Abstract--The time-optimal control design of the double integrator is extended to the finite-time stabilization design that compensates both input saturation and input delay. With the aid of the Artstein＇s transforma...Abstract--The time-optimal control design of the double integrator is extended to the finite-time stabilization design that compensates both input saturation and input delay. With the aid of the Artstein＇s transformation, the problem is reduced to assigning a saturated finite-time stabilizer. Index Terms--Finite-time stabilization, input delay, saturated design.展开更多
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 exponential and prescribed finite-time stabilization with time-varying controller.First,the constraints of boundedness and differentiability on time delays are simultaneously relaxed,the Li...This paper investigates the exponential and prescribed finite-time stabilization with time-varying controller.First,the constraints of boundedness and differentiability on time delays are simultaneously relaxed,the Lipschitz condition for activation function is also relaxed.Second,different from the traditional Lyapunov function,two different time-varying Lyapunov functions are respectively constructed to achieve the exponential and prescribed finite-time stabilization.Significantly,the exponential convergence rate and the settling time are constants that can be given in advance and are not affected by system parameters and initial states.In addition,the time-varying controllers have good tolerance for disturbance caused by discontinuous functions and the disturbance is perfectly resolved and does not affect the control performance.Especially,the form of controllers is relatively simple and there is not necessary to design the fractional-order controllers for prescribed finite-time stabilization.Furthermore,the exponential and prescribed finite-time stabilization for FNNs without delay are respectively established via continuous time-varying state feedback control.Finally,examples show the effectiveness of the proposed control methods.展开更多
The problem of finite-time stabilization for uncertain nonlinear systems is investigated.It is proved that a class of high-order nonlinear systems in the lower-triangular form is globally stabilized via non-Lipschitz ...The problem of finite-time stabilization for uncertain nonlinear systems is investigated.It is proved that a class of high-order nonlinear systems in the lower-triangular form is globally stabilized via non-Lipschitz continuous state feedback.By using the finite-time Lyapunov stability theorem and the method of non-smooth feedback design,a recursive design procedure is provided,which guarantees the finite-time stability of the closed-loop system.The simulation results show the effectiveness of the theoretical results.展开更多
Gyroscopes are one of the most interesting and everlasting nonlinear nonautonomous dynamical systems that exhibit very complex dynamical behavior such as chaos. In this paper, the problem of robust stabilization of th...Gyroscopes are one of the most interesting and everlasting nonlinear nonautonomous dynamical systems that exhibit very complex dynamical behavior such as chaos. In this paper, the problem of robust stabilization of the nonlinear non-autonomous gyroscopes in a given finite time is studied. It is assumed that the gyroscope system is perturbed by model uncertainties, external disturbances, and unknown parameters. Besides, the effects of input nonlinearities are taken into account. Appropriate adaptive laws are proposed to tackle the unknown parameters. Based on the adaptive laws and the finite-time control theory, discontinuous finite-time control laws are proposed to ensure the finite-time stability of the system. The finite-time stability and convergence of the closed-loop system are analytically proved. Some numerical simulations are presented to show the efficiency of the proposed finite-time control scheme and to validate the theoretical results.展开更多
This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve fini...This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple, and one of the uncertain unified chaotic complex systems is robust. For the design of a finite-time controller on uncertain unified chaotic complex systems, only some of the unknown parameters need to be bounded. Simulation results for the chaotic complex Lorenz, Lu¨ and Chen systems are presented to validate the design and analysis.展开更多
Dear editor,This letter designs the event-triggered control(ETC)to achieve finite-time stabilization(FTS)of linear systems with input constraints.The key idea of the established algorithm is that the designed time-var...Dear editor,This letter designs the event-triggered control(ETC)to achieve finite-time stabilization(FTS)of linear systems with input constraints.The key idea of the established algorithm is that the designed time-varying high-gain is only scheduled on a specified time determined by an event-triggered mechanism.展开更多
In this paper, an adaptive feedback controller is proposed to achieve the finite-time stability of dynamical system. In the proposed scheme, the feedback gain of the adaptive feedback controller is automatically tuned...In this paper, an adaptive feedback controller is proposed to achieve the finite-time stability of dynamical system. In the proposed scheme, the feedback gain of the adaptive feedback controller is automatically tuned according to the adaptation law in order to stabilize unstable fixed points of the system. Based on the Lyapunov function method and the finite-time stability theory, we get a sufficient condition for the finite-time stability. Finally, simulation results show the effectiveness and feasibility of the proposed finite-time controller.展开更多
