Adaptive boundary control of stochastic linear distributed parameter systems described by analytic semigroups
A stochastic adaptive boundary control problem for some unknown linear, stochastic distributed parameter system that is described by an analytic semigroup is formulated and solved. The performance index is an ergodic, quadratic cost functional. To simplify the analysis, the ``highest-order'' linear operator in the model is assumed to be known while the ``lower-order'' operators and the linear operators on the boundary contain unknown parameters. For the identification of the unknown parameters a diminishing excitation is used which has no effect on the ergodic cost functional but ensures 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. These switchings are determined to ensure stability of the estimated infinitesimal generator and to satisfy a suitable boundedness for the control. This paper is a continuation of a previous one published in SIAM J. Control Optim. 32, 648-672 (1994; Zbl 0802.93035) by the same authors.
scientific article; zbMATH DE number 870153
scientific article