Note on adaptive prescribed-time stabilization of nonlinear systems with uncertainty

Krishnamurthy et al. investigated the adaptive output feedback control for prescribed-time stability (PTS) of nonlinear uncertain systems on $[0,T)$, where $T>0$. However, there are special constraints on system structure, and the PTS issue is considered on a finite interval $[0,T)$. For systems without required constraints, the existing adaptive output feedback control seems not to be applicable; the PTS issue on $[0,\mathrm{\infty })$ is more practical than that on $[0,T)$. Motivated by the above, an improved observer and controller were proposed to achieve PTS for nonlinearly uncertain systems with lower-triangular linear growth condition on uncertainties. Compared with the existing work, we emphasized the subsequent contributions: 1) Relax the original structure constraint of objective system; 2) achieve PTS on $[T,\mathrm{\infty })$; and 3) keep the proposed controller bounded. The effectiveness of the controller was verified by numerical simulations across varying initial conditions and prescribed times.