By constructing two suitable generalized Lyapunov functions,we derived a generalized ellipsoidal estimate of the globally attractive set and positively invariant set of the unified chaotic system with the parameters ...By constructing two suitable generalized Lyapunov functions,we derived a generalized ellipsoidal estimate of the globally attractive set and positively invariant set of the unified chaotic system with the parameters α=1/29 and 1/29<α<2/29,respectively,which extends some related results of Li,et al. [Li DM,Lu JA,Wu XQ,Chen GR,Estimating the global basin of attraction and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Applications,2006,323(2): 844-853]. The theoretical results obtained in this paper will find wide application in chaos control and synchronization.展开更多
A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized Lorenz system.We derived an ellipsoidal estimate of the ultimate bound and positively invari...A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized Lorenz system.We derived an ellipsoidal estimate of the ultimate bound and positively invariant set for the generalized Lorenz system,for all the positive values of system parameters a,b,and c.Our results extend the related result of Li,et al.[Li DM,Lu JA,Wu XQ,et al.,Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Application,2006,323(2):844-653].展开更多
An efficient algorithm is proposed for computing the solution to the constrained finite time optimal control （CFTOC） problem for discrete-time piecewise affine （PWA） systems with a quadratic performance index. The...An efficient algorithm is proposed for computing the solution to the constrained finite time optimal control （CFTOC） problem for discrete-time piecewise affine （PWA） systems with a quadratic performance index. The maximal positively invariant terminal set, which is feasible and invariant with respect to a feedback control law, is computed as terminal target set and an associated Lyapunov function is chosen as terminal cost. The combination of these two components guarantees constraint satisfaction and closed-loop stability for all time. The proposed algorithm combines a dynamic programming strategy with a multi-parametric quadratic programming solver and basic polyhedral manipulation. A numerical example shows that a larger stabilizable set of states can be obtained by the proposed algorithm than precious work.展开更多
This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative ...This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative dynamic variable and an additive dynamic variable.The addressed DETM-based fuzzy MPC issue is described as a “min-max” optimization problem(OP).To facilitate the co-design of the MPC controller and the weighting matrix of the DETM,an auxiliary OP is proposed based on a new Lyapunov function and a new robust positive invariant(RPI) set that contain the membership functions and the hybrid dynamic variables.A dynamic event-triggered fuzzy MPC algorithm is developed accordingly,whose recursive feasibility is analysed by employing the RPI set.With the designed controller,the involved fuzzy system is ensured to be asymptotically stable.Two examples show that the new DETM and DETM-based MPC algorithm have the advantages of reducing resource consumption while yielding the anticipated performance.展开更多
Constructing a family of generalized Lyapunov functions, a new method is proposed to obtain new global attractive set and positive invariant set of the Lorenz chaotic system. The method we proposed greatly simplifies ...Constructing a family of generalized Lyapunov functions, a new method is proposed to obtain new global attractive set and positive invariant set of the Lorenz chaotic system. The method we proposed greatly simplifies the complex proofs of the two famous estimations presented by the Russian scholar Leonov. Our uniform formula can derive a series of the new estimations. Employing the idea of intersection in set theory, we extract a new Leonov formula-like estimation from the family of the estimations. With our method and the new estimation, one can confirm that there are no equilibrium, periodic solutions, almost periodic motions, wandering motions or other chaotic attractors outside the global attractive set. The Lorenz butterfly-like singular attractors are located in the global attractive set only. This result is applied to the chaos control and chaos synchronization. Some feedback control laws are obtained to guarantee that all the trajectories of the Lorenz systems track a periodic solution, or globally stabilize an unstable (or locally stable but not globally asymptotically stable) equilibrium. Further, some new global exponential chaos synchronization results are presented. Our new method and the new results are expected to be applied in real secure communication systems.展开更多
A sufficient condition of the existence of a positive invariant set in the differential equation on Banach space is given, which improves a theorem of Mitio Nagumo.
