Consensus Control Of Heterogeneous Mixed-order Nonlinear Multiagent Systems

Studies related to multi-agent systems(MASs)are progressing fast over the years and have broad applications in many domains.As the studies deepening and the needs of actual engineering increasing,the mission of MASs is getting more complicated.The agents may belong to non-identical types,and have different control tasks and different states to be synchronized in practical engineering.That means,not only the dynamics of the agents may be different but also the orders of their dynamics may be non-identical.This kind of MASs is usually called as mixed-order MASs.However,most of the existing results of cooperative consensus control are focused on the homogeneous MASs,in which the controlled MASs are considered to have identical-order dynamics.Very few existing papers study the control problem of mixed-order MASs.Moreover,the research on mixed-order MASs mostly considers the agents to be linear and with the dynamics of single-or double-integrators,which obviously cannot solve the control problem of MASs with nonlinear mixed-order dynamics.Therefore,to give the results of MASs more generality and apply the cooperative control to broader domains,this work researches the consensus control problem of mixed-order nonlinear MASs.First,the consensus tracking control problem of the mixed-order nonlinear MASs which are composed of the following agents having first-and second-order dynamics is studied.Here,the agents are considered to have non-identical order dynamics,unknown time-varying nonlinearity and external disturbances.Neural networks and adaptive parameter estimation schemes are used to approximate and compensate the effect of nonlinearity and external disturbances.Novel distributed cooperative control protocols are presented for mixed-order MASs to realize the ultimate synchronization to the leader.The cooperative fault-tolerant control problem of mixed-order nonlinear MASs with actuator and amplifier faults is investigated.Different from the traditional fault-tolerant research on MASs,this paper considers not only the actuator faults,but also the servo amplifier faults for the controlled mechanical MASs.The actuator fault usually appears as a kind of losing actuator effectiveness in real application.And,the amplifier fault is often represented by the fluctuating of amplification value under various operation points,like bandwidth,load and external disturbance.In this paper,a novel distributed cooperative fault-tolerant control strategy is proposed for mixed-order nonlinear MASs to reduce the effect of actuator and amplifier faults.The event-based consensus tracking control problem of mixed-order nonlinear MASs is studied.In practice,the frequent trigger of the actuation may increase the agent's energy consumption,and may lead to more tear and wear.Appropriate event-triggered mechanism can effectively save system resources and increase the control efficiency of MASs.In addition,some practical agents may have only velocity sensors and velocity output.To solve this problem and make the results more general,here we consider that the following agents are of first-order position,first-order velocity and second-order.Based on these three types of agents,novel event-triggered mechanism based control protocols are presented for mixed-order nonlinear MASs to lower the cost of system resources and increase the system performance.The tracking control of mixed-order MASs under the condition of unmeasurable states and unknown external disturbances is studied.In practice,considering economy,complexity and reliability,only part of the agents' states can be measured directly and the full states of the agents may be hard to obtain.The control strategy designed based on the full states may not be able to apply to the nonlinear mixed-order MASs.To address this issue,the distributed observer is designed to approximate the followers'and their neighbors' unmeasurable states,and a novel estimated-state-based disturbance observer is designed to lower the effect of unknown external disturbances.By the observations,a novel distributed consensus control strategy is developed to ensure the synchronization to the leader for the mixed-order nonlinear MASs.Finally,the consensus tracking control problem of mixed-order nonlinear MASs with higher-order dynamics is investigated.In practice,many systems may contain higher-order dynamics.But most of the existing results about mixed-order nonlinear MASs are focused on the MASs with first-and second-order dynamics.Therefore,to solve more practical cooperative control problems,we assume that the orders of agents' dynamics are non-identical and can be arbitrary,first-,second-,or higher-order.Due to the fact that the agents with mixed-order dynamics may have different numbers of states to be synchronized from each other,we establish a new method to define the mixed-order global neighborhood synchronization errors to make the dimensions of each-order global error consistent.The mixed-order sliding-mode errors are designed differently for the agents with different-order dynamics to adjust their control performance more flexibly.Novel distributed cooperative control protocols are presented to achieve the consensus of mixed-order MASs with higher-order dynamics,and the Lyapunov function is chosen based on the newly developed auxiliary state matrices to ensure the stability of the whole mixed-order MASs.