Group Consensus In Networked Lagrangian Systems

Recently, coordinated control of networked Lagrange systems has received sig-nificant attention from various fields of nonlinear dynamics and control. Networked Lagrange systems has a wide range of engineering applications especially in com-plex and integrated production process. In such applications, flexibility, reliability, manipulability, and scalability are highly expected and even necessarily required. On the other hand, compared with complete consensus or synchronization, group consensus is more suitable to deal with cooperative control in complex multi-agent systems in many situations. This dissertation is mainly concerned with the group consensus problem of networked Lagrange systems. The main contents of this dis-sertation are summarized as follows:1. Adaptive group consensus in uncertain networked Lagrange systems. A kind of distributed adaptive group consensus protocols is proposed for the cases of topology graphs with acyclic partition and balanced couple, respectively. A novel decomposition approach is developed by using both algebraic graph the-ory and matrix theory. Based on this approach, convergence analysis is given for controlled Lagrange systems and some necessary and sufficient conditions for solving group consensus problems are established. It is shown that for the case of directed acyclic graphs, the group consensus can always be guaran-teed by the structure of acyclic interaction topology. For the case of directed balanced couple graphs, a simple algebraic criterion for ensuring group con-sensus is presented. For the case of directed balanced couple graphs, a simple algebraic criterion for ensuring group consensus is presented in terms of the eigenvalue computation of Laplacian matrix and thus can be easily applied in practice.2. Group regional consensus of networked Lagrange systems with input distur-bances. The group regional consensus of networked Lagrange systems with input disturbances is studied under directed acyclic topology. An adaptive control protocol is designed to achieve group regional consensus of the net-worked Lagrange systems with parametric uncertainties for both leader and leaderless cases. Compared with the existing work, a distinctive feature of the proposed control algorithm is that the stability analysis indicates the global validity of the obtained consensus result, i.e., the group regional consensus result obtained in this dissertation is valid for any set of initial conditions of parameters.3. Group synchronization of networked Lagrange systems using fundamental e-quation of mechanics. From the analytical dynamics point of view, an optimal control framework is developed to group synchronize networked Lagrange sys-tems using the fundamental equation of mechanics. A distinctive feature of the developed control strategy is the introduction of network structures into the control requirement (constraint). The control law consists of two com-ponents, the first describing the architecture of the network and the second denoting an active feedback control strategy. A corresponding stability analy-sis is performed by the algebraic graph theory and the sufficient conditions for solving group synchronization problems are established. Finally, a represen-tative network gyroscopes is used as an illustrative example to demonstrate the influence of each parameter and the effectiveness of the proposed control methodology.