Adaptive internal model control: \(H_2\) optimization for stable plants
Design and analysis of an adaptive internal model controller (IMC) structure is considered. The plant is assumed open-loop stable, and the on-line identification uses a series-parallel model. Beside the adaptation of the internal model, the scheme is responsible for the adjustment of the IMC parameter, according to a performance index given by the \(L_2\) norm of the tracking error. The optimization problem leads to a pointwise minimization of an \(H_2\) norm criterion. The robust adaptive law is obtained using the gradient method with normalization and parameter projection; this law is further exploited to develop a robust adaptive \(H_2\)-optimal control scheme. Adequate results are formulated for the analysis of stability and robustness with respect to plant modeling errors. These results rely on the fact that the order of the pointwise optimal IMC parameter can be rendered time-invariant by an appropriate choice of the design parameters.
scientific article; zbMATH DE number 1192908
scientific article