A Fast Finite-Time Adaptive Stabilizing Strategy of Uncertain Nonlinear System With Output Constraints and Its Application in Liquid-Level System

This article aims to solve two intricate problems in nonlinear control: 1) the zero-division of the control by requiring its differentiability and 2) the finite-time stabilization via adaptive feedback for a class of uncertain nonlinear systems with asymmetric output constraints. The issue is how to control the system states to converge to the origin quickly while not violating the output constraints. This article develops an adaptive stabilizing controller constituting a piecewise tangent-type barrier function and a series of non-negative integral functions with sign functions, which is bounded over the whole time horizon and ensures the fast convergence of the system states. The innovation is two-fold: a technical lemma is proposed for the first time to make the designed controller completely decoupled from the first state variable of the system. The proposed strategy can handle both constrained and unconstrained systems without reconstructing barrier functions associated with the output constraint. Finally, the stabilization of a liquid-level system is investigated to demonstrate the effectiveness of the control scheme.