Research On A Daptive Finite-Time Consensus And Surrounding Control For Uncertain Nonlinear Multi-Agent Systems

Multi-agent systems(MASs)have attracted the attention of many scholars due to their high cooperation,strong adaptability,high fault-tolerance and scalability,and have been widely used in multiple unmanned aerial vehicle systems,power dispatching systems,surveillance and reconnaissance systems,etc.In practical MASs,nonlinearity and uncertainty inevitably exist,and the uncertainty includes the system uncertainty and network uncertainty.The nonlinearity and uncertainty of different types/attributes have different impacts on the control effectiveness and bring challenges to the design and analysis of distributed cooperative control.In addition to considering the dynamic equations of agents,it is also necessary to consider the impact of complex network topologies characterizing information interactions between agents on system evolution and achieving cooperative goals.Besides,as technology advances,there are more and more time-critical/speedcritical applications,in which cooperative goals need to be accurately achieved within a limited time.This promotes the in-depth research on the finite-time distributed cooperative control of MASs.Therefore,the research on finite-time distributed cooperative control of uncertain nonlinear MASs under different network topologies has important theoretical and practical significance.In this dissertation,we investigate the finite-time distributed cooperative control problem of several classes of uncertain nonlinear MASs under different topologies,mainly focusing on consensus and surrounding.The considered uncertainties include system uncertainties and network uncertainties,i.e.,unknown control coefficients,unknown parameters in nonlinearities and unknown time-varying weights.Topologies include fixed topology and state-dependent topology.Complex system dynamics and network topologies bring challenges to achieve the finite-time consensus and the finite-time surrounding,particularly in establishing feedback compensation mechanisms and finite-time performance mechanisms,and revealing the relationship between different network topologies and the realization of cooperative goals.For several typical uncertain nonlinear MASs,under different network topologies,adaptive finite-time distributed control strategies with stronger feedback capability are developed to compensate multiple uncertainties.Moreover,fully distributed protocols(independent of global graph information)are designed to achieve the finite-time consensus and the fast finite-time surrounding for multiple moving targets.The main works of this dissertation consist of the following four aspects:(Ⅰ)Fully distributed adaptive finite-time consensus for uncertain nonlinear MASsAdaptive finite-time consensus problem is investigated for uncertain nonlinear MASs.The systems not only allow unknown control coefficients,but also allow unknown parameters in nonlinearities,and moreover the consensus protocol is required to be fully distributed.To this end,using adaptive technique based on dynamic high gain,a new fully distributed protocol is designed to achieve the finite-time consensus.Particularly,unlike relevant literature,introducing only one dynamic high gain,rather than multiple gains/estimators,is adequate to simultaneously compensate for unknown control coefficients,unknown parameters in nonlinearities,and the global graph information.Moreover,the adaptive finitetime consensus protocol is extended to the scenario of leader-following MASs.(Chapter 3 in the dissertation)(Ⅱ)Fully distributed adaptive finite-time consensus under uncertain network topologyFinite-time leader-following consensus problem of second-order uncertain nonlinear MASs is studied.Consider the scenario that the communication network may sufer from link failures and network attacks,which is reflected in the unknown weight of network topology in MASs.In addition to the uncertainties in network topology,unknown control coefficients are also allowed in systems.The coexistence of the network uncertainty and system uncertainty challenges the design of the finite-time distributed consensus protocol.For this,it is necessary to introduce a strong compensation mechanism and organically integrate it with the finite-time performance guarantee mechanism.By using the adaptive technique based on dynamic high gain and the method of adding power integration,a fully distributed protocol based on finite-time observers is designed.Moreover,the protocol effectively compensates network uncertainties,system uncertainties,and the unavailable global graph information caused by the network uncertainty,and thereby achieving the finite-time leader-following consensus.(Chapter 4 in the dissertation)(Ⅲ)Fully distributed adaptive finite-time consensus under statedependent network topologyIn many practical MASs,such as wireless sensor networks,the interaction between agents can be characterized by state-dependent topology.Unlike the fixed topology and time-dependent topology,the weight of the state-dependent topology changes with the relative state between agents.In this situation,the finitetime consensus problem for uncertain nonlinear MASs is studied.For nonlinear MASs that allow unknown control coefficients and unknown Lipschitz constant,a dynamic high gain is introduced to effectively compensate these two kinds of uncertainties,and a condition is provided to guarantee that the state-dependent topology is connected.Then,a new fully distributed finite-time control strategy is developed to make agents states reach a same value in a finite time.(Chapter 5 in the dissertation)(Ⅳ)Fast finite-time surrounding control for multiple moving targetsFor uncertain nonlinear MASs with unknown control coefficients,the fast finite-time surrounding problem for multiple moving targets is studied.Considering the fact that only a small portion of followers can directly obtain the target information,fast finite-time distributed observers with dynamic high gains are designed using only the relative information between neighbors to estimate the velocities of targets.It proves that the observation errors can quickly converge to zero within a finite time.Based on this,a fast finite time distributed protocol with dynamic high gains is designed,which guarantees that followers can surround multiple moving targets at an exponential rate in a finite time.Moreover,unlike traditional finite-time control,which has only local rapidity,the obtained finite-time surrounding has global rapidity.(Chapter 6 in the dissertation)...