Distributed Optimization Algorithms Based On Event-triggered Strategy

Recently,with the growing popularity of data science and the vigorous rise of artificial intelligence,a large number of optimization problems with huge scale and high complexity have been born.Compared with the traditional centralized algorithms,the distributed optimization(DO)has higher flexibility,autonomy,robustness and expandability.It is an efficient method to solve this kind of problems.At present,DO can be applied in many fields such as smart grid,resource allocation,unmanned aerial vehicles formation and so on.The existing DO results either can not guarantee that the optimization problem can be solved in limited time,or the operation process of the algorithm consumes more system resources due to the continuous communication among agents.Therefore,in view of current DO algorithms,this paper studies two kinds of fixed-time optimization problems under the connected and undirected fixed communication topology,and adopts event-triggered mechanism to reduce the resource consumption of MAS.The main results are as follows:(1)The event-triggered strategy is introduced into the design of DO algorithms to reduce the communication frequency among agents,which can save communication resources of the system.In the proposed two fixed-time DO algorithms,the event-triggered conditions and corresponding communication protocols are designed respectively.Only when event-triggered conditions are met,the MAS will respond and perform operations,such as information interaction,protocol update and so on.Therefore,the algorithms in this paper can not only ensure that the convergent time is fixed,but also avoid the waste of system computing and communication resources.(2)For the DO problem with consensus constraint and strongly convex local cost functions,a fixed-time distributed optimization algorithm involving two stages is designed.The first stage is to make each agent converge to its own locally optimal state(the minimizer of local cost function)from any initial value in fixed time by designing local optimization controllers.The second one is to realize the goal that all agents achieve the globally optimal state(the minimizer of global cost function)in fixed time under the global optimization protocol and Zeno behavior is avoided.Hence,the DO problem can be solved in fixed time by the proposed two-stage algorithm whose flexibility is higher because it is independent of initial states.Combining simpler controllers and event-triggered strategy,computing complexity and communication resource of the system are declined.Finally,the effectiveness and accuracy of the presented optimization algorithm is demonstrated by a simulation example.(3)A fixed-time optimization algorithm is designed to solve the strongly convex distributed optimization problem with equality constraints.This problem can be regarded as an MAS in which each agent has a local objective function,and there are equality constraints about agents’ states.The optimization goal is to find the state of each agent that minimizes the global objective function(the sum of local objective functions).Firstly,the original optimization problem is transformed into another one which is about auxiliary variables and without constraints by using matrix analysis and function derivation.Secondly,the communication protocol is designed for each agent.By constructing Lyapunov function,it is proved that the algorithm can converge to the optimal solution in fixed time and Zeno phenomenon does not occur.Lastly,the algorithm is applied to solve the supply-demand balance problem of power grid with six generators.