Adaptive $\mathcal{H}_{\infty}$ Synthesis for Linear Systems with Uncertain Parameters

A performance-based approach is developed for adaptive robust control of linear systems with uncertain parameters. The dual control objective involves the disturbance attenuation and worst case identification of the unknown parameters. The proposed synthesis procedure relies on sufficient conditions, given in terms of suitable solutions of perturbed differential Riccati equations to exist. Although being reminiscent from the standard $\mathcal{H}_{\infty}$ synthesis, the resulting Riccati equations are to be updated on-line with estimated values of the unknown plant parameters. Capabilities of the proposed synthesis are illustrated by simulations made for a scalar linear system with unknown parameters.

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