Abstract:
In recent years, multi-agent systems (MASs) have been applied in many practical fields, such as multi-vehicle field and multi-robot field. Moreover, the research on the consensus control of MASs has received more and more attention. The objective of consensus control for MASs is to drive the states of the agents converge to the uniform value, based on the local state information of agent. To obtain consensus of MASs, it is essential to design the distributed consensus control strategy. In the paper, the consensus control problem of MASs under unknown state and external disturbance is studied, where it behaves the Markov switching topology. To handle unknown state and external disturbance, the reduced-order state observer and disturbance observer are respectively designed. To reduce the controller update times and save cost, the self-triggering mechanism is constructed. Then based on the design of reduced-order state observer, disturbance observer, and self-triggering mechanism, the consensus controller is designed to obtain the mean square consensus of MASs under Markov switching topology. The design details are described as follows. Firstly, a self-triggering mechanism is designed to predict the next triggering moment of consensus controller. When it is developed, the monotonicity and positive characteristics of the exponential function are fully utilized and an exponential term is used to increase the triggering threshold in the triggering function. As a result, the self-triggering mechanism achieves a further reduction in the number of controller updates. Besides, the estimate information of external disturbance is considered. At the same time, it avoids using the global information. Simultaneously, the self-triggering mechanism considers the balance between the immediately handling the adverse influence of external disturbance and the reduction of triggering times. Then resource cost reduction is achieved. It is analyzed that the designed self-triggering mechanism does not have Zeno behavior. Secondly, a reduced-order observer is constructed to solve the problem of unknown states. To design it, the model of MASs is transformed and the control input and external disturbance is combined into a single variable. Then, a new variable is defined based on the state information of the followers and the new form for the follower’s state is derived. Thus, a new model expression of MASs is obtained. Based on the above, the expression of the reduced-order model is obtained and a reduced-order observer is designed to estimate the unknown state of the follower. Next, it is proven that the observation error converges to zero. Thirdly, based on the estimate information of unknown state, a disturbance observer is designed to handle external disturbance. A Lyapunov function is designed for the estimation error. Then it is analyzed that the estimation error converges to zero, a consensus controller is designed based on the observers and self-triggering mechanism, and the mean square consensus of MASs is proved by Lyapunov theory. Then the consensus controller is designed and the mean square consensus of MASs is proved by the Lyapunov theory. Finally, the effectiveness of the designed observer, self-triggering mechanism and consensus controller is verified by numerical simulation and multi-UAVs simulation.