Adaptive finite-time stabilisation of output-constrained low-order uncertain nonlinear systems with time-varying powers

This paper investigates adaptive finite-time stabilisation for a class of output-constrained low-order nonlinear systems with unknown time-varying powers, parametric and dynamic uncertainties. Due to low-order nonlinear systems being merely continuous but not smooth, and the presence of time-varying powers and multiple unknowns, all the existing control methods of output-constrained nonlinear systems are inapplicable. By characterising unmeasured dynamic uncertainty with finite-time input-to-state stability (FTISS), applying finite-time stability theory and introducing the tan-type barrier Lyapunov function, low-power and high-power terms into control design, a unified adaptive state-feedback controller, which can deal with both constrained and unconstrained systems, is constructed. It is proved that all the closed-loop signals are uniformly bounded, the output constraint is not violated, and system states converge to zero in a finite time. Finally, a simulation example is given to illustrate the effectiveness of this control scheme.