This article deals with the consensus problem of multi-agent systems by developing a fixed-time consensus control approach with a dynamic event-triggered rule. First, a new fixedtime stability condition is obtained wh...This article deals with the consensus problem of multi-agent systems by developing a fixed-time consensus control approach with a dynamic event-triggered rule. First, a new fixedtime stability condition is obtained where the less conservative settling time is given such that the theoretical settling time can well reflect the real consensus time. Second, a dynamic event-triggered rule is designed to decrease the use of chip and network resources where Zeno behaviors can be avoided after consensus is achieved, especially for finite/fixed-time consensus control approaches. Third, in terms of the developed dynamic event-triggered rule, a fixed-time consensus control approach by introducing a new item is proposed to coordinate the multi-agent system to reach consensus. The corresponding stability of the multi-agent system with the proposed control approach and dynamic eventtriggered rule is analyzed based on Lyapunov theory and the fixed-time stability theorem. At last, the effectiveness of the dynamic event-triggered fixed-time consensus control approach is verified by simulations and experiments for the problem of magnetic map construction based on multiple mobile robots.展开更多
In this work we consider the following class of elliptic problems{−Δ_(A)u+u=a(x)|u|^(q−2)u+b(x)|u|^(p−2)u in R^(N),u∈H_(A)^(1)(R^(N)),(P)with 2<q<p<2^(∗)=2N/N−2,a(x)and b(x)are functions that can change sig...In this work we consider the following class of elliptic problems{−Δ_(A)u+u=a(x)|u|^(q−2)u+b(x)|u|^(p−2)u in R^(N),u∈H_(A)^(1)(R^(N)),(P)with 2<q<p<2^(∗)=2N/N−2,a(x)and b(x)are functions that can change sign and satisfy some additional conditions;u∈H_(A)^(1)(R^(N))and A:R^(N)→R^(N) is a magnetic potential.Also using the Nehari method in combination with other complementary arguments,we discuss the existence of infinitely many solutions to the problem in question,varying the assumptions about the weight functions.展开更多
基金supported in part by the National Natural Science Foundation of China (62073108)the Zhejiang Provincial Natural Science Foundation(LZ23F030004)+1 种基金the Key Research and Development Project of Zhejiang Province (2019C04018)the Fundamental Research Funds for the Provincial Universities of Zhejiang (GK229909299001-004)。
文摘This article deals with the consensus problem of multi-agent systems by developing a fixed-time consensus control approach with a dynamic event-triggered rule. First, a new fixedtime stability condition is obtained where the less conservative settling time is given such that the theoretical settling time can well reflect the real consensus time. Second, a dynamic event-triggered rule is designed to decrease the use of chip and network resources where Zeno behaviors can be avoided after consensus is achieved, especially for finite/fixed-time consensus control approaches. Third, in terms of the developed dynamic event-triggered rule, a fixed-time consensus control approach by introducing a new item is proposed to coordinate the multi-agent system to reach consensus. The corresponding stability of the multi-agent system with the proposed control approach and dynamic eventtriggered rule is analyzed based on Lyapunov theory and the fixed-time stability theorem. At last, the effectiveness of the dynamic event-triggered fixed-time consensus control approach is verified by simulations and experiments for the problem of magnetic map construction based on multiple mobile robots.
基金grants from FAPESP 2017/16108-6grants from FAPESP 2019/24901-3 and CNPq 307061/2018-3supported by CAPES/Brazil and the paper was completed while the second author was visiting the Departament of Mathematics of UFJF whose hospitality she gratefully acknowledges.
文摘In this work we consider the following class of elliptic problems{−Δ_(A)u+u=a(x)|u|^(q−2)u+b(x)|u|^(p−2)u in R^(N),u∈H_(A)^(1)(R^(N)),(P)with 2<q<p<2^(∗)=2N/N−2,a(x)and b(x)are functions that can change sign and satisfy some additional conditions;u∈H_(A)^(1)(R^(N))and A:R^(N)→R^(N) is a magnetic potential.Also using the Nehari method in combination with other complementary arguments,we discuss the existence of infinitely many solutions to the problem in question,varying the assumptions about the weight functions.