This paper presents control strategies for finite-time stabilization of a class of nonholonomic dynamic systems with unknown virtual control coefficients and system parameters. The minimal dilation degree technique an...This paper presents control strategies for finite-time stabilization of a class of nonholonomic dynamic systems with unknown virtual control coefficients and system parameters. The minimal dilation degree technique and the terminal sliding mode control scheme with finite-time convergence are used to design the controllers. The systematic control strategy development involves the introduction of state transformations and the application of recursive terminal sliding mode structure. Depending on whether the system in question can be converted into a time-invariant linear system or not, two control schemes are proposed respectively guaranteeing that system states converge to zero in finite time. The effectiveness and the robust feature of the developed control approaches are testified by two practical examples： the simplified underactuated hovercraft system and the parking problem for a mobile robot of the unicycle type.展开更多
Aimed at the finite-time stabilization problem of a class of flexible manipulators,a finite-time state feedback stabilization controller was proposed in this paper.Firstly,the nonlinear model of flexible manipulators ...Aimed at the finite-time stabilization problem of a class of flexible manipulators,a finite-time state feedback stabilization controller was proposed in this paper.Firstly,the nonlinear model of flexible manipulators was transformed into linear system through the exact state feedback linearization,and then using the finite time stabilization control method of the linear system,a finite-time state feedback stabilization controller was designed for the flexible manipulators.Furthermore,it was proved that all the states of flexible manipulators could be stabilized to equilibrium in finite-time under the proposed controller.The simulation results show that the performance of the flexible manipulators under the proposed finite-time state feedback controller is better than the traditional state-feedback controller.The proposed finite-time stabilization controller can improve the performance of the flexible manipulators.展开更多
Many practical systems in physics, biology, engineer- ing and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynami- cal processes. The problems of finit...Many practical systems in physics, biology, engineer- ing and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynami- cal processes. The problems of finite-time stab!lity analysis are investigated for a class of Markovian switching stochastic sys- tems, in which exist impulses at the switching instants. Multiple Lyapunov techniques are used to derive sufficient conditions for finite-time stochastic stability of the overall system. Furthermore, a state feedback controller, which stabilizes the closed loop sys- tems in the finite-time sense, is then addressed. Moreover, the controller appears not only in the shift part but also in the diffu- sion part of the underlying stochastic subsystem. The results are reduced to feasibility problems involving linear matrix inequalities （LMIs）. A numerical example is presented to illustrate the proposed methodology.展开更多
This article is concerned with the finite-time stabilization(FTSB) of a class of delayed-Hopfield neural networks with a timevarying delay in the leakage term in the presence of parameter uncertainties. To accomplish ...This article is concerned with the finite-time stabilization(FTSB) of a class of delayed-Hopfield neural networks with a timevarying delay in the leakage term in the presence of parameter uncertainties. To accomplish the target of FTSB, two new finitetime controllers are designed for uncertain delayed-Hopfield neural networks with a time-varying delay in the leakage term. By utilizing the finite-time stability theory and the Lyapunov-Krasovskii functional(LKF) approach, some sufficient conditions for the FTSB of these neural networks are established. These conditions, which can be used for the selection of control parameters,are in the form of linear matrix inequalities(LMIs) and can be numerically checked. Additionally, an upper bound of the settling time was estimated. Finally, our theoretical results are further substantiated by two numerical examples with graphical illustrations to demonstrate the effectiveness of the results.展开更多
In this paper, global finite-time stabilization problem for a large class of nonlinear control systems is considered. An iterative design approach is given based on Lyapunov function. The finite time stabilizing contr...In this paper, global finite-time stabilization problem for a large class of nonlinear control systems is considered. An iterative design approach is given based on Lyapunov function. The finite time stabilizing control laws are constructed in the form of continuous but non-smooth time-invariant feedback.展开更多
In this paper,the problem of making an input-delay system with saturating actuators finite-time stable by virtue of digital control is investigated.A digital state feedback controller and digital observer-controller c...In this paper,the problem of making an input-delay system with saturating actuators finite-time stable by virtue of digital control is investigated.A digital state feedback controller and digital observer-controller compensator are designed for two cases:when the state of the input-delay system are available or when it is unavailable.Sufficient conditions which guarantee finite-time stability of a closed-loop input-delay system are given and the proof procedure is presented in a heuristic way by constructing appropriate comparison functions.The condition can be transformed into the intersection of two curves satisfying some constraints,which reveals the relationship between designed parameters clearly.Finally,simulation results are presented to validate the method proposed in this paper.展开更多
