Discrete Time Model Reference Adaptive Control for Continuous Time Systems using Generalized Sampled Data Hold Functions

This paper extends the "generalized sampled-data hold functions" approach of [1] to the control of linear time invariant systems with unknown parameters. The idea of the generalized sampled-data hold functions approach is to periodically sample the plant output and define the control as the sampled output plus a discrete time reference, each multiplied by an individual modulating function. Such a control allows us to assign an arbitrary discrete time transfer function for the sampled closed loop system and does not make assumptions on the plant other than controllability and observability. In the present paper we propose an indirect adaptive controller which is based on this approach and estimates the modulating functions on line. In particular, the control is modified so that persistent excitation of the continuous time plant is ensured without making an assumption on the reference signal, and discrete time asymptotic model following is nevertheless obtained. The only assumptions we make on the plant are minimality, for the continuous and sampled plant, and known order.