Designing a high performance, stable ℒ₁ adaptive output feedback controller

This paper presents a deeper analysis of the ℒ₁ adaptive output feedback controller for systems of unknown dimension, presented by Cao and Hovakimyan. The adaptive output feedback controller ensures uniformly bounded transient and asymptotic tracking for SISO system signals, both input and output, simultaneously. This is an exciting new approach for designing adaptive controllers, since knowledge of the order of the system is not required, nor is the system state, which is often unavailable. In this paper, the effect of selecting different reference models and lowpass filters on system performance and stability is explored. Also, conditions on the adaptive gain that affect the stability of the adaptive signal are examined through use of root locus techniques. It is demonstrated that for minimum phase systems, stable or unstable, the design decisions can be straightforward and systematically pursued to achieve the required performance criteria. However, for systems that are non-minimum phase, or where the relative degree of the plant and the model do not match, difficulties may arise that limit the choice of reference model and lowpass filters, which restricts the achievable adaptive system performance.