Control Of Multi-agent Systems Based On Barrier Lyapunov Functions

Centralized control has the disadvantages like the total system is too huge,the maintenance cost is high and the information acquisition is limited by computer performance.Due to the robustness,low maintenance cost and strong expansibility,distributed control has been widely concerned by researchers.As a popular topic,the multi-agent system has extensive application prospect in both military and civil areas.The distributed multi-agent control has been widely studied in several years.The consensus control problem is a classical problem of in the multiagent system research.It is always the focus of researches on the multi-agent system.In the case of multiple leaders,the consensus control problem can be extended to the containment control problem.Besides,in reality working environment,agents are always needed to collaborate in a definite formation,such as timing cruise or fire field cooperation rescue.This gives formation control problem an important role in multi-agent control problems.In this dissertation,the typical control problems of multi-agent system like consensus control,containment control and formation control are studied in detail.The main contribution of this dissertation is summarized as follows:The formation control of the first order and higher order multi-agent system is studied.The communication distance and obstacle avoidance are also necessary to be considered in the control law design of the formation control.In the study of the first order problem,in addition to adding the logarithmic term in the Lyapunov function to ensure the constraint condition,the disturbance term is added to the control law.It disappears only when the expected formation is formed.It is added to ensure the formation generating.It is more complex to study the formation control of higher order multi-agent system,but it is worth noting that most of the systems have high order characteristics in reality.The design of constraint conditions for high-order state is more challenging than first order systems.Different from the previous one,by establishing an integral barrier Lyapunov function,the control conditions can be obtained directly with less conservatism according to the derivation characteristic of the integral form.By combining the method of backstepping and the integral barrier Lyapunov function,the control law is proposed,which can effectively restrain the states of high-order.Finally,the system can reach form a fixed formation with all the state constraint condition not being violated.The containment control of the multi-agent system is studied.The system performance is limited with the capability of the single leader in a multi-agent system with one leader.A system with multiple leaders reduce the risk and construction cost.Based on the construction of the barrier Lyapunov function,constraint conditions on synchronous error are set.When the followers move to the convex hull formed by multiple leaders,the synchronous error is limited in a desired range.Finally,the synchronous error is reduced to zero when the control object is achieved.The multi-agent consensus problem and formation problem in nonholonomic system are studied.Due to the fact that the amount of control variables is less than the number of state variables,the control law construction of the nonholonomic system is very challenging.The Lyapunov function which contains the connectivity of the agent and the obstacle avoidance is constructed,the angle and speed control law of the nonholonomic system is constructed by the gradient function method.It ensures that agents achieve consensus control objective while in the limited area.In the stability analysis of Lyapunov function,the parameter relation of system stability is proposed.