On a quantitative theory of robust adaptive control: an interval plant approach

This paper considers a robust direct-model reference adaptive control scheme, where the components of the estimated controller parameter vector are constrained to vary in certain prespecified intervals. This interval constraint facilitates the quantitative analysis of the robustness of the closed-loop adaptive control system. Extending existing results from the area of robust parametric stability, a tractable procedure is developed for verifying a condition which guarantees the boundedness of all the closed-loop signals. The robustness verification using this procedure involves the calculation of worst-case “shifted” H_∞ norms over certain extremal one-parameter families. This makes the condition easily verifiable, whereas otherwise one is faced with the formidable task of determining the worst-case norms over higher-dimensional compact convex sets in the plant and controller parameter spaces. A simple example is used in the paper to illustrate the theoretical development