Adaptive Optimal Stabilization of Discrete-Time Plant under Uncertainties and Biased Disturbance

This paper addresses the problem of adaptive optimal robust stabilization of discrete-time plant with autoregressive nominal model. The coefficients of the transfer function, the norms of time-varying coprime factor perturbations as well as the norm and bias of external bounded disturbance are assumed to be unknown. The problem is to ensure near minimal asymptotic upper bound on the plant output. The adaptive optimal robust control is based on polyhedral estimation of unfalsified parameters and treating the control criterion as the identification criterion. Nonconvex problem of optimal online estimation is reduced to computationally tractable linear fractional programming via suitable change of estimated parameters.