In this paper we present the first stage of a unified two-stage approach to analyzing stochastic adaptive control. In the first stage, we study the issue of potential self-tuning where we ask the question whether a certainty-equivalence adaptive control scheme achieves the same control objective as the ideal control design at the potential convergence points of the estimation algorithm. We exploit the fact that this important property can be analyzed independent of the estimation method that is used, without restoring to complicated convergence analysis. For linear time-invariant systems, this reduces to simply studying two identifiability equations; the Identifiability Equation for Internal Excitation (IEIE) and the the Identifiability Equation for External Excitation () whose solutions determine the potential convergence points of the parameter estimates. Sufficient conditions and necessary conditions are then derived for potential self-tuning and identifiability of general control schemes. Applications of these general results to specific adaptive control policies then show that regardless of the external excitation, the certainty-equivalence adaptive control based on generalized Minimum-Variance, generalized predictive, and pole-placement control are potentially self-tuning. On the other hand, the LQG feedforward and feedback control designs are shown to require sufficient external excitation. In the next stage, we will show how to proceed from potential self-tuning to asymptotic self-tuning.

Back to Adaptive Control, Filtering, and Signal Processing Table of Contents