Consensus Of Multi-agent Systems With Semi-Markov Switching Topologies

In practice,the communication topology among agents may change over time,due to obstacles,limitation of communication range and disturbances.In order to describe the time-varying topology among the agents,a common method is that the time-varying topology is assumed to be switching among a finite set of known topologies and the switching between these topologies is modeled as a Markov process.However,the time-varying topology described by the Markov process has many limitations in applications,since the jump time of a Markov chain is,in general,exponentially distributed,and the results obtained on Markov switching topologies are conservative in some senses.Recently,the problem of synchronization for complex networks with semi-Markov switching topologies has received some attention.Compared with conventional Markov switching topologies,the sojourn-time in semi-Markov switching topologies is subject to a more general probability distribution.Hence,semi-Markov switching topologies have much broader applications than the conventional Markov switching topologies.However,there are no results on the consensus of multi-agent systems with semi-Markov switching topologies.For this reason,this dissertation focuses on this issue.It is organized as follows.(1)The leader-following consensus problem for nonlinear multi-agent systems with semi-Markov switching topologies is investigated.Firstly,the dynamics of the leader agent and the follower agents are all described by a general linear system.Secondly,markov switching topologies are extended to the semi-markov switching topologies.Since the transition rates of the semi-Markov switching topologies are time-varying,they are more general than the classic Markov switching topologies.A novel consensus protocol based on outdated states is proposed for multi-agent systems.By a system transformation,the consensus problem of multi-agent systems is converted to the stability problem of semi-Markov switching systems.The controller design condition is derived utilizing the semi-Markov jump system theory and algebraic graph theory,which can guarantee that the multi-agent systems achieve consensus with an exponential decay rate.(2)The leader-following consensus problem for multi-agent systems subject to actuator saturation with semi-Markov switching topologies is studied.Firstly,the randomly switching between the time-varying topologies is modeled as a semi-Markov process,and the effect of actuator saturation is considered.Based on the above two considerations,a new consensus protocol is proposed.The consensus problem of multi-agent system with actuator saturation is studied by using sector bound method and convex combination method respectively.Two sufficient conditions are derived,which guarantee that the leader-following consensus can be locally achieved in mean-square sense.Based on the derived sufficient conditions,two optimization problems are proposed to compute the consensus feedback gains and to find a maximal estimate of the domain of consensus attraction.(3)The event-triggered consensus problem for multi-agent systems with semi-Markov switching topologies is considered.A sampled-data-based event-triggered transmission scheme is first introduced,where event-triggered condition is only required to be measured at sampling instants.On this basis,by modeling the switching of network topologies by a semi-Markov process and considering the effect of event-triggered transmission scheme,a new consensus protocol is proposed.It should be pointed out that,the Laplacian matrices of switching topologies need not to be symmetric.By constructing a mode-dependent Lyapunov-Krasovskii functional and employing the reciprocal convex combination method,some sufficient conditions have been proposed to ensure that the leader-following consensus can be achieved in mean-square sense.Furthermore,the parameter matrices of consensus gain and the event-triggered scheme are all obtained.(4)The adaptive consensus problem for leader-following multi-agent systems with semi-Markov switching topologies and actuator saturation is addressed.By using the low-gain feedback technique and adaptive technique,a new fully distributed protocol with adaptive coupling weights is proposed.Under the assumption that every possible graph has a directed spanning tree with the leader as its root,using an appropriate Lyapunov-Krasovskii functional and semi-markov switching system theory,some semi-global consensus sufficient conditions are obtained.It should be pointed out that each agent considered here needs to be asymptotically null controllable with bounded controls.(5)The event-based consensus problem for second-order multi-agent systems with actuator saturation and semi-Markov switching topologies is studied.By a model transformation,the consensus problem is first converted into the stability problem of the error system.Using discontinuous Lyapunov functional approach,a sufficient condition on the consensus is derived for second-order multi-agent systems with semi-Markov switching topologies.The discontinuous Lyapunov functions take full account of the characteristics of the sawtooth delay,and thus lead to a less conservative consensus criterion.It is shown that the consensus condition depends on the parameters of sampling period,Laplacian matrix,and event-triggered parameter.In addition,this chapter provides an effective method to co-design both the consensus controller and the event-triggered parameter.