In this paper,the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced.The fixed point theorems satisfying generalized contractive conditions are obtained,without appealing to c...In this paper,the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced.The fixed point theorems satisfying generalized contractive conditions are obtained,without appealing to completeness of X or normality of the cone.The continuity of the mapping is relaxed.Furthermore,we prove that the completeness in cone metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X.These results greatly generalize several well-known comparable results in the literature.展开更多
The mobile loading arm(MLA)system is one of the most important mechanical equipments in the petrochemical industry consisting of rigid pipelines and rotating elbows.This paper researches the problems of dynamical mode...The mobile loading arm(MLA)system is one of the most important mechanical equipments in the petrochemical industry consisting of rigid pipelines and rotating elbows.This paper researches the problems of dynamical modelling and tracking control.At first,an MLA dynamic model is built by using Euler-Lagrange function.And then,an adaptive third-order fixed time sliding mode(FDTSM)tracking controller with chattering free is represented,which enables the MLA system to dock with the vehicle tank mouth.In this paper,a new double-layer third-order fixed time sliding mode controller is first proposed to address the tracking problem in model-based MLA systems with known parameters.Moreover,considering the presence of modeling uncertainty and external disturbances,a nerual network adaptive FDTSM controller is designed to ensure that the close-loop system state tracking error converges to a bounded region around zero within a fixed time.Further,the stability of the close-loop system is proven by using the Lyapunov stability theorem.Simulation results illustrate the validaty of the controller.展开更多
基金Supported by the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities'Association(202101BA070001-045)the Science and Technology Development Fund,Macao SAR(0019/2021/A1).
文摘In this paper,the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced.The fixed point theorems satisfying generalized contractive conditions are obtained,without appealing to completeness of X or normality of the cone.The continuity of the mapping is relaxed.Furthermore,we prove that the completeness in cone metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X.These results greatly generalize several well-known comparable results in the literature.
基金supported by the Beijing University of Posts and Telecommunications(BUPT)Excellent Ph.D.Students Foundation under Grant No.CX2020116。
文摘The mobile loading arm(MLA)system is one of the most important mechanical equipments in the petrochemical industry consisting of rigid pipelines and rotating elbows.This paper researches the problems of dynamical modelling and tracking control.At first,an MLA dynamic model is built by using Euler-Lagrange function.And then,an adaptive third-order fixed time sliding mode(FDTSM)tracking controller with chattering free is represented,which enables the MLA system to dock with the vehicle tank mouth.In this paper,a new double-layer third-order fixed time sliding mode controller is first proposed to address the tracking problem in model-based MLA systems with known parameters.Moreover,considering the presence of modeling uncertainty and external disturbances,a nerual network adaptive FDTSM controller is designed to ensure that the close-loop system state tracking error converges to a bounded region around zero within a fixed time.Further,the stability of the close-loop system is proven by using the Lyapunov stability theorem.Simulation results illustrate the validaty of the controller.
