Indirect Computation of Robustness and Performance Guarantees for Adaptive Controllers

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Due to the high safety requirements in the field of aviation, flight control systems of modern aircraft need to provide exceptional robustness characteristics. To that end, flight control systems have to satisfy certain minimal performance requirements for all expected uncertainties and disturbances. As the performance of a conventional flight control system degrades with increasing modeling uncertainty, an unsatisfactory tradeoff between robustness and performance is often inevitable. As opposed to this, adaptive control allows for a more favorable tradeoff between these contradictory objectives. In contrast to conventional flight control systems, the controller gains of an adaptive controller adjust to the plant during runtime. While the capabilities of adaptive flight control systems have been demonstrated in several flight test campaigns, they have not been deployed in commercial applications. A major obstacle for their commercial use is the lack of reliable methods, which guarantee robustness and performance. For this reason, this proposal aims at the development of novel methods for the computation of measures for robustness and performance of adaptive control systems. Up to now, the computation of robustness and performance measures followed a direct approach. As an example, consider the computation of bounds for Lp-norms of the tracking error between the desired closed-loop response and the actual closed-loop response. In practice, computable bounds of these measures are highly conservative such that they do not provide acceptable guarantees for robustness and performance. For this reason, an indirect approach shall be investigated within this proposal. This approach derives from the observation that a conventional flight control system provides satisfactory robustness and performance in the presence of all expected uncertainties. In order to mitigate these uncertainties, the conventional control system is augmented by an additional adaptive control loop. Unlike most adaptive controllers, this adaptive controller aims at reducing the error between the nominal plant model and the actual plant. Hence, from the conventional flight control system's perspective, the adaptive controller corresponds to additional unmodeled dynamics. The indirect approach shall therefore prove that these unmodeled dynamics never deteriorate the robustness and performance of the conventional flight control system. To that end, novel metrics are to be developed which verify that the plant, enhanced with adaptation, is always closer to the nominal plant model than the plant without an additional adaptive element. In this case, the robustness and performance guarantees of the conventional flight control system transfer to the adaptively augmented flight control system.