Escape time formulation of robust stochastic adaptive control

Abstract

A formulation of the robustness of a stochastic adaptive control problem is given in terms of escape time properties. That is, the objective criterion of adaptation is recast to address issues of quantifying and maximizing the expected time for the parameter estimate to exit from a particular compact set, in place of the usual goal of achieving guaranteed boundedness of all signals. This respecification of the aim deviates from the usual goal of achieving global boundedness and/or asymptotic optimality and is more closely tied to issues of deriving workable adaptive control laws. Specifically, the authors advance this as a potential objective and draw some comparisons with problems in queuing systems and in linear controller design. The theory of large deviations is then naturally applied to attempt to evaluate, or at least approximate, these escape times, and rudimentary analysis indicates that with such an objective a concordance emerges between stochastic and deterministic adaptive control methodologies. >