Abstract

In this paper an adaptive control problem for some stochastic semilinear systems is formulated and the solution is described. The linear part of the semilinear equation is a negative, self-adjoint generator of an analytic semigroup. The semilinear equation has a unique invariant measure that is shown to be continuous with respect to parameters. The optimal control for the stochastic control of the known semilinear equation with a cylindrical noise is a continuous function of parameters. A family of least squares estimates is strongly consistent for a class of adaptive controls. A certainty equivalence adaptive control law is self-optimizing, that is, the family of average costs using this adaptive control converges (almost surely) to the optimal ergodic cost. >

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