Finite-time Consensus Tracking Of Multi-agent Systems

With the development of computers, communications networks, and embedded technologies, the distributed control problem of multi-agent systems (MAS) has been widely attracted and used in the control areas, including consensus, formation control, clusters, sensor networks and collaborative monitoring and so on. As one of the basis of distributed control of MAS, the consensus plays an important role for a long time. Considering the requirement of disturbance rejection of MAS, several different consensus tracking protocols are designed to solve the finite-time consensus tracking problem of MAS with disturbances. The main contents of the thesis are as follows:Firstly, the finite-time stability theory of single nonlinear system is introduced. By analyzing the single nonlinear system, we further apply the theory of homogeneous finite-time stability to MAS. The distributed consensus protocols are designed by combining homogeneous finite-time stablility and integral sliding mode (ISM) algorithm for the MAS with second-order dynamic under matched disturbances. Under the condition of absolute state feedback, the discontinuous protocols and continuous supet-twisting protocols are designed to solve the finite-time consensus tracking problem of MAS.Secondly, the protocols based on homogeneous finite-time stability theory are designed for high-order MAS, and the control coefficients of homogeneous consensus protocols are chosen according to Hurwitz polynomial theory. In order to avoid using the global information, the distributed observer is designed to estimate the leader’s input, and the stability of MAS with finite-time observer-based distributed protocol is analyzed. Under the frame of nominal protocols, the protocols based on ISM are designed to solve the finite-time consensus tracking problem of high-order MAS with matched disturbances.Then, under the case of relative states feedback, the ISM variables based on the relative states are designed, and combining homogeneous finite-time consensus protocols, the discontinuous protocols and continuous super-twisting protocols are designed to solve the finite-time consensus tracking problem of MAS with dynamic leader. When the available information is reduced to the relative output, the state observer based on relative output feedback is designed to estimate the unknown relative state. Combining the ISM algorithm and homogeneous finite time stability theory, the protocols based on the distributed observer are designed to solve the finite-time consensus tracking of high-order MAS where only relative output feedback is available.Finally, the finite-time consensus tracking problem of MAS with mismatched disturbances, and the finite-time exact differentiator is used to estimate the mismatched disturbances and their high-order differential. The new variables combining the observer values of mismatched disturbances and their high-order differential with state variables are used for feedback control. Further, the protocols are designed by combining homogeneous finite-time stability theory to solve the finite-time output consensus tracking problem of MAS with mismatched disturbances.