent of Anhui Province(gxydZD201701)
文摘This paper studies the sliding mode controller design problems for a class of nonlinear system. The nonlinear function is considered to satisfy conic-type constraint condition. A novel finite-time boundedness(FTB) based sliding mode controller design theory is proposed. And then a sufficient condition is obtained in terms of linear matrix inequalities(LMIs), which guarantees the resulted sliding mode dynamics to be FTB wrt some predefined scalars. Thereafter, a FTB-based sliding mode control(SMC) law is synthesized to ensure the state of the controlled system is driven into a novel desired switching surface s(t) = c(c is a constant) in a finite time. Simulation results illustrate the validity of the proposed FTB-based SMC design theory.
基金This work was supported in part by the Central Government Drects Special Funds for Scientific and Technological Development of China(2019L3009)Natural Science Foundation of Fujian Province of China(2020J02045).
文摘This article addresses the finite-time boundedness(FTB)problem for nonlinear descriptor systems.Firstly,the nonlinear descriptor system is represented by the Takagi-Sugeno(T-S)model,where fuzzy representation is assumed to be appearing not only in both the state and input matrices but also in the derivative matrix.By using a descriptor redundancy approach,the fuzzy representation in the derivative matrix is reformulated into a linear one.Then,we introduce a fuzzy sliding mode control(FSMC)law,which ensures the finite-time boundedness(FTB)of closed-loop fuzzy control systems over the reaching phase and sliding motion phase.Moreover,by further employing the descriptor redundancy representation,the sufficient condition for designing FSMC law,which ensures the FTB of the closed-loop control systems over the entire finite-time interval,is derived in terms of linear matrix inequalities(LMIs).Finally,a simulation study with control of a photovoltaic(PV)nonlinear system is given to show the effectiveness of the proposed method.
基金supported by National Natural Science Foundation of China (No.60504007)the PhD Programs Foundation of Ministry of Educationof China (No.20070286040)the Scientific Research Foundation of Graduate School of Southeast University
文摘In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.
文摘Several boundedness criteria for the impulsive integro-differential systems with fixed moments of impulse effects are established, employing the method of Lyapunov functions and Razumikhin technique.