This paper presents a constructive design of new controllers that force underactuated ships under constant or slow time-varying sea loads to asymptotically track a parameterized reference path, that guarantees the dis...This paper presents a constructive design of new controllers that force underactuated ships under constant or slow time-varying sea loads to asymptotically track a parameterized reference path, that guarantees the distance from the ship to the reference path always be within a specified value. The control design is based on a global exponential disturbance observer, a transformation of the ship dynamics to an almost spherical form, an interpretation of the tracking errors in an earth-fixed frame, an introduction of dynamic variables to compensate for relaxation of the reference path generation, p-times differentiable step functions, and backstepping and Lyapunov＇s direct methods. The effectiveness of the proposed results is illustrated through simulations.展开更多
In order to investigate a complicated physical system, it is convenient to consider a simple, easy to solve model, which is chosen to reflect as much physics as possible of the original system, as an ideal approximati...In order to investigate a complicated physical system, it is convenient to consider a simple, easy to solve model, which is chosen to reflect as much physics as possible of the original system, as an ideal approximation. Motivated by this fundamental idea, we propose a novel asymptotic method, the nonsensitive homotopy-Pade approach. In this method, homotopy relations are constructed to link the original system with an ideal, solvable model. An artificial homotopy parameter is introduced to the homotopy relations as the normal perturbation parameter to generate the perturbation series, and is used to implement the Padd approximation. Meanwhile, some other auxiliary nonperturbative parameters, which are used to control the convergence of the perturbation series, are inserted to the approximants, and are fixed via the principle of minimal sensitivity. The method is used to study the eigenvalue problem of the quantum anharmonic oscillators. Highly accurate numerical results show its validity. Possible further studies on this method are also briefly discussed.展开更多
This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are as...This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then we further show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which indicates that V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Our main technique is the supersolutions and subsolutions method coupled with the comparison principle.展开更多
In this paper, we introduce stochasticity into an SIR epidemic model with vaccina- tion. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by t...In this paper, we introduce stochasticity into an SIR epidemic model with vaccina- tion. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by the method of stochastic Lyapunov functions, we carry out a detailed analysis on the dynamical behavior of the stochastic model regarding of the basic reproduction number R0. If R0 ≤ 1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model. If R0 〉 1, there is a stationary distribution and the solution has the ergodic property, which means that the disease will prevail.展开更多
基金Supported in Part by the Australian Research Council Under Grant No.DP0988424
文摘This paper presents a constructive design of new controllers that force underactuated ships under constant or slow time-varying sea loads to asymptotically track a parameterized reference path, that guarantees the distance from the ship to the reference path always be within a specified value. The control design is based on a global exponential disturbance observer, a transformation of the ship dynamics to an almost spherical form, an interpretation of the tracking errors in an earth-fixed frame, an introduction of dynamic variables to compensate for relaxation of the reference path generation, p-times differentiable step functions, and backstepping and Lyapunov＇s direct methods. The effectiveness of the proposed results is illustrated through simulations.
基金Supported by the National Natural Science Foundations of China under Grant Nos.10735030,10475055,10675065 and 90503006National Basic Research Program of China (973 Program) under Grant No.2007CB814800+2 种基金Program for Changjiang Scholars and Innovative Research Team (IRT0734)the Research Fund of Postdoctoral of China under Grant No.20070410727Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20070248120
文摘In order to investigate a complicated physical system, it is convenient to consider a simple, easy to solve model, which is chosen to reflect as much physics as possible of the original system, as an ideal approximation. Motivated by this fundamental idea, we propose a novel asymptotic method, the nonsensitive homotopy-Pade approach. In this method, homotopy relations are constructed to link the original system with an ideal, solvable model. An artificial homotopy parameter is introduced to the homotopy relations as the normal perturbation parameter to generate the perturbation series, and is used to implement the Padd approximation. Meanwhile, some other auxiliary nonperturbative parameters, which are used to control the convergence of the perturbation series, are inserted to the approximants, and are fixed via the principle of minimal sensitivity. The method is used to study the eigenvalue problem of the quantum anharmonic oscillators. Highly accurate numerical results show its validity. Possible further studies on this method are also briefly discussed.
基金supported by National Natural Science Foundation of China(Grant Nos.11031003,11271172 and 11071105)the Fundamental Research Funds for the Central Universities(Grant No.HIT.NSRIF.2014063)+2 种基金China Postdoctoral Science Foundation Funded Project(Grant No.2012M520716)Heilongjiang Postdoctoral Fund(Grant No.LBH-Z12135)New Century Excellent Talents in University(Grant No.NCET-10-0470)
文摘This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then we further show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which indicates that V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Our main technique is the supersolutions and subsolutions method coupled with the comparison principle.
文摘In this paper, we introduce stochasticity into an SIR epidemic model with vaccina- tion. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by the method of stochastic Lyapunov functions, we carry out a detailed analysis on the dynamical behavior of the stochastic model regarding of the basic reproduction number R0. If R0 ≤ 1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model. If R0 〉 1, there is a stationary distribution and the solution has the ergodic property, which means that the disease will prevail.
