The Rationale for Second Level Adaptation
For control engineers, this work provides a rigorous validation of a new adaptive control paradigm that promises better performance and robustness.
The paper theoretically and experimentally examines the claimed advantages of second level adaptation for adaptive control of linear time-invariant plants, including stability, performance, and robustness, confirming significant improvements over existing methods.
Recently, a new approach to the adaptive control of linear time-invariant plants with unknown parameters (referred to as second level adaptation), was introduced by Han and Narendra in [1]. Based on $N (\geq m+1)$ fixed or adaptive models of the plant, where $m$ is the dimension of the unknown parameter vector, an unknown parameter vector $α\in R^{N}$ is estimated in the new approach, and in turn, is used to control the overall system. Simulation studies were presented in [1] to demonstrate that the new method is significantly better than those that are currently in use. In this paper, we undertake a more detailed examination of the theoretical and practical advantages claimed for the new method. In particular, the need for many models, the proof of stability, and the improvement in performance and robustness are explored in depth both theoretically and experimentally.