Robust adaptive controller scheduling using mixing

Abstract

The performance of an identifier-based adaptive controller depends on the properties of its certainty equivalence control law and the choice for the design parameters of its estimator. The adaptive control literature has largely focused on model-following and pole-placement control objectives, which may not capture the true control objective as effectively as LTI robust control designs, e.g., µ-synthesis. Moreover, the rigorous analysis of adaptive systems have focused on qualitative results of signal boundedness and convergence, not on how to choose the design variables. In this paper we focus on these practical issues of designing adaptive controllers. The recently proposed adaptive mixing control approach addresses the first issue, in so much as the entire suite of LTI tools are available to design the underlying parameterized control law, assuming the unknown plant parameter belongs to a compact set.We examine the factors that dictate the choice of design variables. We also examine a modification of the adaptive mixing scheme that is capable of maintaining stability for cases when none of the off-line designed candidate controllers can. This is done by mixing in a conventional adaptive controller. Numerical simulations are presented to illustrate the results.