Optimal l1-robust tracking for autoregressive plant with unknown nominal model

This paper addresses the problem of adaptive optimal robust tracking for a discrete-time plant with unknown parameters of autoregressive nominal model and unknown bias of bounded external disturbance. Upper bounds of unbiased external disturbance and gains of uncertainties in output and control are assumed to be know. The optimal tracking problem is to minimize the guaranteed worst-case steady-state upper bound of the tracking error for a given bounded reference signal. Solution of the problem is based on optimal set-membership estimation of unknown non-identifiable parameters and treating the control criterion as the identification criterion. Optimal on-line set-membership estimation becomes computationally tractable due to a linear-fractional representation of the control criterion.