Further results on fixed-time control for nonlinear systems with asymmetric output constraints

This paper concerns the fixed-time control with an arbitrarily prescribed upper bound of settling-time (UBST) for nonlinear systems with asymmetric output constraints. We introduce a novel time-varying gain function that effectively addresses the issue of infinite-gain, which has been a challenge in related research. By utilizing this gain function, we present two theorems that employ the Lyapunov function for constrained nonlinear systems. These theorems serve as guidelines for constructing controllers without violation of constraints. In addition, a novel barrier Lyapunov function (BLF) is exploited which is equivalent to the classical one for nonlinear systems without constraints. By using the proposed theorems, BLF and fixed-time backstepping design procedure, a state-feedback controller is constructed and analyzed for output-constrained nonlinear systems. It is proved that the designed controller can render the closed-loop system converges to the origin within a fixed settling time while maintaining at the origin thereafter, the controller is uniformly bounded and the output constraints are not violated. Finally, simulations and comparisons are provided to verify the proposed control schemes.