Multirate constrained adaptive control

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Abstract
An adaptive servo control law with input constraints is derived for application to linear time-invariant systems with unknown parameters and two sampling rates: a slower one for the output, and a faster one for the input. The error between the actual and a reference performance index is shown to be bounded by the product of a finite gain and the parameter estimation error in the limit sense. Sufficient conditions for parameter convergence are proven under which the performance of the multirate, adaptive constrained control system asymptotically approaches that of the analogous single (fast) rate, constrained control system with known, constant parameters. The advantages of the multirate, adaptive constrained control algorithm are demonstrated by numerical simulations.