This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nomina...This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.展开更多
A nonautonomous multispecies competition-predator system with type Ⅱfunctional response is studied in this paper. It is proved that the system is per-manent under some appropriate conditions. Further, if the system i...A nonautonomous multispecies competition-predator system with type Ⅱfunctional response is studied in this paper. It is proved that the system is per-manent under some appropriate conditions. Further, if the system is a periodic one, a set of easily verifiable suflficient conditions which guarantee the existence, uniqueness and global attractivity of a strictly positive periodic solution are ob-tained.展开更多
文摘By constructing two suitable generalized Lyapunov functions,we derived a generalized ellipsoidal estimate of the globally attractive set and positively invariant set of the unified chaotic system with the parameters α=1/29 and 1/29<α<2/29,respectively,which extends some related results of Li,et al. [Li DM,Lu JA,Wu XQ,Chen GR,Estimating the global basin of attraction and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Applications,2006,323(2): 844-853]. The theoretical results obtained in this paper will find wide application in chaos control and synchronization.
文摘A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized Lorenz system.We derived an ellipsoidal estimate of the ultimate bound and positively invariant set for the generalized Lorenz system,for all the positive values of system parameters a,b,and c.Our results extend the related result of Li,et al.[Li DM,Lu JA,Wu XQ,et al.,Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Application,2006,323(2):844-653].
基金supported by the National Natural Science Foundation of China (60702033)Natural Science Foundation of Zhe-jiang Province (Y107440)
文摘An efficient algorithm is proposed for computing the solution to the constrained finite time optimal control （CFTOC） problem for discrete-time piecewise affine （PWA） systems with a quadratic performance index. The maximal positively invariant terminal set, which is feasible and invariant with respect to a feedback control law, is computed as terminal target set and an associated Lyapunov function is chosen as terminal cost. The combination of these two components guarantees constraint satisfaction and closed-loop stability for all time. The proposed algorithm combines a dynamic programming strategy with a multi-parametric quadratic programming solver and basic polyhedral manipulation. A numerical example shows that a larger stabilizable set of states can be obtained by the proposed algorithm than precious work.
基金supported by the National Natural Science Foundation of China (62073303,61673356)Hubei Provincial Natural Science Foundation of China (2015CFA010)the 111 Project(B17040)。
文摘This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative dynamic variable and an additive dynamic variable.The addressed DETM-based fuzzy MPC issue is described as a “min-max” optimization problem(OP).To facilitate the co-design of the MPC controller and the weighting matrix of the DETM,an auxiliary OP is proposed based on a new Lyapunov function and a new robust positive invariant(RPI) set that contain the membership functions and the hybrid dynamic variables.A dynamic event-triggered fuzzy MPC algorithm is developed accordingly,whose recursive feasibility is analysed by employing the RPI set.With the designed controller,the involved fuzzy system is ensured to be asymptotically stable.Two examples show that the new DETM and DETM-based MPC algorithm have the advantages of reducing resource consumption while yielding the anticipated performance.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.60274007,60474011)the Guangdong Povince Science Foundation for Program of Research Team(Grant No.04205783).
文摘Constructing a family of generalized Lyapunov functions, a new method is proposed to obtain new global attractive set and positive invariant set of the Lorenz chaotic system. The method we proposed greatly simplifies the complex proofs of the two famous estimations presented by the Russian scholar Leonov. Our uniform formula can derive a series of the new estimations. Employing the idea of intersection in set theory, we extract a new Leonov formula-like estimation from the family of the estimations. With our method and the new estimation, one can confirm that there are no equilibrium, periodic solutions, almost periodic motions, wandering motions or other chaotic attractors outside the global attractive set. The Lorenz butterfly-like singular attractors are located in the global attractive set only. This result is applied to the chaos control and chaos synchronization. Some feedback control laws are obtained to guarantee that all the trajectories of the Lorenz systems track a periodic solution, or globally stabilize an unstable (or locally stable but not globally asymptotically stable) equilibrium. Further, some new global exponential chaos synchronization results are presented. Our new method and the new results are expected to be applied in real secure communication systems.
文摘A sufficient condition of the existence of a positive invariant set in the differential equation on Banach space is given, which improves a theorem of Mitio Nagumo.
基金supported in part by the National Defense Basic Scientific Research Program of China(JCKY2018603C015)Cultivation Plan of Major Research Program of Harbin Institute of Technology(ZDXMPY20180101)
文摘This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.
基金Supported by the NNSF of China(19972058) and the NSF of Yunnan Province (2001A0001M).
文摘A nonautonomous multispecies competition-predator system with type Ⅱfunctional response is studied in this paper. It is proved that the system is per-manent under some appropriate conditions. Further, if the system is a periodic one, a set of easily verifiable suflficient conditions which guarantee the existence, uniqueness and global attractivity of a strictly positive periodic solution are ob-tained.
