Stochastic adaptive control: a unified analysis

In this paper we present the first stage of a unified two-stage approach to analyzing stochastic adaptive control. Here, we study the issue of potential self-tuning where we ask the question whether a certainty-equivalence (CE) 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 identifiability equation for external excitation (IE³) 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