ADAPTIVE BOUNDARY CONTROL OF STOCHASTIC LINEAR DISTRIBUTED-PARAMETER SYSTEMS DESCRIBED BY ANALYTIC SEMIGROUPS

A stochastic adaptive control problem is formulated and solved for som e unknown linear, stochastic distributed parameter systems that are de scribed by analytic semigroups. The control occurs on the boundary. Th e ''highest-order'' operator is assumed to be known but the ''lower-or der'' operators contain unknown parameters. Furthermore, the linear op erators of the state and the control on the boundary contain unknown p arameters. The noise in the system is a cylindrical white Gaussian noi se. The performance measure is an ergodic, quadratic cost functional. For the identification of the unknown parameters a diminishing excitat ion is used that has no effect on the ergodic cost functional but ensu res sufficient excitation for strong consistency. The adaptive control is the certainty equivalence control for the ergodic, quadratic cost functional with switchings to the zero control.