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Gain-Sensitivity Augmentation for Near-Optimal Control of Parameter-Dependent Linear Plants

This paper presents the synthesis of an adaptive near-optimal LQG controller for a parameter-dependent linear plant. The parameters are assumed to be available from direct measurement or estimation. The approach is based on a gain-sensitivity augmentation to the nominal LQG controller. The gain-sensitivity terms are derived from a Taylor series expansion. The controller may be made arbitrarily robust to large parameter variations by retention of sufficient terms in the augmentation. The sensitivity matrices are precomputed off-line making it attractive for on-line implementation. Performance and stability properties are addressed. The approach is illustrated with a vibration control application containing a parameter-dependent disturbance.