Quadratic robust tracking control — A Polynomial Matrix Approach

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Abstract
A quadratic robust tracking problem is solved using a polynomial matrix approach. Because of the possibly unstable mode of the control sequence we propose a new quadratic cost function of error and control sequences to facilitate the optimization. The optimal controller makes the plant output track the reference sequence robustly and minimizes the proposed quadratic cost function. We also present the parametrized set of suboptimal controllers which yield finite costs so that there exists the central optimal controller in the set when the parameter is set to zero. The usefulness of our proposed cost function is demonstrated by simulation examples. Our design procedure has advantages over two other possible approaches: the LQ state‐space approach and the Wiener–Hopf approach which may be tried to tackle the same problem. Our approach obviates the need to construct a dynamic observer compared to the state‐space approach and it is computationally attractive compared to the Wiener–Hopf approach.

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