Pulse-modulated intermittent control in consensus of multiagent systems

This paper proposes a control framework, called pulse-modulated intermittent control, which unifies impulsive control and sampled control. Specifically, the concept of pulse function is introduced to characterize the control/rest intervals and the amplitude of the control. By choosing some specified functions as the pulse function, the proposed control scheme can be reduced to sampled control or impulsive control. The proposed control framework is applied to consensus problems of multiagent systems. Using discretization approaches and stability theory, several necessary and sufficient conditions are established to ensure the consensus of the controlled system. The results show that consensus depends not only on the network topology, the sampling period and the control gains, but also the pulse function. Moreover, a lower bound of the asymptotic convergence factor is derived as well. For a given pulse function and an undirected graph, an optimal control gain is designed to achieve the fastest convergence. In addition, impulsive control and sampled control are revisited in the proposed control framework. Finally, some numerical examples are given to verify the effectiveness of theoretical results.