We propose a novel approach called the robust fractional-order proportional-integral-derivative（FOPID）controller, to stabilize a perturbed nonlinear chaotic system on one of its unstable fixed points. The stability ...We propose a novel approach called the robust fractional-order proportional-integral-derivative（FOPID）controller, to stabilize a perturbed nonlinear chaotic system on one of its unstable fixed points. The stability analysis of the nonlinear chaotic system is made based on the proportional-integral-derivative actions using the bifurcation diagram. We extract an initial set of controller parameters, which are subsequently optimized using a quadratic criterion. The integral and derivative fractional orders are also identified by this quadratic criterion. By applying numerical simulations on two nonlinear systems, namely the multi-scroll Chen system and the Genesio-Tesi system,we show that the fractional PI~λD~μ controller provides the best closed-loop system performance in stabilizing the unstable fixed points, even in the presence of random perturbation.展开更多
The consensus problem for fractional multi-agent systems(MASs)with time delay is considered.The distributed fractional proportional-integral(PI)-type controller is designed so that the consensus of the proposed system...The consensus problem for fractional multi-agent systems(MASs)with time delay is considered.The distributed fractional proportional-integral(PI)-type controller is designed so that the consensus of the proposed systems is achieved.Moreover,explicit condition to determine the crossing directions is developed.The results show that with the increase of time delay,the closed-loop system has two different dynamic characteristics:From consensus to nonconsensus and consensus switching.Furthermore,delay margin within which consensus of MASs will always hold is determined.The results should provide useful guidelines in the consensus analysis and in the analytical design of the distributed controllers.展开更多
基金Project supported by the Ministry of Higher Education and Scientific Research,Algeria(CNEPRU No.A10N01UN210120150002)
文摘We propose a novel approach called the robust fractional-order proportional-integral-derivative（FOPID）controller, to stabilize a perturbed nonlinear chaotic system on one of its unstable fixed points. The stability analysis of the nonlinear chaotic system is made based on the proportional-integral-derivative actions using the bifurcation diagram. We extract an initial set of controller parameters, which are subsequently optimized using a quadratic criterion. The integral and derivative fractional orders are also identified by this quadratic criterion. By applying numerical simulations on two nonlinear systems, namely the multi-scroll Chen system and the Genesio-Tesi system,we show that the fractional PI~λD~μ controller provides the best closed-loop system performance in stabilizing the unstable fixed points, even in the presence of random perturbation.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.61773207,62173183the Natural Science Fund for Distinguished Young Scholars of Jiangsu Province under Grant No.BK20190020.
文摘The consensus problem for fractional multi-agent systems(MASs)with time delay is considered.The distributed fractional proportional-integral(PI)-type controller is designed so that the consensus of the proposed systems is achieved.Moreover,explicit condition to determine the crossing directions is developed.The results show that with the increase of time delay,the closed-loop system has two different dynamic characteristics:From consensus to nonconsensus and consensus switching.Furthermore,delay margin within which consensus of MASs will always hold is determined.The results should provide useful guidelines in the consensus analysis and in the analytical design of the distributed controllers.
