DADS under unknown input coefficients

This short note shows that the Deadzone-Adapted Disturbance Suppression (DADS) adaptive control scheme is applicable to systems with unknown input coefficients. We study time-invariant, control-affine systems that satisfy the matching condition for which no bounds for the disturbance and the unknown parameters are known. The input coefficients can be time-varying as well as the unknown parameters. The only thing assumed for the input coefficients is their sign. The adaptive control design is Lyapunov-based and can be accomplished for every system for which a smooth globally stabilising feedback exists when the disturbances are absent and all unknown parameters are known. The design is given by simple, explicit formulas. The proposed controllers guarantee an attenuation of the plant state to an assignable small level, despite unknown bounds on the parameters and disturbance, without a drift of the gain, state, and input.