Iterative unfalsified adaptive control: analysis of the disturbance-free case

The paradigm of classical linear system identification is to assume that the system generating the data belongs to an uncertainty model set consisting of unknown transfer function coefficients and unknown noise variances. However, this uncertainty model set does not provide a means for estimating the size of the unmodeled dynamics, although formulae exist for large data length and large model order]. A philosophical shift from identification to unfalsification allows the uncertainty model set to include dynamic uncertainty with an unknown bound which can be estimated (unfalsified) along with the usual system identification parameters. We examine the use of uncertainty model unfalsification for direct and indirect iterative adaptive control. Specifically, we analyze three approaches to iterative adaptive control: (1) indirect control design via classical system identification, (2) indirect control design via plant uncertainty model unfalsification, and (3) direct controller unfalsification. Each approach is analyzed under the same simplifying assumptions: infinite data, the plant is linear-time-invariant and disturbance-free, and the iterative controller is also linear-time-invariant