Adaptive control has the potential to improve the performance and reliability of aircraft systems. Implementation of adaptive control on commercial and military aircraft requires the flight control system to be verified and validated with respect to modeling error, uncertainty, and time delay. Currently, there is a lack of tools available to rigorously analyze the robustness of adaptive controllers due to their inherently nonlinear dynamics. Newly proposed nonlinear 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-delay margins are computed for various combinations of design parameters in the adaptive control law, as well 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.
Bibliographical noteFunding Information:
also partially supported by the U.S. National Science Foundation under grant no. NSF-CNS-0931931.
This research was partially supported under the NASA Langley NASA Research Announcement contract no. NNH077ZEA001N titled “Analytical Validation Tools for Safety Critical Systems” and the NASA Langley NASA Research Announcement contract no. NNX08AC65A titled “Fault Diagnosis, Prognosis, and Reliable Flight Envelope Assessment.” The technical contract monitors are Christine Belcastro and Suresh Joshi, respectively. The research was