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Lagrangian Stochastic LQ Adaptation

Authors: [tex2html_wrap4416]D. Levanony, P.E. Caines

Investigator username: peterc

Category: systems and control theory


A novel constrained optimization approach is developed to overcome the well-known problem of suboptimal performance of standard, certainty equivalence, linear quadratic adaptive control schemes (a consequence of insufficient excitation). With no dither injected, the Lagrangian stochastic adaptive control law yields optimal (long-run) performance. The adaptive scheme involves the recursive solution of a (time-varying) constrained optimization problem, producing a strongly consistent maximum-likelihood type estimate; this is based on a search procedure which results from a geometric study of the set of manifolds of systems with indistinguishable closed-loop dynamics.