Distributed Resource Allocation Over Networks Of Nonlinear Multi-agent Systems

In the past few years,distributed optimal resource allocation over networks has gained increasing research interest,and many valuable results have been obtained.However,the related achievements mainly focus on single-integrator networks or a small part of double-integrator networks.There are rare results on the distributed optimal resource allocation problem for networks having complex dynamics,which is interesting and desirable in practice.Consequently,this paper studies the distributed optimal resource allocation problem of nonlinear networks having uncertain nonlinearities.To seek the optimal resource allocation with low communication costs,event-triggered mechanism is taken into consideration.Finally,the effectiveness of the designed algorithm is verified by numerical simulation.Firstly,a novel distributed adaptive optimal resource allocation algorithm comprising an auxiliary optimization dynamics and an adaptive stabilizer is proposed to solve the distributed resource allocation of uncertain nonlinear multi agent systems with strict feedback form.In this paper,we firstly construct an auxiliary dynamics that can generate a reference signal converging to the necessary optimal resource allocation solution and convert the distributed resource allocation problem into a trajectory tracking problem.On account of uncertain dynamic uncertainties and uncertain nonlinearities in the actual system,the adaptive distributed controllers are designed respectively on the basis of state feedback and output feedback to solve the latter tracking problem,leading to a distributed optimal resource allocation algorithm.By constructing suitable Lyapunov function,it is proved that the proposed algorithm assures the convergence of system output to the desired optimization solution of the resource allocation problem even in the presence of uncertain nonlinearities.Then,to seek the optimal resource allocation with low communication costs,a distributed optimal resource allocation algorithm on the basis of dynamic event-triggered strategy is proposed for the distributed resource allocation problem over uncertain nonlinear multi-agent networks.In the proposed dynamic event trigger mechanism,the differential equation is established on the basis of system status and state error between agent and its neighbour's,which is able to realize the dynamic update of trigger threshold.Theoretical proof and simulation results show that the distributed optimal resource allocation algorithm with dynamic event-triggered strategy can reduce the communication power consumption and avoid Zeno behavior while ensuring the optimal distributed allocation.Finally,simulations of the foundation model and the economic dispatch problem are given to illustrate the effectiveness of the authors' results.