On Consensus Problem Of Nonlinear Fractional-Order Multi-Agent Systems

Consensus problem is a hot and basic problem in coordination control of multi-agent systems.The critical problem of consensus is how to design appropriate protocols or algorithms which describes the process of exchanging information among each agent and its neighbors so that the multi-agent systems can reach to a certain desired state.As an extension of integer-order system,fractional-order system can improve the char-acterization,design and control ability of real dynamic system,which has become a hot research topic in control field.Based on the existing results,this paper introduces the fractional calculus model into the consensus control problem of multi-agent system to improve and enrich the existing related research results.The fractional Lyapunov direct method is used in this paper to study the distributed consensus control of some classes of nonlinear fractional-order multi-agent systems(FOMASs),the specific work is as follows.In chapter 2,we consider the consensus problem of FOMASs with directed net-work topologies.At first,for the consensus problem without one leader,a constant and adaptive gain control algorithms are designed to ensure the consensus can be achieved,respectively.Then,for the tracking problem with one leader,we also design a constant and adaptive gain control algorithms respectively.By using the designed algorithms,it is theoretically proved that all agents with nonlinear fractional-order dynamics can reach consensus.Finally,some simulation examples are given to demonstrate the ef-fectiveness of the corresponding theoretical results.In chapter 3,we study the consensus tracking problem of nonlinear FOMASs with general directed network topologies.Due to the existence of heterogeneous control gains as well as a time-varying unknown leader in the nonlinear systems,the fractional-order dynamics of each agent is in essence heterogeneous.At first,a discontinuous distributed controller is constructed to guarantee that the distributed tracking control problem can be solved if some conditions are satisfied.Next,a continuous distributed controller is further proposed to eliminate the undesirable chattering phenomenon of the discontinuous controller,where the upper bound of the tracking error is uniformly bounded and can be made small enough by choosing the parameters appropriately.Finally,some simulation examples are presented to verify the effectiveness of the main results.In chapter 4,we investigate the robust consensus tracking problem for a class of uncertain FOMASs with a leader whose input is unknown and bounded.More specif-ically,multiple fractional-order systems with heterogeneous unknown nonlinearities and external disturbances are considered in this paper,which include the second-order MASs as its special cases.Firstly,a discontinuous neural network-based(NN-based)distributed robust adaptive algorithm is designed to guarantee the consensus tracking error exponentially converges to zero under a fixed topology.Also the derived results are further extended to the case of switching topology by appropriately choosing multi-ple Lyapunov functions.Secondly,a continuous NN-based distributed robust adaptive algorithm is further proposed to eliminate the undesirable chattering phenomenon of the discontinuous controller,where the consensus tacking error is uniformly ultimately bounded and can be reduced as small as desired.It is worth noting that all the proposed NN-based robust adaptive algorithms are independent of any global information and thus are fully distributed.Finally,numerical simulations are provided to validate the correctness of the proposed algorithms.In chapter 5,we address the robust consensus tracking problem for a class of uncertain nonlinear FOMASs under general directed topologies.More specifically,FOMASs in the presence of heterogeneous unknown nonlinearities and external distur-bances are considered in this paper,which include the second-order MASs as its special cases.Firstly,we design two distributed saturated observers to overcome the deficiency of the traditional tracking control strategies.Secondly,when there exists a dynamic-s leader with unknown and bounded state trajectory,a discontinuous observer-based distributed controller with ?-modification adaptive schemes is presented to guarantee the tacking error converges to zero asymptotically.Next,a continuous observer-based distributed controller is further proposed,under which the consensus tacking error is uniformly ultimately bounded and can be reduced as small as desired.A NN,whose weights are tuned online,is used in the designed controllers to approximate the un-known nonlinearities.Motivated by the ?-modification adaptive method,all the pro-posed adaptation algorithms require only local information and allow for robust even in the presence of heterogeneous unknown disturbances and fractional-order dynamics.Finally,the simulation results validate the efficacy of our proposed method.