Identification and adaptive control of some stochastic distributed parameter systems

An important class of controlled linear stochastic distributed parameter systems is that with boundary or point control. A survey of some existing adaptive control problems with their solutions for the boundary or the point control of a partially known linear stochastic distributed parameter systems is presented. The distributed parameter system is described by an analytic semigroup with cylindrical white noise and a control that occurs only on the boundary or at discrete points. The unknown parameters in the model appear affinely in both the infinitesimal generator of the semigroup and the linear transformation of the control. The noise in the system is a cylindrical white Gaussian noise. Strong consistency is verified for a family of least-squares estimates of the unknown parameters. For a quadratic cost functional of the state and the control, the certainty equivalence control is self-optimizing, that is the family of average costs converges to the optimal ergodic cost. Copyright (C) 2001 John Wiley & Sons, Ltd.