Consensus of multi-agent systems with network constraints

Multi-agent systems (MASs) have attracted the attention of researchers in various fields in recent years. The research of MASs is motivated by observations of interesting phenomena in nature and is deepened by its applications in engineering. Consensus is a fundamental and important research topic in the decentralized control of MASs. Network communication plays an important role in cooperative control of MASs and network constraints are usually unavoidable in network communication. Many interesting and good results have been obtained for the consensus of MASs with comparatively simple dynamics under some network constraints. In this thesis, we synthesize the complexity in agent dynamics and the complexity in network constraints. Specifically, we consider the robust consensus of a group of second-order nonlinear heterogeneous agents with uncertainty in agent dynamics under two kinds of network constraints, communication delays and jointly connected topologies, respectively. A consensus problem is initially studied for the class of second-order nonlinear heterogeneous MASs under the network with nonuniform time delay in communication links. We design a class of novel decentralized control protocols for the consensus problem whose solvability is converted into a stability analysis of an associated closed-loop system with uncertainty and time delay. Using an explicitly constructed Lyapunov functional, the stability conditions or the solvability conditions of the consensus problem are given in terms of a set of linear matrix inequalities (LMIs), apart from a small number of scalar parameters that appear nonlinearly. The solvability of LMIs is further verified when time delays are sufficiently small. When the topologies are jointly connected, we begin with consensus analysis of the class of second-order nonlinear heterogeneous MASs by showing that there always exists some state-dependent switching signal such that consensus can be achieved under a properly designed control protocol. The consensus problem is converted into a stabilization problem for a switched system with unstable subsystems satisfying the assumption of stable convex combination. It is revealed that there always exists some state-dependent sets such that if the switching signal belongs to these sets, consensus can always be achieved. This result uses the fact that there is at least one subsystem projected in a direction that approaches the equilibrium point at any instant of time. Afterwards, we design a new consensus protocol such that the consensus of this kind of MAS can be guaranteed under jointly connected topologies in a state-independent switching pattern. The consensus problem is converted into a stability problem of an interconnected nonlinear switched system. The main difficulty relies on input-to-state stability analysis of a class of linear switched control systems where none of the subsystems are input-to-state stable (ISS). Then the overall stability of the interconnected switched system is investigated by the small gain theorem.