Relaxation of excitation conditions in adaptive control: a survey

In the early stages of adaptive control development, most methods relied on the persistent excitation (PE) condition to completely eliminate the effects of model uncertainties. It is widely recognised that ensuring and verifying the PE condition presents considerable difficulties, which in turn restricts the applicability of adaptive control. It can be regarded as a constraint on both time and space, regarding the persistence and richness of excitation. Significant efforts have been devoted to relaxing this condition, with the resulting contributions broadly categorised into classical and data-driven approaches. Classical methods often present certain limitations, including the need for specific prior knowledge or a potential decline in control performance. Most data-driven methods relax the time constraint by leveraging historical excitation, though they still rely on the sufficient excitation (SE) condition. Furthermore, it is demonstrated that the excitation space constraint can be relaxed through the partial identification principle. This suggests that the excitation conditions can be entirely excluded. This article categorises adaptive control methods based on the collection and utilisation of excitation information, as well as associated excitation conditions.