Uncertainty equivalence principle and H∞-based robust adaptive control: stable plants

A novel idea, termed as uncertainty equivalence principle, is proposed, based on which an equivalent measure to the H_∞-norm is adopted for unmodeled dynamics using time-domain measurement data. Such an equivalent description for modeling errors is consistent with H_∞-based robust control, and allows H_∞ optimization to be successfully used in adaptive control to achieve robust stability and performance comparable to H_∞ control. Specifically a new adaptive control systems is proposed in this paper, focusing on stable plants. It employs the recursive least-squares (RLS) algorithm for adaptive model estimation, and weighted sensitivity minimization plus robust stabilization for adaptive controller design. Our results show that the proposed adaptive control system admits robust stability and performance asymptotically, provided that the estimated plant model converges.