The Study In The Consensus Problem Of Second Order Multi-agent Systems

In recent decades, the multi-agent system has attracts the attentions ofresearchers form control, physics, biology, computer science fields etc. It’s maybebecause of the wide application of MAS in UAV, alignment for cluster of satellites,collective motion of particles, flocking of birds and distributed computations. Lots ofproblems of MAS can be transform into the consensus problems. Leader-followingconsensus problem is one of the most important problems in MAS.He considers leader-following consensus problem of second-order multi-agentsand higher order linear multi-agent system in which the dynamics of each agent andthe leader is a linear system. In Chapter2, the leader-following consensus problemof second-order multi-agent under switching topology is studied. In this system theleader moves at a constant speedv d. To achieve consensus, a neighbor-basedcontrol protocol is proposed for each second-order agent. By constructing aparameter dependent common Lyapunov function and with the help of graph theoryas well as matrix theory, a sufficient condition are established to guarantee that allthe agents can achieve consensus and move with a given desired velocity as timegoes on. In Chapter3, we consider a multi-agent consensus problem with anaccelerated motion leader and variable interconnection topology. To track such aleader, a neighbor-based local controller together with a neighbor-basedstate-estimation rule is proposed for each second-order follower-agent. Theneighbor-based estimation rule is used to estimate the acceleration of the leader,which is assumed not to be measured by follower agents. By constructing aparameter-dependent common Lyapunov function (CLF), a sufficient condition is proposed to guarantee that each agent can follow the leader although the leadermoves with an unknown time-variant acceleration. Moreover, the tracking error isestimated for the case that the unknown acceleration part of the leader has boundedderivative. The leader-following consensus problem of higher order multi-agentsystems is considered in Chapter4. In this system, the dynamics of each agent andthe leader is a linear system. State-observer is constructed for each agent, Thecontrol of each agent using the constructed state and information of itself is designed,detailed analysis of the leader-following consensus is presented for switchinginteraction topologies, which describe the information exchange between themulti-agent systems. He proved the efficiency of control law proposed by usingalgebraic graph theory, Riccati function and Lyapunov function.