Stochastic linear-quadratic adaptive control: A conceptual scheme

A conceptual adaptive linear-quadratic (LQ) control scheme is proposed. Its derivation is based on a study of a family of asymptotic maximum likelihood (AML) estimators, and their associated limit sets. The geometric properties of such limit sets, lead to the formulation of a time-varying, constrained optimization problem, whose solution is an inherently consistent estimate of the system´s unknown parameters. When incorporated within a certainty- equivalence adaptive control scheme, these estimates yield optimal long-run LQ closed-loop performance.