Distributed Consensus Control For A Class Of Multi-agent Systems With Unmatched Nonlinearities

In recent years,inspired by the human sociological and the biology study,researches on multi-agent systems(MASs)have been attracted much attentions.Compared with the single system,by transferring and sharing information,MASs can cooperate with each other to complete a complicated task which can not be completed by the single system,and thus it has extensive applications in reality.Currently,the researches on consensus control for MASs mainly focus on the systems with first order-,high order-integrator and matched nonlinear dynamics.Actually,a lot of mechanical systems,such as flexible manipulator and spacecraft etc,are formulated by the complicated nonlinear equations.However,the studies on consensus control for complicated nonlinear MASs are difficult and not yet mature,especially for the cases with complex network environment,limited control and communications energy and rapid convergence rate for system.Motivated by this,we consider the distributed consensus problem for a class of complicated nonlinear MASs with unmatched nonlinearities.The main works of this paper include:Firstly,the leader-following consensus problem is investigated for second order MASs with unmatched nonlinearities and unknown model parameters.By introducing adaptive control,a fully distributed controller which is independent of eigenvalues of communication graph is designed.It guarantees all followers' state variables to consensus with that of leader asymptotically.Based on the Lyapunov stability theory and nonlinear adaptive control theory,the effectiveness of the proposed controller is proved.Secondly,the finite-time leader-following consensus problem is addressed for a class of high-order MASs with lower-triangular nonlinear dynamics.By using backstepping control method,we develop the finite-time consensus control design scheme which can deal with the unmatched nonlinearities step by step and further enable the followers' state variables to consensus with that of leader in finite-time.The topology matrix is introduced for the design of Lyapunov function,which guarantees the distributedness of designed controller.Thirdly,the leader-following consensus problem is investigated for high-orderstochastic nonlinear MASs with immeasurable states.Each agent is modeled by lower-triangular system.By using dynamic output feedback control method,a novel distributed observer-type consensus protocol is proposed based only on the relative output measurements.It not only ensures that all the agents in network reach 1th moment exponential leader-following consensus,but also reduces the amounts of information exchanging among agents.In addition,the controller is constructed without using the traditional backstepping method,which makes the design procedure simple and convenient for use.Furthermore,in practice,agents are often equipped with a small embedded digital micro-processor which usually has limited computing,communicating and actuating capabilities.Thus,the event-based leader-following consensus problem is investigated for high-order nonlinear MASs whose dynamics are in lower-triangle form.By using event-triggered control scheme and dynamic output feedback control method in combination,a new class of distributed event-triggered consensus protocols are proposed.It is noted that the proposed controller only requires the output information of neighboring agents to be shared and it only updates when a certain important events occur,thus the communication cost is reduced significantly.Finally,the distributed event-triggered consensus problem is investigated for a class of nonlinear MASs subject to actuator saturation.A new distributed event-based dynamic output feedback controller is put forward via only the relative output measurements of neighbouring agents.By introducing event-triggered control method,the controllers for agents only update when a certain important events occur.Based on the Lyapunov stability theory and saturated control theory,sufficient conditions are derived to guarantee the exponential leader-following consensus.Furthermore,the problem of designing distributed event-triggered controller such that the domain of attraction(DOA)for consensus errors is enlarged is formulated and solved as an optimization problem with matrix inequality constraints.