Switching Markov jump linear system(SMJLS),a special hybrid system,has attracted a lot of studies recently.SMJLS is governed by stochastic and deterministic commutations.This paper focuses on the switching strategy wh...Switching Markov jump linear system(SMJLS),a special hybrid system,has attracted a lot of studies recently.SMJLS is governed by stochastic and deterministic commutations.This paper focuses on the switching strategy which stabilizes the SMJLS in a finite time interval in order to further expand the existing results and investigate new aspects of such systems.Several sufficient conditions for finite-time stability of discrete-time SMJLS are provided,and the numerical problems in these sufficient conditions are solved by solving linear matrix inequalities(LMIs).Finally,numerical examples are given to show the feasibility and effectiveness of the results.展开更多
Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimati...Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimating settling-time function (STF) of the hybrid systems.When switching dynamics are FTS and impulsive dynamics involve destabilizing delay-dependent impulses, the FTS is retained if the impulses occur infrequently.展开更多
This paper reports that the performance of permanent magnet synchronous motor （PMSM） degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear...This paper reports that the performance of permanent magnet synchronous motor （PMSM） degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system＇s security operation.展开更多
Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse, which severely threatens the secure and stable operation of the power system...Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse, which severely threatens the secure and stable operation of the power system. Based on the finite-time stability theory, two control strategies are presented to achieve finite-time chaos control. In addition, the problem of how to stabilize an unstable nonzero equilibrium point in a finite time is solved by coordinate transformation for the first time. Numerical simulations are presented to demonstrate the effectiveness and the robustness of the proposed scheme. The research in this paper may help to maintain the secure operation of power systems.展开更多
This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the F...This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.展开更多
Finite-time stability of a class of fractional-order neural networks is investigated in this paper. By Laplace transform, the generalized Gronwa11 inequality and estimates of Mittag-Leffier functions, sufficient condi...Finite-time stability of a class of fractional-order neural networks is investigated in this paper. By Laplace transform, the generalized Gronwa11 inequality and estimates of Mittag-Leffier functions, sufficient conditions are pre- sented to ensure the finite-time stability of such neural models with the Caputo fractionM derivatives. Furthermore, results about asymptotical stability of fractional-order neural models are also obtained.展开更多
基金partially supported by the National Natural Science Foundation of China(61374024,61321003,61325309)the Natural Science Foundation of Hunan Province(14JJ2016)the Teacher Research Foundation of Central South University(2013JSJJ023)
文摘Abstract--The time-optimal control design of the double integrator is extended to the finite-time stabilization design that compensates both input saturation and input delay. With the aid of the Artstein＇s transformation, the problem is reduced to assigning a saturated finite-time stabilizer. Index Terms--Finite-time stabilization, input delay, saturated design.
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National Natural Science Foundation of China under Grants 62203338,61936004,61821003,62173259 and 62176192Postdoctoral Science Foundation of China under Grant 2022M722485.
文摘This paper investigates the exponential and prescribed finite-time stabilization with time-varying controller.First,the constraints of boundedness and differentiability on time delays are simultaneously relaxed,the Lipschitz condition for activation function is also relaxed.Second,different from the traditional Lyapunov function,two different time-varying Lyapunov functions are respectively constructed to achieve the exponential and prescribed finite-time stabilization.Significantly,the exponential convergence rate and the settling time are constants that can be given in advance and are not affected by system parameters and initial states.In addition,the time-varying controllers have good tolerance for disturbance caused by discontinuous functions and the disturbance is perfectly resolved and does not affect the control performance.Especially,the form of controllers is relatively simple and there is not necessary to design the fractional-order controllers for prescribed finite-time stabilization.Furthermore,the exponential and prescribed finite-time stabilization for FNNs without delay are respectively established via continuous time-varying state feedback control.Finally,examples show the effectiveness of the proposed control methods.
基金Sponsored by the National Natural Science Foundation of China (Grant No. 61174001)
文摘The problem of finite-time stabilization for uncertain nonlinear systems is investigated.It is proved that a class of high-order nonlinear systems in the lower-triangular form is globally stabilized via non-Lipschitz continuous state feedback.By using the finite-time Lyapunov stability theorem and the method of non-smooth feedback design,a recursive design procedure is provided,which guarantees the finite-time stability of the closed-loop system.The simulation results show the effectiveness of the theoretical results.
