Elliptical circumnavigation control for a stratospheric airship with performance constrained under same-side monotone boundaries

This paper presents an elliptical circumnavigation control method for stratospheric airships with user-assigned tracking performance. By employing a new continuous time-varying scaling function, an improved prescribed-time stability criterion involving bounded gain is developed, avoiding the infinite gain phenomenon on classical prescribed-time stability. To compress the feasible domain of the tracking error and to address the shortcoming of most prescribed performance control (PPC) studies depending on the initial conditions, a tuning mechanism and a new barrier Lyapunov function (BLF) are integrated into the proposed algorithm to force the tracking error to evolve within predefined same-side boundaries, thus guaranteeing non-overshooting transient behaviors and prespecified steady-state performances. Meanwhile, the control strategy is independent of the initial conditions. The proposed scheme ensures that the airship achieves synchronized convergence of position and attitude tracking errors during elliptical circumnavigation within the user-assigned time. Finally, numerical simulations are presented to verify the effectiveness of the proposed method.