Consensus Analysis And Control Design Of Linear Multi-agent Systems

Multi-agent systems come from the actual control system. Research on them not only is the need of the development of modern control theory, and is urged to solve a large number of actual demands. The consensus problem of multi-agent systems is a fundamental problem of cooperative control problem, which is currently research hotspot. In the dissertation, combining the linear system theory, singular system theory, control theory, algebraic graph theory and matrix analysis, the consensus problems for both linear normal and linear singular multi-agent systems are investigated systemat-ically. The innovative work and key points of this dissertation can be summarized as follows:The accelerated consensus problem of linear normal multi-agent systems is stud-ied. Based on a modified algebraic Riccati equation, an approach without nonlinear protocol is proposed and investigated for discrete-time case under time-invariant topolo-gies. A sufficient condition is derived, which guarantees that the multi-agent system solves consensus with prescribed consensus speed index. The algorithm is given to achieve the joint design of an expected consensus function and a prescribed consen-sus speed. For the consensus problems of continuous-time and discrete-time normal multi-agent systems with directed switching topologies, the switched behavior of com-munication topologies is transmitted to the dynamic systems which are transformed into switched subsystems. Then the consensus problem is solved under the assumption that each agent is stabilizable. Finally, it is shown that the consensus state is zero state. The sufficient condition to get bounded consensus state is derived by analyzing a vector whose norm is equal to consensus state’s. The algorithms of improving the consensus speed have been given. Although many references have discussed the consensualization problem of multi-agent systems under switching topologies, few gave the expression of the consensus state and improved the consensus speed. It is found that the overquick consensus speed may destroy the stability of the closed-loop multi-agent system, i.e., high gain has bad effect for dynamic system and it is not advisable to only pursue speed.Cooperative control problem for homogeneous singular multi-agent systems is discussed. Under the restricted system equivalence, the modified consensus proto-cols are proposed. The admissible consensus problems of both continuous-time and discrete-time multi-agent singular systems are investigated. Based on the communica-tion topologies containing a spanning tree, the sufficient and necessary conditions are presented for continuous-time multi-agent singular systems, and the sufficient condi-tions are presented for discrete-time multi-agent singular systems. The formulas of the consensus states are given and the algorithms of constructing the protocols for achieving admissible consensualization are provided. In contrast with the previous results which gave sufficient conditions that are composed of linear matrix inequalities to be deter-mined, this dissertation gives the sufficient and necessary conditions and the conditions are easy to be checked, verified and satisfied for the continuous-time multi-agent sys-tems. On the other hand, for continuous-time multi-agent singular systems, the tracking problem of single leader is discussed, and it is proved that the strong stabilization of each agent is a sufficient and necessary condition, and the algorithm to construct the protocol is given. The containment control problem of multiple leaders is studied. It is also shown that a sufficient and necessary condition of solving the above problem is strong stabilizable. The algorithms of the protocols are given. Compared with the ex-isting results which gave sufficient conditions for the tracking problem of single leader, the condition here is sufficient and necessary. Compared with the consensus state for multi-agent normal systems in the presence of multiple leader, the states of the follow-ers for multi-agent singular systems asymptotically converge to the convex hull formed by the dynamic states of the leaders.The admissible consensus problem of heterogeneous singular multi-agent systems is investigated. The modified protocols with identical models and different gains are designed for individual agent. The consensus error vector must be regular, impulse free (causal) and asymptotically stable. The above request is applied to obtain the sufficient conditions and construct the algorithms of consensus protocols. In essence, the consen-sus protocols given here solve the tracking problems of single leaders. Compared with the tracking problem for homogeneous singular multi-agent system, here the leader and the followers are heterogeneous. In contrast with the existing references about hetero-geneous singular multi-agent systems, this dissertation has three advantages:First, the sufficient conditions given are mild and easy to be verified. Second, the input matrix which is nonsingular in previous results is only requested to be column full rank here, and this reduces the rigorous condition greatly. Finally, the consensus protocols con-structed here eliminate two shortcomings:singular agent may have impulse term and the impulse term in the dynamics of consensus error vector is removed. Furthermore, the results given here are general, and they may be applied to leader-following con-sensus of multi-agent homogeneous singular systems, and they also may be applied to leader-following consensus of multi-agent heterogeneous normal systems.