文摘Gyroscopes are one of the most interesting and everlasting nonlinear nonautonomous dynamical systems that exhibit very complex dynamical behavior such as chaos. In this paper, the problem of robust stabilization of the nonlinear non-autonomous gyroscopes in a given finite time is studied. It is assumed that the gyroscope system is perturbed by model uncertainties, external disturbances, and unknown parameters. Besides, the effects of input nonlinearities are taken into account. Appropriate adaptive laws are proposed to tackle the unknown parameters. Based on the adaptive laws and the finite-time control theory, discontinuous finite-time control laws are proposed to ensure the finite-time stability of the system. The finite-time stability and convergence of the closed-loop system are analytically proved. Some numerical simulations are presented to show the efficiency of the proposed finite-time control scheme and to validate the theoretical results.
基金the National Natural Science Foundation of China(Grant Nos.60874009 and 10971120)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2010FM010)
文摘This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple, and one of the uncertain unified chaotic complex systems is robust. For the design of a finite-time controller on uncertain unified chaotic complex systems, only some of the unknown parameters need to be bounded. Simulation results for the chaotic complex Lorenz, Lu¨ and Chen systems are presented to validate the design and analysis.
基金supported in part by the National Natural Science Foundation of China(52075132,51907038)the State Key Laboratory of Digital Manufacturing Equipment&Technology(Huazhong University of Science and Technology)(DMETKF2020024)。
文摘Dear editor,This letter designs the event-triggered control(ETC)to achieve finite-time stabilization(FTS)of linear systems with input constraints.The key idea of the established algorithm is that the designed time-varying high-gain is only scheduled on a specified time determined by an event-triggered mechanism.
文摘In this paper, an adaptive feedback controller is proposed to achieve the finite-time stability of dynamical system. In the proposed scheme, the feedback gain of the adaptive feedback controller is automatically tuned according to the adaptation law in order to stabilize unstable fixed points of the system. Based on the Lyapunov function method and the finite-time stability theory, we get a sufficient condition for the finite-time stability. Finally, simulation results show the effectiveness and feasibility of the proposed finite-time controller.
基金supported by National Natural Science Foundation of China(No.61273091)Project of Taishan Scholar of Shandong Province of China,and the Ph.D.Programs Foundation of Ministry of Education of China
文摘This paper presents control strategies for finite-time stabilization of a class of nonholonomic dynamic systems with unknown virtual control coefficients and system parameters. The minimal dilation degree technique and the terminal sliding mode control scheme with finite-time convergence are used to design the controllers. The systematic control strategy development involves the introduction of state transformations and the application of recursive terminal sliding mode structure. Depending on whether the system in question can be converted into a time-invariant linear system or not, two control schemes are proposed respectively guaranteeing that system states converge to zero in finite time. The effectiveness and the robust feature of the developed control approaches are testified by two practical examples： the simplified underactuated hovercraft system and the parking problem for a mobile robot of the unicycle type.
基金Sponsored by the Doctoral Fund of Ministry of Education of China(20070288022)the Natural Science Foundation of Jiangsu Province of China(BK2008404)the Young Teacher Academic Foundation of Nanjing University of Technology(39710013)
文摘Aimed at the finite-time stabilization problem of a class of flexible manipulators,a finite-time state feedback stabilization controller was proposed in this paper.Firstly,the nonlinear model of flexible manipulators was transformed into linear system through the exact state feedback linearization,and then using the finite time stabilization control method of the linear system,a finite-time state feedback stabilization controller was designed for the flexible manipulators.Furthermore,it was proved that all the states of flexible manipulators could be stabilized to equilibrium in finite-time under the proposed controller.The simulation results show that the performance of the flexible manipulators under the proposed finite-time state feedback controller is better than the traditional state-feedback controller.The proposed finite-time stabilization controller can improve the performance of the flexible manipulators.
基金supported in part by the National Natural Science Foundation of China(60374015)
文摘Many practical systems in physics, biology, engineer- ing and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynami- cal processes. The problems of finite-time stab!lity analysis are investigated for a class of Markovian switching stochastic sys- tems, in which exist impulses at the switching instants. Multiple Lyapunov techniques are used to derive sufficient conditions for finite-time stochastic stability of the overall system. Furthermore, a state feedback controller, which stabilizes the closed loop sys- tems in the finite-time sense, is then addressed. Moreover, the controller appears not only in the shift part but also in the diffu- sion part of the underlying stochastic subsystem. The results are reduced to feasibility problems involving linear matrix inequalities （LMIs）. A numerical example is presented to illustrate the proposed methodology.
