Two-degree optimal robust tracking control based on \(\ell_\infty\) and \(\ell_1\) norm minimization (Q2785176)

We investigate the problem of optimal robust tracking control of plants with multiplicative perturbations and unknown disturbances. By making use of the Youla parametrization of a two-parameter compensation scheme, the optimal robust tracking problem can be transformed into two independent problems that are called the tracking problem and the robustness design problem, respectively. The tracking performance is optimized by minimizing the \(\ell_\infty\) norm of the tracking error. The robustness design ensures stability with multiplicative perturbations and minimizes the \(\ell_1\) norm of the system's sensitivity from the tracking error to various disturbances including that one caused by model perturbations. These two optimizations are set up as linear programs by truncation techniques. The relation between truncation degree and approximation error is provided. Simulations show that the new robust tracking control is effective.