Stable adaptive control for not-necessarily stable discrete linear plants with bounded non-linear inputs

This paper deals with the design of stable adaptive control schemes for discrete plants under non-linear bounded inputs. Two algorithms are studied, one of them being a generalization of the d-step-ahead standard algorithm, while the second one involves the use of a time-decreasing adaptation gain. The class of inputs for which the algorithms perform in a stable fashion include saturations, relays and saturated dead-zones. The plant stability assumption is not requested to prove standard (non-asymptotic) stability results. The mechanism to achieve scheme's stability is the use of an extra weighted additive term in the adaptation error which takes into account the output deviation with respect to that associated with linear inputs.