Barrier lyapunov function-based homogeneous fixed-time controller design for a double integrator system

This study proposes a controller design for the fixed-time stabilisation of a double integrator system (DIS), taking into account both output and state constraints. The controller combines Barrier Lyapunov Function (BLF)-based control method with homogeneous fixed-time controllers to provide faster convergence, eliminate the singularity of BLF-based fixed-time control algorithms, and guarantee precise convergence to the origin while maintaining the constraints. Three different cases including output constraint, output and state constraints, and fixed-time extended-state observer-based control for the disturbed DIS are studied. Several sets of simulations are carried out and comparisons are made with several finite-time and fixed-time controllers. In addition, the proposed control system is applied to the lateral control of an autonomous vehicle. Simulation results outline faster convergence, faster response, less sensitivity to sensor noise, more capability in disturbance rejection, and more accurate positioning compared to previous control systems.