Fixed-time-synchronized control: a system-dimension-categorized approach

This study addresses the fixed-time-synchronized control problem of perturbed multi-input multi-output (MIMO) systems. In the task of fixed-time-synchronized control, different dimensions of the output signal in MIMO systems are required to reach the desired value simultaneously within a fixed time interval. The MIMO system is categorized into two cases: the input-dimension-dominant and the state-dimension-dominant cases. The classification is defined according to the dimension of system signals and, more importantly, the capability of converging at the same time. For each kind of MIMO system, sufficient Lyapunov conditions for fixed-time-synchronized convergence are explored, and the corresponding robust sliding mode controllers are designed. Moreover, perturbations are compensated using the super-twisting technique. The brake control of the vertical takeoff and landing aircraft is considered to verify the proposed method for the input-dimension-dominant case, which shows the essential advantages of decreasing the energy consumption and the output trajectory length. Furthermore, comparative numerical simulations are performed to show the semi-time-synchronized property for the state-dimension-dominant case.