Fast Consensus Of Multi-agent Systems

Cooperative control of multi-agent systems,a typical field of artificial intelligence,has attracted more and more attention in recent years.Consensus is one of the most fundamental control tasks in cooperative control.The goal of consensus is to design appropriate distributed control protocols and control parameters so that each agent can reach the same state through local information interaction.Convergence speed is an important indicator of consensus performance.In this dissertation,the fast consensus problem of multi-agent systems is further studied by combining the methods of RouthHurwitz stability criterion,Jury stability criterion,graph Fourier transform and robust gain margin optimization.The research can be summarized as the following four parts:(1)The problem of fast consensus for first-order multi-agent systems is considered.A general protocol with memory information from the node and its neighbors is designed.By the graph Fourier transform,the consensus problem is transformed into the simultaneous stabilization problem of multiple subsystems in the graph spectral domain.For the case where the network topology is known,the optimal convergence rate and control parameters with one-tap memory are derived explicitly,and it is proved that onetap neighbors’ memory cannot accelerate the convergence rate.For the case where the network is uncertain,the method of robust gain margin optimization is applied to give the optimal convergence rate in the worst-case scenario.It is proved that one-tap node memory is sufficient to achieve the worst-case optimal convergence rate.In addition,multi-tap memory is found to further improve the consensus convergence rate on some special network topologies.The convergence rates with two-tap node and neighbor memory and with three-to five-tap node memory are given explicitly for the special case of star graphs.(2)The problem of fast consensus for second-order multi-agent systems is studied.A new consensus protocol for second-order multi-agent systems is designed by using the memory information.For the case of one-tap memory,explicit formulas for the optimal consensus convergence rate and control parameters are derived by applying the Jury stability criterion.It is proved that the optimal consensus convergence rate with one-tap memory is faster than that without memory.For the case of more than one-tap memory,an iterative algorithm based on gradient descent is designed for solving the numerical solutions of the control parameters and convergence rates.Moreover,the accelerated consensus with memory is extended to the formation control,and the optimal control parameters to achieve the desired formation are derived.(3)The problem of accelerated and finite-time consensus of high-order multi-agent systems is considered.First,a protocol with constant control parameters is designed,and the sufficient and necessary conditions for high-order multi-agent systems to achieve consensus are given.Next,the accelerated consensus problem is transformed into an optimization problem of convergence rate,and a gradient descent based algorithm is proposed to optimize the convergence rate.Then,the lower bound on the convergence rate is derived by the Routh-Hurwitz stability criterion,and explicit control gains are given as necessary conditions to achieve the optimal convergence rate.Due to the limitation of constant control,consensus can’t be achieved in finite time.Finally,a protocol with time-varying control parameters is designed to achieve the finite-time consensus,and an explicit formula for the time-varying control parameters is given.(4)The problem of fast queue consensus for multi-agent systems is studied.A consensus-based control protocol is designed on directed networks to make the agents form a prescribed queue while moving with a common reference velocity.By model transformation,the queue consensus problem is transformed into the stabilization problem of the error system.The necessary and sufficient condition for achieving queue consensus is given,and explicit solutions to the queue consensus algorithm for the fastest convergence of the system are solved.Furthermore,to further accelerate the convergence rate,the update rule of the agents’ reference velocity is redesigned by utilizing the memory information,and the explicit formulas of the improved optimal convergence rate and corresponding control parameters are derived.