Researches On Ultra-Fast Consensus And Multi-Tracking Control For Multi-Agent Systems

With the acceleration of the network structure of the control system and the deepening of the complexity of the system control task,the coordination and co-operation theory of multi-agent system has become one of the most important and cutting-edge research directions in the field of control.For any control system,in addition to the stability,the dynamic performance and steady-state performance are also important indicators of system performance.Obviously,in the premise of ensuring the stability of the multi-agent systems,how to design the corresponding distributed control protocol to improve the dynamic performance and steady-state accuracy of systems is theoretical and practical values.The dynamic performance of multi-agent systems usually refers to the convergence rate of multi-agent systems,i.e.,not only requires the whole system to achieve consensus,but also to accom-plish the goal quickly.And,the steady-state performance of multi-agent systems is closely related to its corresponding tracking control problem.Based on the dis-tributed control theory,this dissertation deeply researches ultra-fast consensus and multi-tracking control of multi-agent network systems,and provides lots of impor-tant theoretical results.The main work and research results of this paper are as follows:(1)Research on ultra-fast consensus of a class of simple high-order discrete-time multi-agent systems.Based on the predictive capability of agents,we establish a distributed multi-step output information prediction mechanism.Further,we propose an ultra-fast consensus protocol with multi-step output prediction information.Under this control protocol,the asymptotic convergence factor of multi-agent systems becomes an exponential function related to a new vari-able q.The theoretical result reveals that the larger the q value,the smaller the asymptotic convergence factor and the faster the convergence rate.In addition,based on the control idea,we further study the ultra-fast formation control,ultra-fast tracking control and ultra-fast robust consensus of multi-agent systems,and obtain the corresponding theoretical results.(2)Research on ultra-fast consensus of high-order discrete-time multi-agent sys-tems with a general dynamic model.Based on the predictive capability of agents,we establish a distributed multi-step neighbor-error information pre-diction mechanism.In order to solve the influence of the general dynamic model,we introduce the multi-step self-feedback prediction information on the basis of the prediction mechanism,and propose an ultra-fast consensus control protocol with state self-feedback.Under this control protocol,the asymptotic convergence factor of multi-agent systems becomes an exponential function related to a new variable q.This fact not only indicates that we can control the convergence speed of consensus for multi-agent systems by adjust-ing the value for q,but also indirectly solves the problem of solving the optimal control gain of high-order multi-agent systems.In addition,we further give the specific design method of ultra-fast consensus control protocol.The de-sign method not only decouples the complex relationship between the system control parameters and the communication graph,but also clearly reveals how the dynamic model and the communication graph affect the convergence rate of consensus for multi-agent systems.(3)Research on ultra-fast formation control of high-order discrete-time multi-agent systems with a general dynamic model.Based on the predictive ability of agents and the expected formation information,we establish a distribut-ed multi-step regulation-error information prediction mechanism.Further,we propose an ultra-fast formation control protocol with multi-step prediction in-formation.Under this control protocol,the asymptotic convergence factor of multi-agent systems becomes an exponential function related to a new variable q.When the value for q is larger,the corresponding asymptotic convergence factor is smaller,and the convergence rate of the multi-agent system is faster.Similarly,we further give the specific design method of ultra-fast formation control protocol.The design method not only decouples the complex relation-ship between the system control parameters and the commmnication graph,but also clearly reveals how the dynamic model and the communication graph affect the convergence rate of formation control for multi-agent systems.(4)Research on multi-tracking control of high-order heterogeneous multi-agent systems with a directed acyclic graph.First,we convert the multi-tracking control of multi-agent systems into zero-steady-state error control for some in-dependent subsystems.Then,based on the commnication topology between agents,we introduce the idea of signal flow graph,and obtain the quantita-tive relationship between the steady-state error of multi-agent systems and the network system structure,the dynamic model of agents and the expected tracking objects by the final-value theorem and Mason's rule.Further,we propose a computational method and formula of the steady-state error of the corresponding network control system.In addition,we study the influence of time delay on the multi-tracking control of multi-agent systems,and design the PI controller to solve the static multi-tracking control problem of a class of multi-agent systems with internal time delay.(5)Research on multi-tracking control of closed-loop stable high-order heteroge-neous multi-agent systems.Considering a general directed graph,based on the complex frequency domain method,we give a sufficient and necessary con-dition for the multi-tracking control of closed-loop stable multi-agent systems.This result quantitatively reveals a fact,i.e.,the larger the number of integral element in the subsystems,the smaller the steady-state error of network con-trol systems.Furthermore,we propose a computational method and formula of the steady-state error of the network control system with a general directed graph.This theoretical result is not only very important,but also simple and practical.The control ideas and theoretical results proposed in this dissertation not only enrich the cooperative control theory of multi-agent systems,but also provide a new method and framework to study the dynamic performance and steady-state performance of complex network control systems.A series of simulation examples further validate the correctness and effectiveness of these methods.