Prescribed-time time-varying formation tracking control for heterogeneous linear multi-agent systems with a nonautonomous leader

The paper investigates the prescribed-time formation tracking control problem of heterogeneous linear multi-agent systems with a nonautonomous leader whose control input is unknown a priori. To achieve this, a novel two-layer hierarchical design framework is proposed, consisting of an upper-layer distributed observer to estimate the leader state information in prescribed-time, and a lower-layer distributed prescribed-time formation tracking controller based on the designed distributed observer. On the one hand, unlike existing finite-time and fixed-time control strategies, the control strategy introduced in this paper can guarantee the convergence time of the closed-loop heterogeneous multi-agent systems remains independent of the initial states and the control parameters of the multi-agent system. On the other hand, the leader-follower formation tracking control in presence of the unknown input of the leader is addressed by introducing a compensation term in the prescribed-time controller design. Utilizing Lyapunov and prescribed-time stability theory, it is shown that the leader-follower formation tracking control of the heterogeneous multi-agent systems is achieved within a prescribed-time regardless of the unknown leader input. Finally, simulation results demonstrate the efficiency of the proposed method.