| Consensus control problem is a fundamental problem in the field of Multi-Agent Systems(MASs)research,and the results on consensus research provide a solid theoretical foundation for solving various engineering problems,such as cooperative controls of robotic systems,state estimations of wireless networks and optimal controls of smart power grids.In a multi-agent system with a leader-following configuration,when there is only one agent serving as the leader,the purpose of collaborative control is to design a proper control law so that leader-following consensus is achieved;when there exists more than one leader,the containment control problem arises.Convergence speed is an important factor to be considered in controller design.Finite-time consensus control and fixed-time consensus control can make the system converge in a finite time,but the estimate of the upper bound of the convergence time is related to the system parameters,and sometimes it is even impossible to estimate.In prescribed-time consensus control,the expected convergence time can be preassigned in advance,and then the control protocol is designed according to the given expected value to achieve the goal of consensus control.Obviously,prescribed-time consensus research is more in line with actual application requirements.However,there are very few research results on prescribed-time collaborative control of MASs,and most of existing research focuses on relatively simple first-order MASs.Therefore,this thesis discusses the consensus control problem of second-order MASs with a leader-following configuration,and the event-trigger mechanism,sliding mode control method and adaptive control scheme are considered in the control protocol designs to achieve the defined consensus for MASs with various constraints.The main research works are as follows.(1)Based on the L2 gain control and event-trigger scheme,a new distributed control protocol is proposed to solve asymptotical leader-following consensus con-trol problem for a class of second-order MASs with bounded disturbances.Under the proposed control scheme,Less data needs to be transmitted on the network,and the frequency of control signal updates is also reduced.A sufficient condition for the system to achieve L2 leader-following asymptotical consensus is obtained based on Lyapunov's stability theory.(2)The problem of prescribed-time lag consensus control for nonlinear second-order MASs is investigated.A control protocol with time-varying control gains based on a time generator is proposed,so that the system can achieve lag con-sensus within any specified time.Furthermore,considering that sometimes the agents may be divided into several groups to carry out a task cooperatively,a prescribed-time cluster lag consensus control strategy is designed.Through theo-retical analysis,the sufficient conditions for the system to achieve prescribed-time lag consensus and prescribed-time cluster lag consensus are obtained respectively,and simulations are given to verify the effectiveness of the two proposed control protocols.(3)For the prescribed-time tracking control problem of nonlinear second-order MASs with time-varying Lipschitz coefficients and bounded disturbances,two distributed control protocol based on sliding mode control method are pro-posed.First,we consider the model without disturbances,and the designed controller can effectively compensate for the rapid growth of the time-varying Lipschitz coefficient.After that,the result is extended to the prescribed-time consensus control for MASs with bounded disturbances by designing a control protocol based on integral sliding mode control method.Finally,a different con-trol protocol based on terminal sliding mode method is proposed,which can make the position and velocity tracking errors of the followers converge to zero at the same time instant in preassigned time.(4)The prescribed-time leader-following consensus problem of stochastic second-order MASs subject to Actuator Failures is studied.Under the premise that the information about the loss of actuator effectiveness is known,a prescribed-time control protocol based on sliding mode control scheme is designed.In the case that parameters related to the actuator failures cannot be obtained,an adaptive control protocol based on sliding mode method is proposed which can make the state tracking errors converge to a given small sphere centered on the origin within any specified time.(5)The prescribed-time consensus control problem for second-order MASs with unmeasurable velocity states is investigated,and a control protocol based on observers and output state feedbacks is proposed.The designed observers can make the state tracking errors of each follower converge to zero within a specified time.Moreover,the control protocol only relies on its own observers and does not need the data from observers of its neighbor nodes.The sufficient conditions for the system to achieve prescribed-time leader-following consensus and the goal of prescribed-time containment control are respectively given. |
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