Prescribed performance control for uncertain underactuated systems via constraint-following with application to a PVTOL aircraft

Guaranteeing prescribed transient and steady state performance (TSSP) for mechanical systems is of great significance to their motion control, motivating the prescribed performance control (PPC). This study investigates the PPC for uncertain underactuated systems. We consider time-varying (possibly fast), bounded uncertainty including large mismatched portions, however the bound is unknown. The control design is implemented via constraint-following, that is, rendering the system to follow a series of servo constraints. We hence impose the prescribed TSSP on the constraint-following error. An approximation-free adaptive robust PPC based on a state transformation technique is designed, achieving approximate constraint-following and guaranteeing the prescribed TSSP to be satisfied. It employs an adaptive law to online estimate the unknown bounds for uncertainty compensation. It does not assume sufficiently small mismatched uncertainties, hence admitting large mismatched uncertainties. The stability of the controlled underactuated systems is sustained by rigorous proofs. By the proposed approach, the PPC of a planar vertical take-off and landing aircraft is explored, which also illustrates the effectiveness of the approach.