Removing SPR-like Conditions in Adaptive Feedforward Control of Uncertain Systems

This paper presents the current developments of a novel approach to robust Adaptive Feedforward Control (AFC) of uncertain linear systems affected by harmonic disturbance of known frequency. The features that set the proposed method apart from existing ones are the following: (i) knowledge of the sign of both the real and imaginary parts of the transfer function at the frequency of excitation is not needed; (ii) persistence of excitation is not required; (iii) stability analysis tools based on averaging are avoided, hence the requirement of an exponentially stable equilibrium is circumvented. The methodology reposes upon recent results on adaptive regulation of uncertain linear systems with weak immersions as well as on classic tools in adaptive control. A noticeable drawback of the proposed controller – at this stage of the research – is its relatively high dimensionality, which stems from the necessity of a convexification of a non-convex parameter set.