Adaptive control of distributed parameter systems: The ultimate reduced-order problem

For many distributed parameter systems (DPS), such as highly mechanically flexible structures, it is essential to provide stable on-board/on-line adaptive control in the presence of poorly known system parameters. However, such a controller must be based on a reduced-order model of the DPS and spillover from the unmodeled residuals can deteriorate the performance of the controller and, in some cases, defeat the whole purpose of the adaptive control. In this paper, we investigate direct and indirect adaptive controllers based on reduced-order models of a DPS and point out the mechanisms whereby spillover can upset the stability of adaptive controllers. We present some conditions under which the adaptive controllers remain stable in closed-loop with the actual DPS and point out certain generic problems that must be overcome for successful operation of adaptive DPS control.