Research On H? Distributed Cooperative Control Problem Of Multi-agent Systems With Switching Topologies And Random Delays

In recent years,distributed cooperative control problem of multi-agent sys-tems has gained more and more attention.Generally speaking,the main task of the problem is to design a distributed control protocol for every agent by using local information from its neighbors,such that the multi-agent systems achieve prescribed behaviors.The dissertation studies H? distributed cooperative control problem of multi-agent systems in several cases.The main results of the paper are listed as below:Robust H? leader-f'ollowing consensus problem of multi-agent systems over random uncertain topologies and Markovian switching topologies with partially unknown transition rates is investigated in Chapter 2.Markovian process can be used to describe the random switching phenomenon among finite states and has good properties,such as the property of no aftereffect.In practical systems,some of the transition rates are unknown or not easy to access,thus the transition rates of the Markovian jump process are considered to be partially unknown.And random uncertain topologies described by the Bernoulli distributed sequences are considered.A neighbor-based protocol with random uncertain communication links and mode-dependent control gains is proposed.The external disturbance is considered and dealt with by using H? control theory.By stochastic stability theory,sufficient conditions expressed in the form of linear matrix inequalities are derived,under which all the followers will asymptotically track with the leader in the mean square sense with a prescribed H? performance index.H? leader-following consensus problem of nonlinear multi-agent systems un-der semi-Markovian switching topologies with partially unknown transition rates is discussed in Chapter 3.The sojourn-time of a Markovian jump process follows exponential distribution,while the sojourn-time of a semi-Markovian jump pro-cess may follow some other probability distributions rather than an exponential distribution,thus a Markovian jump process can be viewed as a special case of a semi-Markovian jump process.Compared with many works on the consensus of multi-agent systems with Markovian switching topologies,a model of nonlinear multi-agent systems described by semi-Markovian topologies is proposed,which is more general.Moreover,in practical systems,some of the transition rates are unknown or not easy to access,thus the transition rates of the semi-Markovian jump process are considered to be partially known.The external disturbance is considered in the multi-agent systems.By graph theory,H? control theory and stochastic theory,sufficient conditions are derived to ensure that all the follow-ers can asymptotically track with the leader in the mean square sense with a prescribed H? performance index.H? containment control problem of multi-agent systems with Bernoulli ran-dom delays is studied in Chapter 4.During the communication among the a-gents,the information can be sometimes transmitted instantly,and sometimes delayed.Such phenomenon can be described by random communication delays,characterized by a Bernoulli process.Distributed protocol is proposed with such random delays.The distributed control problem for multi-agents with multiple leaders when there exits external disturbance is studied.By H? control theory and stochastic stability for time-delay systems,sufficient conditions are obtained to make sure that all the followers can asymptotically converge to the convex spanned by the leaders with a prescribed H? performance index.H? leader-following consensus problem of multi-agent systems with Marko-vian random delays is discussed in Chapter 5.Time delays exist not only during the communication among the agents,but also in each agent.It is assumed that randomly switching topologies are governed by a Markovian process,and there exits a corresponding time-varying delay for each topology,thus the delays are Markovian random delays,which can be also called as mode-dependent delay.Then a protocol based on the neighbor rule is proposed,and the external distur-bance is considered.By constructing Lyapunov functional,sufficient conditions are deduced to solve H? leader-following consensus problem.H? leader-following consensus problem of multi-agent systems with semi-Markovian random delays is studied in Chapter 6.As semi-Markovian are more general than Markovian process,thus it is important to use semi-Markovian to describe random time delays.Based on Chapter 5,the randomly switching topolo-gies are supposed to be governed by a semi-Markovian process,and there exits a corresponding time-varying delay for each topology,thus the delays are Marko-vian random delays,which can be also named as mode-dependent delay.Then a protocol with semi-Markovian topologies is proposed,and the external distur-bance is considered.By graph theory,H? control theory,stochastic stability theory of time delay system and using the upper and lower bounds of the tran-sition rates,sufficient conditions are derived to ensure that all the followers can asymptotically track with the leader in the mean square sense with a prescribed H? performance index.The practical leader-following consensus problem of heterogeneous multi-agent systems under a sampled-data-based event-triggered condition is investigat-ed in Chapter 7,with the fixed topology and semi-Markovian switching topolo-gies,respectively.In practical environment,the agents are often heterogeneous,thus it is important to study the consensus problem of heterogeneous multi-agent systems.On the other hand,the event-triggered control strategy is an effective way to save communication and computation resources.For many works on con-tinuous event-triggered strategy,where the event-triggered condition need to be continuously monitored,which also may lead to a waste of communication and computation resources.Therefore,the sample-based event-triggered strategy is designed,where the event-triggered condition need to be only monitored in the sampled instants.If the event-triggered condition is satisfied,the information or data can be transmitted.By constructing a Lyapunov functional,conditions in terms of LMIs are derived to solve the the practical leader-following consen-sus problem with the fixed topology and semi-Markovian switching topologies,respectively.