文摘This article is concerned with the finite-time stabilization(FTSB) of a class of delayed-Hopfield neural networks with a timevarying delay in the leakage term in the presence of parameter uncertainties. To accomplish the target of FTSB, two new finitetime controllers are designed for uncertain delayed-Hopfield neural networks with a time-varying delay in the leakage term. By utilizing the finite-time stability theory and the Lyapunov-Krasovskii functional(LKF) approach, some sufficient conditions for the FTSB of these neural networks are established. These conditions, which can be used for the selection of control parameters,are in the form of linear matrix inequalities(LMIs) and can be numerically checked. Additionally, an upper bound of the settling time was estimated. Finally, our theoretical results are further substantiated by two numerical examples with graphical illustrations to demonstrate the effectiveness of the results.
基金supported by the National Natural Science Foundation of China(Grant Nos.60425307,10472129 and 60221301).
文摘In this paper, global finite-time stabilization problem for a large class of nonlinear control systems is considered. An iterative design approach is given based on Lyapunov function. The finite time stabilizing control laws are constructed in the form of continuous but non-smooth time-invariant feedback.
基金supported by the National Natural Science Foundation of China(61773216)Natural Science Foundation of Jiangsu Province of China(BK20171386)
文摘In this paper,the problem of making an input-delay system with saturating actuators finite-time stable by virtue of digital control is investigated.A digital state feedback controller and digital observer-controller compensator are designed for two cases:when the state of the input-delay system are available or when it is unavailable.Sufficient conditions which guarantee finite-time stability of a closed-loop input-delay system are given and the proof procedure is presented in a heuristic way by constructing appropriate comparison functions.The condition can be transformed into the intersection of two curves satisfying some constraints,which reveals the relationship between designed parameters clearly.Finally,simulation results are presented to validate the method proposed in this paper.
基金the National Natural Science Foundation of China(No.61573237)the“111 Project”(No.D18003)the Program of China Scholarship Council(No.201906895021)。
文摘Switching Markov jump linear system(SMJLS),a special hybrid system,has attracted a lot of studies recently.SMJLS is governed by stochastic and deterministic commutations.This paper focuses on the switching strategy which stabilizes the SMJLS in a finite time interval in order to further expand the existing results and investigate new aspects of such systems.Several sufficient conditions for finite-time stability of discrete-time SMJLS are provided,and the numerical problems in these sufficient conditions are solved by solving linear matrix inequalities(LMIs).Finally,numerical examples are given to show the feasibility and effectiveness of the results.
基金supported by the National Natural Science Foundation of China(61833005)
文摘Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimating settling-time function (STF) of the hybrid systems.When switching dynamics are FTS and impulsive dynamics involve destabilizing delay-dependent impulses, the FTS is retained if the impulses occur infrequently.
基金Project supported by the Hi-Tech Research and Development Program of China (863) (Grant No 2007AA05Z229)National Natural Science Foundation of China (Grant Nos 50877028, 60774069 and 10862001)Science Foundation of Guangdong Province (Grant No 8251064101000014)
文摘This paper reports that the performance of permanent magnet synchronous motor （PMSM） degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system＇s security operation.
基金supported by the National High Technology Research and Development Program of China (Grant No. 2007AA041401)Tianjin Natural Science Foundation,China (Grant Nos. 08JCZDJC18600 and 09JCZDJC23900)the University Science and Technology Development Foundation of Tianjin City,China (Grant No. 2006ZD32)
文摘Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse, which severely threatens the secure and stable operation of the power system. Based on the finite-time stability theory, two control strategies are presented to achieve finite-time chaos control. In addition, the problem of how to stabilize an unstable nonzero equilibrium point in a finite time is solved by coordinate transformation for the first time. Numerical simulations are presented to demonstrate the effectiveness and the robustness of the proposed scheme. The research in this paper may help to maintain the secure operation of power systems.
基金supported by the Mathematical Tianyuan Foundation (No. 10826078)the National Natural Science Foundation of China (No. 60874006)
文摘This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20093401120001the Natural Science Foundation of Anhui Province under Grant No.11040606M12+1 种基金the Natural Science Foundation of Anhui Education Bureau under Grant No.KJ2010A035the 211 Project of Anhui University under Grant No.KJJQ1102
文摘Finite-time stability of a class of fractional-order neural networks is investigated in this paper. By Laplace transform, the generalized Gronwa11 inequality and estimates of Mittag-Leffier functions, sufficient conditions are pre- sented to ensure the finite-time stability of such neural models with the Caputo fractionM derivatives. Furthermore, results about asymptotical stability of fractional-order neural models are also obtained.
