Research On Consensus Problems Of Multi-agent Systems Without Velocity Measurements

During the past decade,distributed cooperative control of multi-agent systems has attracted a great deal of attention in many fields.As a fundamental problem in distributed cooperative control,consensus has become one of hot topics in multi-agent systems.This paper mainly investigates the consensus tracking problems of second-order multi-agent systems,which means that multiple second-order agents cooperate with each other to track a common moving target eventually.Till now,lots of results about the consensus tracking problems of multi-agent systems have been obtained.Most of existing consensus tracking protocols need to utilize position information and velocity information of an agent.However,in real application,it is quite difficult to measure the velocity information owing to the technological limitations and environmental disturbances.Therefore,it is important to consider the consensus tracking problems of second-order multi-agent systems without velocity measurements.Meanwhile,in many cases,due to the application of digital sensors and controllers,only sampled-data of an agent and its neighbors at discrete sampling instants is available for the synthesis of control laws.Thus,it is necessary to investigate the sampled-data consensus tracking problems of second-order multi-agent systems without velocity measurements.This paper studies the consensus tracking problems of second-order multi-agent systems based on sampled-data without velocity measurements.The following results are obtained:(1)The consensus tracking problems of second-order multi-agent systems with a bounded-velocity target based on sampled-data without velocity measurements are considered.The observer-based method is used to estimate the velocity of an agent,and the consensus tracking protocol without velocity measurements is proposed.The augmented matrix method,the eigenvalue analysis method and the algebraic graph theory are used to obtain the necessary and sufficient conditions guaranteeing second-order multi-agent systems with a bounded-velocity target to achieve asymptotic bounded consensus tracking.Furthermore,numerical simulations illustrate the effectiveness of the proposed protocol.(2)The consensus tracking problems of second-order multi-agent systems with a bounded-acceleration target based on sampled-data without velocity measurements are studied.A sampled-data consensus tracking protocol without velocity measurements is obtained by using the numerical derivative to approximate the velocity.The augmented matrix method,the eigenvalue analysis method and the algebraic graph theory are employed to theoretically prove that under certain conditions,second-order multi-agent systems with an asymptotically-unbounded-velocity and bounded-acceleration target,applying the proposed protocol,can achieve asymptotic bounded consensus tracking.Last,numerical simulations are provided to illustrate the effectiveness of the proposed protocol.(3)The consensus tracking problems of second-order multi-agent systems with a bounded-jerk target based on sampled-data without velocity measurements are investigated.By using the numerical derivative to approximate the velocity,this paper proposes a sampled-data consensus tracking protocol without velocity measurements.The augmented matrix method,the eigenvalue analysis method and the algebraic graph theory are utilized to derive the necessary and sufficient conditions guaranteeing that second-order multi-agent systems with an asymptotically-unbounded-acceleration and bounded-jerk target achieve asymptotic bounded consensus tracking.Moreover,numerical simulations are given to illustrate the effectiveness of the proposed protocol.