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Optimal adaptive LQG control for systems with finite state process parameters

The situation where a totally observed process yt is generated by a stochastic differential equation whose parameters evolve on a finite set {1,....N} according to a stochastic differential equation is considered. The optimal control law is sought with respect to quadratic loss functions on yt and the control ut. The auxilliary P.D.E. technique of Hijab [1983] is used together with a non-linear filter to obtain the solution whose existence depends upon that of a smooth solution to the auxillary P.D.E. and strong solutions to the system S.D.E. under the given control inputs. Work supported by the Faculty of Engineering, and, the Faculty of Graduate Studies and Research, McGill University, the NSERC International Scientific Exchange Programme and NSERC Grant A1329, while the first author was visiting McGill University for the academic year 1982-83.