In this paper, we surveyed the development of maximum-entropy clustering algorithm, pointed out that the maximum-entropy clustering algorithm is not new in essence, and constructed two examples to show that the itera... In this paper, we surveyed the development of maximum-entropy clustering algorithm, pointed out that the maximum-entropy clustering algorithm is not new in essence, and constructed two examples to show that the iterative sequence given by the maximum-entropy clustering algorithm may not converge to a local minimum of its objective function, but a saddle point. Based on these results, our paper shows that the convergence theorem of maximum-entropy clustering algorithm put forward by Kenneth Rose et al. does not hold in general cases.展开更多
In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly sm...In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.展开更多
The problem of guidance law is investigated for multiple interceptors to attack a target cooperatively.A leader-following cooperative guidance strategy is presented to render the leader and the followers reach the tar...The problem of guidance law is investigated for multiple interceptors to attack a target cooperatively.A leader-following cooperative guidance strategy is presented to render the leader and the followers reach the target at specified impact time.The guidance law of leader is given to meet the demand of specified impact time.The arrival time is synchronized by enforcing the ranges-to-go of followers keep consensus with that of leader.The convergence time bound is estimated without dependence on the initial states,since the proposed leader-following cooperative guidance law is fixed-time convergent.The simulation is developed to validate the availability of proposed cooperative guidance law.展开更多
Corrected explicit-implicit domain decomposition(CEIDD) algorithms are studied for parallel approximation of semilinear parabolic problems on distributed memory processors. It is natural to divide the spatial domain i...Corrected explicit-implicit domain decomposition(CEIDD) algorithms are studied for parallel approximation of semilinear parabolic problems on distributed memory processors. It is natural to divide the spatial domain into some smaller parallel strips and cells using the simplest straightline interface(SI) . By using the Leray-Schauder fixed-point theorem and the discrete energy method,it is shown that the resulting CEIDD-SI algorithm is uniquely solvable,unconditionally stable and convergent. The CEIDD-SI method always suffers from the globalization of data communication when interior boundaries cross into each other inside the domain. To overcome this disadvantage,a composite interface(CI) that consists of straight segments and zigzag fractions is suggested. The corresponding CEIDD-CI algorithm is proven to be solvable,stable and convergent. Numerical experiments are presented to support the theoretical results.展开更多
This paper proposes a novel fixed-time sliding mode control approach for trajectory-tracking tasks of a mecanum-wheeled omnidirectional mobile robot.First,the idea of two-phase attractors is introduced into the domain...This paper proposes a novel fixed-time sliding mode control approach for trajectory-tracking tasks of a mecanum-wheeled omnidirectional mobile robot.First,the idea of two-phase attractors is introduced into the domain of sliding mode control,and a new fixed-time sliding surface is proposed.Then,according to this sliding surface,a new type of nonsingular fast terminal sliding mode control algorithm is designed for the omnidirectional mobile robot,which can realize a fast fixed-time convergence property.The stability of the control system is proven scrupulously,and a guideline for control-parameter tuning is expounded.Finally,experiments are implemented to test the trajectory-tracking performance of the robot.Experimental results demonstrate the superiority of the proposed sliding surface and the corresponding control scheme in comparison with benchmark controllers.展开更多
文摘 In this paper, we surveyed the development of maximum-entropy clustering algorithm, pointed out that the maximum-entropy clustering algorithm is not new in essence, and constructed two examples to show that the iterative sequence given by the maximum-entropy clustering algorithm may not converge to a local minimum of its objective function, but a saddle point. Based on these results, our paper shows that the convergence theorem of maximum-entropy clustering algorithm put forward by Kenneth Rose et al. does not hold in general cases.
基金the National Natural Science Foundation of China (10771050)
文摘In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.
基金This work was supported by the National Key Research and Development Program of China(Grant No.2017YFB1400702)and the National Natural Science Foundation of China(Grant Nos.61932014,61972018 and 61803357).
文摘The problem of guidance law is investigated for multiple interceptors to attack a target cooperatively.A leader-following cooperative guidance strategy is presented to render the leader and the followers reach the target at specified impact time.The guidance law of leader is given to meet the demand of specified impact time.The arrival time is synchronized by enforcing the ranges-to-go of followers keep consensus with that of leader.The convergence time bound is estimated without dependence on the initial states,since the proposed leader-following cooperative guidance law is fixed-time convergent.The simulation is developed to validate the availability of proposed cooperative guidance law.
基金supported by National Natural Science Foundation of China (Grant No. 10871044)
文摘Corrected explicit-implicit domain decomposition(CEIDD) algorithms are studied for parallel approximation of semilinear parabolic problems on distributed memory processors. It is natural to divide the spatial domain into some smaller parallel strips and cells using the simplest straightline interface(SI) . By using the Leray-Schauder fixed-point theorem and the discrete energy method,it is shown that the resulting CEIDD-SI algorithm is uniquely solvable,unconditionally stable and convergent. The CEIDD-SI method always suffers from the globalization of data communication when interior boundaries cross into each other inside the domain. To overcome this disadvantage,a composite interface(CI) that consists of straight segments and zigzag fractions is suggested. The corresponding CEIDD-CI algorithm is proven to be solvable,stable and convergent. Numerical experiments are presented to support the theoretical results.
基金supported by the National Natural Science Foundation of China(62003305)the Natural Science Foundation of Zhejiang Province(LQ21F030015)+1 种基金the Key Research and Development Program of Zhejiang Province(2022C03029)the Public Welfare Application Research Project of Huzhou City(2022GZ15).
文摘This paper proposes a novel fixed-time sliding mode control approach for trajectory-tracking tasks of a mecanum-wheeled omnidirectional mobile robot.First,the idea of two-phase attractors is introduced into the domain of sliding mode control,and a new fixed-time sliding surface is proposed.Then,according to this sliding surface,a new type of nonsingular fast terminal sliding mode control algorithm is designed for the omnidirectional mobile robot,which can realize a fast fixed-time convergence property.The stability of the control system is proven scrupulously,and a guideline for control-parameter tuning is expounded.Finally,experiments are implemented to test the trajectory-tracking performance of the robot.Experimental results demonstrate the superiority of the proposed sliding surface and the corresponding control scheme in comparison with benchmark controllers.
