This paper considers the pose synchronization problem of a group of moving rigid bodies under switching topologies where the dwell time of each topology may has no nonzero lower bound. The authors introduce an average...This paper considers the pose synchronization problem of a group of moving rigid bodies under switching topologies where the dwell time of each topology may has no nonzero lower bound. The authors introduce an average dwell time condition to characterize the length of time intervals in which the graphs are connected. By designing distributed control laws of angular velocity and linear velocity,the closed-loop dynamics of multiple rigid bodies with switching topologies can be converted into a hybrid dynamical system. The authors employ the Lyapunov stability theorem, and show that the pose synchronization can be reached under the average dwell time condition. Moreover, the authors investigate the pose synchronization problem of the leader-following model under a similar average dwell time condition. Simulation examples are given to illustrate the results.展开更多
In this paper, the authors consider an on-line scheduling problem of rn （m≥ 3） identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance tim...In this paper, the authors consider an on-line scheduling problem of rn （m≥ 3） identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance time interval is larger than the largest processing time of jobs, the authors prove that any on-line algorithm has not a constant competitive ratio. For the case that the length of maintenance time interval is less than or equal to the largest processing time of jobs, the authors prove a lower bound of 3 on the competitive ratio. The authors give an on-line algorithm with competitive 1 ratio 4 - 1/m. In particular, for the case of m = 3, the authors prove the competitive ratio of the on-line algorithm is 10/3.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.61473189 and 61621003the National Key Basic Research Program of China(973 program)under Grant No.2014CB845302
文摘This paper considers the pose synchronization problem of a group of moving rigid bodies under switching topologies where the dwell time of each topology may has no nonzero lower bound. The authors introduce an average dwell time condition to characterize the length of time intervals in which the graphs are connected. By designing distributed control laws of angular velocity and linear velocity,the closed-loop dynamics of multiple rigid bodies with switching topologies can be converted into a hybrid dynamical system. The authors employ the Lyapunov stability theorem, and show that the pose synchronization can be reached under the average dwell time condition. Moreover, the authors investigate the pose synchronization problem of the leader-following model under a similar average dwell time condition. Simulation examples are given to illustrate the results.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271338,11171313,61070229,10901144,11001117supported by the Ph.D.Programs Foundation of Ministry ofEducation of China under Grant No.20111401110005the Henan Province Natural Science Foundation under Grant No.112300410047
文摘In this paper, the authors consider an on-line scheduling problem of rn （m≥ 3） identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance time interval is larger than the largest processing time of jobs, the authors prove that any on-line algorithm has not a constant competitive ratio. For the case that the length of maintenance time interval is less than or equal to the largest processing time of jobs, the authors prove a lower bound of 3 on the competitive ratio. The authors give an on-line algorithm with competitive 1 ratio 4 - 1/m. In particular, for the case of m = 3, the authors prove the competitive ratio of the on-line algorithm is 10/3.
