A Generalization to Set-Theoretic MRAC with Arbitrary Initial Values

In traditional set-theoretic model reference adaptive control (MRAC) architecture, it is crucial for the initial value to remain within the safe set, as this ensures that the system trajectory follows the command at all times. However, maintaining the initial state within this safe set presents a significant challenge. To address this issue, this paper proposes a new architecture. A key feature of the proposed architecture is the application of a compression function that generates a nominal error signal, guiding the real error signal back into the safe set. The effectiveness of this method is mathematically proven, and two examples are provided to demonstrate its efficacy.