Study On Containment Control Of Linear Multi-agent Systems

Containment control problem means that the followers are to be driven into agiven geometric space spanned by the leaders under the control protocol. It is animportant research topic in the control field, which has attracted the attention ofthe researchers. Using algebraic graph theory, matrix theory and Hopf bifurcationtheory, this paper studies containment control problems of multi-agent systems.Here, our main results and contribution of this dissertation are as follows.1. This paper investigates the containment control issue of multi-agent sys-tems with time-delay. For continuous-time case, our results show that both topol-ogy structure and time-delay play an important role in the containment controlof multi-agent systems, no matter whether the system is first-order system (sta-tionary leaders) or second-order system (dynamic leaders with constant velocity).Furthermore, the maximum value of time-delay to guarantee the achievement ofcontainment control is established by Hopf bifurcation theory. Then, we extendthe results to sampled-data case. Finally, numerical simulations are given to il-lustrate our main results.2. The reduced-order observer-based containment control problems of generallinear multi-agent systems (MASs) with multiple interaction leaders are investi-gated. Assuming that (A, B, C) is stabilizable and detectable and the directedgraph is weakly connected, we establish the necessary and sufcient containmentcontrol criteria for continuous-time MASs and discrete-time MASs, respectively.Our main results show that the eigenvalues of the Laplacian matrix, the communi-cation topology graph, the selection of protocol parameters and gain matrices playan important role in the achievement of containment control. Finally, numericalsimulations are given to illustrate our main results.