**Authors: **[tex2html_wrap4414]*P.E. Caines, P. Florchinger, D. Levanony*

**Investigator username:** peterc

**Category: ** systems and control theory

**Subcategory:**

Work on stochastic adaptive control has focused on two topics:

In work with P. Florchinger the stability results of Hale for ordinary differential equations have been extended to stochastic differential equations. This work gives results that permit the analysis of the stability of stochastic systems with significant non-linear perturbations around an underlying stable linear system. This work with D. Levanony involves a basic reformation of the stochastic adaptive control problem in which it is conceptualized as an optimization problem which is solved in real time subject to constraints. The constraints are given by parameter estimates generated via a modified recursive maximum likelihood algorithm. Consistency of the parameter estimates and hence asymptotic optimality of a certainty equivalence control law (with respect to an LQG criterion) is established. (See entry of D. Levanony for details.)

baron@cim.mcgill.ca