Time-Delay Margin Analysis for an Adaptive Controller

robustness analysis tools are applied to adaptive flight control in this paper. A standard model reference adaptive controller with sigma modification is designed for a linear short-period aircraft model. The resulting nonlinear closed-loop system is governed by polynomial dynamics. The nonlinear analysis algorithms rely on sum-of-squares polynomial optimization to assess the robustness of the adaptive closed-loop system with respect to a time delay. Time-delaymarginsarecomputedforvariouscombinationsofdesignparametersintheadaptivecontrollaw,aswell as in the presence of parametric model uncertainty. Advantages and limitations of the proposed sum-of-squaresbased robustness analysis are presented. Analysis results show a significant promise in the context of recent development in nonlinear robustness analysis. I. Introduction A DAPTIVEcontrolhasthepotentialtoimprovetheperformance and reliability of aircraft systems. Typical adaptive control architectures are inherently nonlinear, which presents a number of challenges. There is currently a lack of tools available to rigorously analyze the robustness and performance of nonlinear control architectures. The inability toverifyrobustnessand performance is a significant roadblock to the implementation of adaptive control architectures on civilian andmilitary aircraft. Thus, the flight control community would greatly benefit from advances in the area of