Research On The Consensus Of Multi-agent Systems Under Complex Environment

The practical environments for multi-agent systems are complex. There exist a lotof constraints, such as limited communication bandwidth, measurement noises with dif-ferent characteristics, time-delays caused by diferent factors, unstable connection struc-ture, and so on. It has important theoretical and practical signifcance to consider theseconstraints, when we study the coordination control of multi-agent systems, includingconsensus, synchronization control, tracking control, formation control, etc. Based onthe previous studies, this dissertation will further research the coordination control ofmulti-agent systems under complex environments, in particularly the consensus. Undercomplex environmental conditions, we further study the traditional consensus protocolsof multi-agent systems. And we also design some new consensus protocols for certaincircumstances. At the same time, we also study the synchronization and tracking controlwith constraints.The main contributions of this dissertation are summarized as follows.1. The background, research signifcance and current situation of the selected topicare reviewed. Then, we indicate the signifcance, difculties and innovations of the dis-sertation.2. Under the digital network environment, the consensus of multi-agent systemsis studied. First, we study the average consensus of multi-agent systems with limitedbandwidth and time-delays. It is proved that the average consensus protocols existed inliteratures have diferent sensitivity for diferent delays. The average consensus protocolexisted in literatures is robust to the fnite symmetric delays. But it is sensitive to theasymmetric delays. Generally, the asymmetric delays would destroy the average consensusof multi-agent systems with limited bandwidth. Furthermore, we also designed some newprotocols to study the average consensus under the same network environment. For theasymmetric network environment, we further studied the weighted average consensus.3. Using the generalized Nyquist stability criterion and Gersgorin disc theorem, theweighted average consensus of continuous-time multi-agent systems with diverse time-delays is considered. It is shown that the classical consensus protocol is robust to time-delays (include communication time-delays among agents and self time-delays of eachagent). It is also shown that the classical consensus protocol has diferent properties fordiferent time-delays. Generally, the consensus of continuous-time multi-agent systemscan not be destroyed by fnite communication time-delays. But the value of consensus would be changed. For a given continuous-time multi-agent systems, the consensus wouldbe destroyed by the too big self time-delays of agents.4. The synchronization of linear and nonlinear multi-agent systems with measure-ment noises is studied. The additive and multiplicative measurement noises are consid-ered respectively, when we study the synchronization of multi-agent systems. In order toachieve synchronization, we design diferent protocols for diferent measurement noises.It is shown that the traditional synchronization control protocol is robust to the multi-plicative measurement noises in mean square. But it has not good robustness to additivemeasurement noises. Furthermore, the synchronization with a guaranteed H∞perfor-mance is studied. It is shown that all agents can achieve synchronization in mean squareand meanwhile maintain a desirable disturbance rejection performance. We also considerthe tracking problem with a guaranteed H∞performance for a leader-follower nonlinearmulti-agent system.5. Under the fxed and switched topology structure, the tracking control of multi-agent systems with an active leader and measurement noises is studied. It is shown thatthe traditional control protocol has good robustness to the measurement noises whichdepend on the measurement value.Finally, the main results of the dissertation are concluded.