Adaptive optimal robust stabilization of autoregressive plant under biased external disturbance

This paper addresses the problem of adaptive optimal robust control of a discrete-time plant with unknown parameters of autoregressive nominal model, unknown upper bound and bias of external disturbance, and unknown gains of coprime factor perturbations. The control criterion is the worst-case steady-state upper bound of the output. Solution of the problem is based on an optimal polyhedral estimation of unknown non-identifiable parameters with the control criterion treated as the identification criterion. A replacement of unknown parameters is proposed that modifies the plant model to a model without perturbation in control. This transforms the nonconvex control criterion to a linear fractional one and thus makes possible online computation of optimal estimates.