The trajectory tracking control problem for underactuated unmanned surface vehicles(USV) was addressed, and the control system took account of the uncertain influences induced by model perturbation, external disturban...The trajectory tracking control problem for underactuated unmanned surface vehicles(USV) was addressed, and the control system took account of the uncertain influences induced by model perturbation, external disturbance, etc. By introducing the reference, trajectory was generated by a virtual USV, and the error equation of trajectory tracking for USV was obtained, which transformed the tracking problem of underactuated USV into the stabilization problem of the trajectory tracking error equation. A backstepping adaptive sliding mode controller was proposed based on backstepping technology and method of dynamic slide model control. By means of theoretical analysis, it is proved that the proposed controller ensures that the solutions of closed loop system have the ultimate boundedness property. Simulation results are presented to illustrate the effectiveness of the proposed controller.展开更多
We consider the multiplicity of solutions to a p(x)-Laplacian problem involving supercritical Sobolev growth via Ricceri’s principle.By means of truncation combined with De Giorgi iteration,we can extend the results ...We consider the multiplicity of solutions to a p(x)-Laplacian problem involving supercritical Sobolev growth via Ricceri’s principle.By means of truncation combined with De Giorgi iteration,we can extend the results of subcritical and critical growth to supercritical growth and obtain at least three solutions to the p(x)-Laplacian problem.展开更多
基金Project(51409061)supported by the National Natural Science Foundation of ChinaProject(2013M540271)supported by China Postdoctoral Science Foundation+1 种基金Project(LBH-Z13055)Supported by Heilongjiang Postdoctoral Financial Assistance,ChinaProject(HEUCFD1403)supported by Basic Research Foundation of Central Universities,China
文摘The trajectory tracking control problem for underactuated unmanned surface vehicles(USV) was addressed, and the control system took account of the uncertain influences induced by model perturbation, external disturbance, etc. By introducing the reference, trajectory was generated by a virtual USV, and the error equation of trajectory tracking for USV was obtained, which transformed the tracking problem of underactuated USV into the stabilization problem of the trajectory tracking error equation. A backstepping adaptive sliding mode controller was proposed based on backstepping technology and method of dynamic slide model control. By means of theoretical analysis, it is proved that the proposed controller ensures that the solutions of closed loop system have the ultimate boundedness property. Simulation results are presented to illustrate the effectiveness of the proposed controller.
基金supported by the Fundamental Research Funds for the Central Universities(2024KYJD2006).
文摘We consider the multiplicity of solutions to a p(x)-Laplacian problem involving supercritical Sobolev growth via Ricceri’s principle.By means of truncation combined with De Giorgi iteration,we can extend the results of subcritical and critical growth to supercritical growth and obtain at least three solutions to the p(x)-Laplacian problem.
