This paper investigates the estimation of domain of attraction for nonlinear port controlled Hamiltonian （PCH） systems with actuator saturation （AS）. Several conditions are established under which an ellipsoid is ...This paper investigates the estimation of domain of attraction for nonlinear port controlled Hamiltonian （PCH） systems with actuator saturation （AS）. Several conditions are established under which an ellipsoid is contractively invariant, and thus can be employed to find the biggest ellipsoid contained in the domain of attraction. It is shown that the proposed conditions can be expressed in the form of the linear matrix inequalities （LMIs） optimization problem with constraints. Study of an illustrative example shows that the proposed method works very well in estimating the domain of attraction for some classes of nonlinear PCH systems with AS.展开更多
This paper considers the problem of disturbance tolerance/rejection of a switched system resulting from a family of linear systems subject to actuator saturation and E-infinity disturbances. For a given set of linear ...This paper considers the problem of disturbance tolerance/rejection of a switched system resulting from a family of linear systems subject to actuator saturation and E-infinity disturbances. For a given set of linear feedback gains, a given switching scheme and a given bound on the E-infinity norm of the disturbances, conditions are established, in terms of linear or bilinear matrix inequalities, under which a set of a certain form is invariant for a given switched linear system in the presence of actuator saturation and E-infinity disturbances, and the closed-loop system possesses a certain level of disturbance rejection capability. With these conditions, the design of feedback gains and switching scheme can be formulated and solved as constrained optimization problems. Disturbance tolerance is measured by the largest bound on the disturbances for which the trajectories starting from a given set remain bounded. Disturbance rejection is measured either by the E-infinity norm of the system output or by the system＇s ability to steer its state into and/or keep it within a small neighborhood of the origin. In the event that all systems in the family are identical, the switched system reduces to a single system under a switching feedback law. Simulation results show that such a single system under a switching feedback law could have stronger disturbance tolerance/rejection capability than a single linear feedback law can.展开更多
In this paper,we introduce the notions of bounded invariance complexity,bounded invariance complexity in the mean and mean Lyapunov-stability for control systems.Then we characterize these notions by introducing six t...In this paper,we introduce the notions of bounded invariance complexity,bounded invariance complexity in the mean and mean Lyapunov-stability for control systems.Then we characterize these notions by introducing six types of equi-invariability.As a by-product,two new dichotomy theorems for the control system on the control sets are established.展开更多
The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibr...The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibrium E0, a boundary equilibrium E1 and a posi- tive equilibrium E. under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E. and E1 and E., respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investi- gate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.展开更多
Earthquake is a violent and irregular ground motion that can severely damage structures. In this paper we subject a single-degree-of-freedom system, consisting of spring and damper, to an earthquake excitation, and me...Earthquake is a violent and irregular ground motion that can severely damage structures. In this paper we subject a single-degree-of-freedom system, consisting of spring and damper, to an earthquake excitation, and meanwhile investigate the response behavior from a novel theory about the dynamical system, by viewing the time-varying signum function of It can reflect the characteristic property of each earthquake through and the second component of f, where is a time-sampling record of the acceleration of a ground motion. The barcode is formed by plotting with respect to time. We analyze the complex jumping behavior in a barcode and an essential property of a high percentage occupation of the first set of dis-connectivity in the barcode from four strong earthquake records: 1940 El Centro earthquake, 1989 Loma earthquake, and two records of 1999 Chi-Chi earthquake. Through the comparisons of four earthquakes, we can observe that strong earthquake leads to large percentage of the first set of dis-connectivity.展开更多
基金supported by the National Nature Science Foundation of China (Nos. 61174036, 61074068, 61034007)the Independent Innovation Foundation of Shandong University (No. 2010TS078)the Research Fund for the Taishan Scholar Project of Shandong Province
文摘This paper investigates the estimation of domain of attraction for nonlinear port controlled Hamiltonian （PCH） systems with actuator saturation （AS）. Several conditions are established under which an ellipsoid is contractively invariant, and thus can be employed to find the biggest ellipsoid contained in the domain of attraction. It is shown that the proposed conditions can be expressed in the form of the linear matrix inequalities （LMIs） optimization problem with constraints. Study of an illustrative example shows that the proposed method works very well in estimating the domain of attraction for some classes of nonlinear PCH systems with AS.
文摘This paper considers the problem of disturbance tolerance/rejection of a switched system resulting from a family of linear systems subject to actuator saturation and E-infinity disturbances. For a given set of linear feedback gains, a given switching scheme and a given bound on the E-infinity norm of the disturbances, conditions are established, in terms of linear or bilinear matrix inequalities, under which a set of a certain form is invariant for a given switched linear system in the presence of actuator saturation and E-infinity disturbances, and the closed-loop system possesses a certain level of disturbance rejection capability. With these conditions, the design of feedback gains and switching scheme can be formulated and solved as constrained optimization problems. Disturbance tolerance is measured by the largest bound on the disturbances for which the trajectories starting from a given set remain bounded. Disturbance rejection is measured either by the E-infinity norm of the system output or by the system＇s ability to steer its state into and/or keep it within a small neighborhood of the origin. In the event that all systems in the family are identical, the switched system reduces to a single system under a switching feedback law. Simulation results show that such a single system under a switching feedback law could have stronger disturbance tolerance/rejection capability than a single linear feedback law can.
基金National Natural Science Foundation of China(Grant No.11771459)supported by Research Funds of Guangdong University of Foreign Studies(Grant Nos.299-X5218165 and 299-X5219222)+3 种基金Guangdong Basic and Applied Basic Research Foundation(Grant No.2019A1515110932)supported by National Natural Science Foundation of China(Grant Nos.11701584 and 11871228)the Natural Science Research Project of Guangdong Province(Grant No.2018KTSCX122)。
文摘In this paper,we introduce the notions of bounded invariance complexity,bounded invariance complexity in the mean and mean Lyapunov-stability for control systems.Then we characterize these notions by introducing six types of equi-invariability.As a by-product,two new dichotomy theorems for the control system on the control sets are established.
文摘The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibrium E0, a boundary equilibrium E1 and a posi- tive equilibrium E. under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E. and E1 and E., respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investi- gate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.
文摘Earthquake is a violent and irregular ground motion that can severely damage structures. In this paper we subject a single-degree-of-freedom system, consisting of spring and damper, to an earthquake excitation, and meanwhile investigate the response behavior from a novel theory about the dynamical system, by viewing the time-varying signum function of It can reflect the characteristic property of each earthquake through and the second component of f, where is a time-sampling record of the acceleration of a ground motion. The barcode is formed by plotting with respect to time. We analyze the complex jumping behavior in a barcode and an essential property of a high percentage occupation of the first set of dis-connectivity in the barcode from four strong earthquake records: 1940 El Centro earthquake, 1989 Loma earthquake, and two records of 1999 Chi-Chi earthquake. Through the comparisons of four earthquakes, we can observe that strong earthquake leads to large percentage of the first set of dis-connectivity.
