Prescribed fixed-time consensus control of multiple second-order systems with communication connectivity assurance

The leader-following consensus tracking problem is investigated for multiple second-order agent systems subject to communication range constraints in this paper. First, a novel fixed-time convergent performance function is developed to quantitatively characterize the consensus tracking performance. Then, an auxiliary state variable is defined by integrating the position and velocity consensus tracking errors with the potential function for removing the communication range constraints. Based on this auxiliary state variable, a fixed-time leader-following consensus controller is devised to guarantee the preassigned consensus tracking performance and communication preservation simultaneously. Compared with the existing consensus control methods, the prominent advantage of the proposed one is that the fixed-time convergence rate of the position and velocity tracking errors can be guaranteed without applying discontinuous control techniques. And the communication connectivity among the multiple agents is assured simultaneously via adding a potential function into the auxiliary state. Finally, two groups of illustrative examples are organized to validate the effectiveness of the proposed consensus control method.