Indirect Computation of Robustness and Performance Guarantees for Adaptive Controllers

由于航空领域的高安全性要求，现代飞机的飞行控制系统需要提供特殊的鲁棒性特性。为此，飞行控制系统必须满足所有预期的不确定性和干扰的某些最低性能要求。随着模型不确定性的增加，传统飞行控制系统的性能下降，鲁棒性和性能之间的折衷往往是不可避免的。与此相反，自适应控制允许在这些矛盾的目标之间进行更有利的权衡。与传统的飞行控制系统相比，自适应控制器的控制器增益在运行期间调整到对象。虽然自适应飞行控制系统的能力已经在几次飞行试验中得到证明，但它们还没有在商业应用中部署。其商业用途的一个主要障碍是缺乏可靠的方法，保证鲁棒性和性能。出于这个原因，本建议的目的是在发展的新方法的计算措施的鲁棒性和自适应控制系统的性能。到目前为止，鲁棒性和性能度量的计算遵循直接的方法。作为一个例子，考虑期望闭环响应和实际闭环响应之间的跟踪误差的Lp范数的界限的计算。在实践中，这些措施的可计算的界限是高度保守的，这样他们不提供可接受的保证的鲁棒性和性能。因此，应在本建议书中研究间接方法。这种方法来自于这样的观察，即传统的飞行控制系统在所有预期的不确定性的存在下提供令人满意的鲁棒性和性能。为了减轻这些不确定性，传统的控制系统是由一个额外的自适应控制回路。与大多数自适应控制器不同，这种自适应控制器旨在减小标称对象模型与实际对象之间的误差。因此，从常规飞行控制系统的角度来看，自适应控制器对应于附加的未建模动态。因此，间接方法应证明，这些未建模动态决不会使常规飞行控制系统的鲁棒性和性能恶化。为此，新的指标是要开发的工厂，增强自适应，总是更接近标称工厂模型比工厂没有一个额外的自适应元件。在这种情况下，传统飞行控制系统的鲁棒性和性能保证转移到自适应增广飞行控制系统。

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.