State-feedback control for full-state constrained nonlinear systems in a prescribed time

Abstract

This study focuses on the unresolved control problems pertaining to full-state constrained nonlinear systems within a prescribed time. Initially, two Lyapunov theorems are established using a time-varying scaling function. These theorems facilitate the achievement of prescribed-time stability while ensuring that constraints are not violated. Building upon these theorems and incorporating completely known nonlinear terms, a state-feedback controller is developed and analyzed by employing an asymmetric barrier Lyapunov function (BLF). The analysis demonstrates that the resulting controller enables the tracking error to converge to the origin within a prescribed time while subsequently maintaining it at the origin without violating any constraints. Additionally, as an extension of the proposed prescribed-time control approach, the adaptive control problem for parameterized constrained nonlinear systems is addressed. The designed adaptive controller ensures boundedness of all signals, maintains the states within the specified constraints, and achieves convergence of the tracking error to the origin within an arbitrarily prescribed time. Finally, simulation examples are presented to validate the effectiveness of the proposed control scheme.