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

摘要

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, e.g., [9]. However, thisuncertainty 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, e.g., [9, Ch.8]. 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.In this paper we will examine the use of uncertainty model unfalsification for direct and indirect iterative adaptive control. Specifically, we will analyze three approaches to iterative adaptive control: (1) indirect control design via classical systemidentification, (2) indirect control design via plant uncertainty model unfalsification, and (3) direct controller unfalsification. Each approach will be analyzed under the same simplifying assumptions: infinite data, the plant is linear-time-invariantand disturbance-free, and the iterative controller is also linear-time-invariant.