Research On Consensus Problems With High Order Sliding Mode Algorithm In Nonlinear Multi-agent Systems

In recent years, cooperative control of multi agent systems has attracted the wide interest of researchers in different fields. The cooperative control of multi agent systems is composed of a number of individual agents, which can solve the complex tasks that a single individual can't complete. The main aim of multi agent systems is to design a suitable distributed control law, each agent completes a specific behavior by using local information from its neighbors and updates its state in real time, such that formation, swarming, consensus and so on. Consensus is one of the most fundamental issues in the cooperative control of multi agent systems. In multi agent systems, there exists one or multiple leaders. When there is a leader, the consensus problem becomes a leader—follower consensus problem. When there are multiple leaders, the consensus problem becomes a containment control problem. With the rapid development of cooperative control of multi agent systems, the multi agent systems has a large number of practical applications. But in the practical applications, due to the existence of inherent nonlinearity, external disturbance and so on, the multi agent systems reflect the nonlinear characteristics. Therefore, research on problems of the leader—follower consensus and containment control for nonlinear multi agent systems has extremely important theory significance and practical value.Based on algebraic graph theory, matrix theory, Lyapunov stability principle and the sliding mode control theory, it is focused on the finite time leader—follower consensus problems and containment control problems for second order nonlinear multi agent systems in this paper.Firstly, with external disturbance of second order nonlinear multi agent systems is the research object. Two conditions are considered with the fixed topology and switching topology structure. The distributed consensus control protocol is designed by second order super twisting sliding mode algorithm. Using sliding mode theory and Lyapunov finite time stability theorem, the sufficient condition is gained that the followers can keep consistent with the leader in finite time. With the simulation study on the two kinds of topology structure, respectively. It can verify the accuracy and effectiveness of the proposed algorithm.Then, the finite time containment control problem is researched for the second order nonlinear multi agent systems. The distributed control protocol is designed by second order super twisting sliding mode algorithm and the appropriate control parameters are given as to achieve finite time containment control. Two conditions are considered with the stationary leaders and dynamic leaders. For stationary leaders, the control objective is to ensure that all the followers will move into the area formed by the stationary leaders in finite time and has remained stationary state in this area. Unlike stationary leaders, dynamic leaders is relatively more complicated. Here the paper mainly consider the changes of leader uniform speed. According to the given network topology, the followers communicate with its neighbors and updates its state in real time using the proposed control protocol. So as to make all the followers converge to the dynamic convex hull formed by the dynamic leaders to achieve finite time containment control. Simulation results verify correctness and availability of the proposed method.