| This dissertation shows how adaptation can be combined with an internal model control based H2 optimal controller to obtain an H2 optimal adaptive internal model control scheme possessing theoretically provable guarantees of stability. The internal model control structure is first reviewed in the context of the YJBK parameterization of all stabilizing controllers and its appropriateness for the control of open-loop stable plants is discussed. Using a series-parallel identification model, it is then shown how, for a stable plant, one can adapt the internal model on-line and guarantee stability and asymptotic performance in the ideal case, i.e. in the absence of modeling errors. This is achieved without having to check any Strictly Positive Real Conditions or requiring any Persistent Excitation. By robustifying the adaptive law using standard approaches from the robust adaptive control literature, the robustness of the scheme to the presence of modeling errors, such as unmodeled dynamics, is also established. Finally, the design and analysis of a pointwise optimal adaptive internal model control scheme is considered. The time-varying internal model control "parameter" is chosen in a certainty equivalence fashion to pointwise minimize an H2 performance index. Stability of the resulting scheme and its robustness to plant modeling errors are established. The results here provide a suitable theoretical basis for analytically justifying some of the reported industrial successes of Adaptive Internal Model Control schemes. |
