| Due to the important applications in the formation control of cluster unmanned systems,control and optimization of smart grids,intelligent transportation systems,industrial Internet and other aspects,the cooperative control theories of multi-agent systems(MASs)have been extensively and deeply studied in the past two decades.A large number of theoretical and applied results have been obtained.MAS is an open wide-area system,which is generally widely distributed in geography and connected via wired/wireless networks.Therefore,MASs are vulnerable to various types of attacks.After encountering external attacks,some individuals in the system may not be controlled by the pre-set algorithm,and even send wrong information to other individuals.Thereby,the cooperative behaviors of MASs are destroyed.Obviously,the previously established cooperative control theories in the non-attack environment are no longer applicable.Therefore,it is necessary to study the cooperative control theories in the attack environment to improve the resilience of MASs.This dissertation conducts the detailed research from resilient consensus.Furthermore,based on resilient consensus,the Byzantine-resilient optimization problem is studied.The main contents are listed as follows.For the continuous-time first-order MAS containing unknown number of malicious agents,the resilient consensus problem under switching topologies is considered.By introducing trusted agents,an algorithm based on trusted region is proposed to reach resilient consensus.Compared with the traditional Mean-Subsequence-Reduced(MSR)method,the advantage of the proposed algorithm is independent on the upper bound on the number of malicious agents.Under the assumption on switching topologies,it is successfully proved that the resilient consensus of the controlled MAS is reached.Numerical experiments are used to verify the effectiveness of the proposed algorithm and the correctness of the results.For the continuous-time second-order MAS containing trusted agents and malicious agents,a necessary and sufficient condition on the communication topology is established to guarantee resilient consensus.In the case of unknown number of malicious agents,a resilient consensus algorithm for continuous-time second-order MAS is proposed.Under appropriate control gains and sampling period,it is proved that resilient consensus can be achieved if and only if the subgraph induced by trusted agents is a directed spanning tree dominating subgraph of the communication topology.Finally,the numerical experiments verify the correctness of the obtained results,and show that the designed algorithm converges faster than the traditional MSR-based algorithms.Moreover,the proposed algorithm is less sensitive to the number of malicious agents.For the continuous-time second-order MAS with time-varying communication delays,a resilient consensus algorithm based on impulsive control is proposed.Compared with other control methods,the impulsive control not only saves energies,but also enables normal agents keep moving at a constant speed in each sampling interval.Therefore,the maximum and minimum values of normal agents’ position states only appear at the sampling instants,which makes it easy to obtain the exact safety interval.The effectiveness of the proposed algorithm based on impulsive control is verified by the numerical experiments.For the multi-agent resilient distributed optimization problem under Byzantine attacks,the optimization approach under the redundancy of cost functions is studied.Under the traditional assumptions on strongly convex global costs and Lipschitz continuous gradients,the MSR-based distributed comparative gradient elimination(MSR-DCGE)resilient optimization algorithm is proposed.Under this algorithm,if the number of in-neighbors of each normal agent is greater than some constant and the parameters satisfy certain conditions,normal agents’ local estimations will reach consensus and converge to the optimized solution to the sum of normal agents’ cost functions.Compared with the previous work on Byzantine-resilient optimization problems,it is worth noting that the communication topology is not required to be fully connected in this dissertation.Finally,the numerical experiments successfully verify the correctness of the theoretical results,which indicate that the proposed MSR-DCGE algorithm can solve the Byzantine-resilient multi-agent exact optimization problem without fully connected topology. |
