Set-membership identification for adaptive control: input design

An input design to guarantee the boundedness and the decreasing volume of the uncertainty set is proposed in the scenario of open-loop identification for control. The estimated system is described by a linear time-invariant SISO system of known order n with unknown-but-bounded modeling error in discrete time. Key in this approach is to consider a 2n-periodic input sequence and to establish sufficient conditions ensuring boundedness of the uncertainty set in finite time. An iterative input design involving a single design parameter leads then to an uncertainty set which uniformly decreases with time.