Model reference control with ℋ∞ loop shaping

Model reference control (MRC) has been used extensively in adaptive control. However, due to the lack of stability guarantees in the presence of model uncertainties, robustness of adaptive control based on MRC is not ensured. The paper considers MRC from a different perspective. Reference model is used to represent the frequency shape of the ideal sensitivity function. The central objective is to design a feedback controller such that it achieves the desired frequency shape specified by the reference model within a prescribed tolerance in ℋ _∞ norm. This leads to the ℋ_∞ loopshaping for MRC. It is shown that the resulting ℋ_∞ controller has an observer structure as in the LQG/LTR case. An efficient algorithm is developed for solving the required ℋ_∞ controller. The results reported enhance the robustness for MRC