Research On Distributed Optimization And Control Problem For The Multi-agent Systems

This paper mainly studies the distributed optimization and control problems of first order multi-agent systems under strongly connected and weighted balance digraph as well as strongly convex local objective functions with globally Lipschitz gradients.Firstly,in the practical engineering,when the information between agents is exchanged,the problem of time-delay inevitably exists in the process of information transmission and reception.In view of this situation,we study the distributed optimization and control problems of multi-agent system with communication delay;a continuous-time distributed optimization algorithm is designed.By using the stability theory of time-delay system,we construct a suitable Lyapunov-Razumikhin function and sufficient conditions are given to such that the system converges to the global optimal solution.Secondly,it requires less data and can effectively save network bandwidth and communication costs if the state information is only transmitted at the sampling time,we study the distributed optimization and control problems for multi-agent systems with delayed sampled-data.It is assumed here that there is a time-delay between the sampling time and the available time.Based on the synchronous sampling and asynchronous sampling mechanism,continuous-time distributed optimization algorithms are designed by using distributed control method and delayed sampled-data,respectively.According to the stability theory,suitable Lyapunov functions are constructed and sufficient conditions are given to such that the system converges to the global optimal solution.Finally,based on algebraic graph theory,stability theory,linear system theory and so on,the stability analysis of the above algorithms are derived,respectively.Furthermore,the correctness of the theory is verified through simulation examples.