Research On Consensus Of A Class Of Heterogeneous Multi-agent System With Time Delays

Multi-agent system is ubiquitous in nature but intricate magical phenomenon. In recent years, multi-agent system was paid more and more attention by researchers from all kinds of fields such as control, physics, mathematics, biology, computer, etc. Since the functional and structural differences exist in the actual multi-agent systems, the description of the system is often a hybrid of variable dynamic equations, some scholars began to study the heterogeneous multi-agent system consisting of first-order and second-order integrator which had a typical physically meaning consensus problem Based on the existing research works, this paper proposed the concept of heterogeneous systems group consensus, and studied the consensus and group consensus of the heterogeneous multi-agent system consisting of first-order and second-order integrator based on the algebraic graph theory, matrix theory, linear system theory, stability theory, linear matrix inequality(LMI).The main work and contributions of this dissertation are as follows:1) This section focuses on the consensus problem of a class of heterogeneous multi-agent system mixed first-order agent with second-order agent as well as time delays. Firstly, consensus protocol is proposed for the heterogeneous system without delays. By system decoupling and model transformation, it decomposes the original system into several simple subsystems. The sufficient condition to solve the consensus problem is given by employing the graph theory and matrix theory. In the meantime, the exact expression of the consensus state is also given. Secondly, based on the result above, it adds the time-delay and gives the system sufficient conditions to achieve the average consensus in the form of linear matrix inequalities by employing Lyapunov-Krasovskii theory and linear matrix inequality. The compact admissible upper bounds of multiple delays are obtained by solving the feasible linear matrix inequalities. Finally, some numeral examples and simulations are presented.2) This section focuses on the group consensus problem of a class of heterogeneous multi-agent system mixed first-order agent with second-order agent as well as time delays. Firstly, group consensus algorithm is proposed for the heterogeneous system without delays. The sufficient condition to solve the group consensus problem is given by employing the graph theory, matrix theory and linear system theory. Secondly, based on the result above, it adds the constant delay and gives the system sufficient conditions to achieve the group consensus by employing linear system theory and frequency domain analysis method. Thirdly, it obtains the system with time-varying delays sufficient conditions to achieve the group consensus by linear matrix inequalities. Finally, some numeral examples and simulations are presented.