ARX modeling of controlled ARMAX plants and LQ adaptive controllers

Conditions under which controlled ARMAX (autoregressive moving-average models with auxiliary inputs) plants can be described by ARX (autoregressive models with auxiliary inputs) models are studied. Among all possible ARX models, the ones that can be correctly used in long-range LQ (linear quadratic) adaptive control are characterized. Within this framework, LQ adaptive controllers embodying standard recursive least-squares identifiers are singled out and shown to have equilibrium points solving related underlying LQ control problems for the true ARMAX plant.<>