Robust dynamic programming approach to aircraft control problems with disturbances

该项目提案旨在继续DFG正在进行的“具有干扰的飞机控制问题的鲁棒动态规划方法”赠款，涉及慕尼黑工业大学数学建模组（M6）和飞行系统动力学研究所。本项目探讨了博弈论方法在飞机鲁棒控制中的应用。该控制方法的基础是提出飞机控制与扰动（风）之间的冲突控制问题，从而得到鲁棒状态反馈控制律。正在进行的项目的主要部分是一方面实现一个高度并行化的微分博弈求解器，该求解器是为“莱布尼茨超级计算中心”的大型网格计算机SuperMUC量身定制的。这个求解器可以离线解决非线性微分博弈，最多可达7维。在飞行系统动力学研究所完成了与现实飞行模拟器在线控制概念的集成。另一方面，基于微分对策和最优控制理论的关于连续扰动的新测试程序正在开发中。该项目的继续建议侧重于增强所开发方法的两个具体方面：首先，将研究微分博弈论在鲁棒轨迹控制中的新应用。该应用旨在通过微分博弈解决方案实时适应控制器参数（例如增益）来增强现有控制概念的鲁棒性。这一概念将在飞行系统动力学研究所的飞行模拟器中进行集成和测试，使用关键飞行阶段（如起飞和着陆）的真实参考轨迹。此外，除了已经考虑过的扰动（风），我们还将传感器测量误差作为扰动纳入公式。其次，将扩展基于非线性和线性微分对策方法以及直接最优控制方法的测试程序。对于直接最优控制方法，需要解决稀疏结构的有效利用和动力学中高度非线性元素的处理。一方面，微分对策方法是基于非线性模型的，它对模型的子部分产生最优最坏情况干扰，并具有简化的状态空间。另一方面，采用线性微分对策方法对高维线性化模型进行检验。这两种方法都需要在SuperMUC系统上扩展求解器，以便在非线性情况下计算最多9维的微分博弈问题的解，在线性情况下计算最多24维的微分博弈问题的解。

The project proposal aims towards a continuation of the ongoing DFG grant “Robust dynamic programming approach to aircraft control problems with disturbances” involving the Mathematical Modeling Group (M6) and the Institute of Flight System Dynamics at the Technical University of Munich. This project deals with the application of game theoretical approaches for robust aircraft control. The basis for this control approach is the formulation of a conflict control problem between the aircraft control and the disturbance (wind), which yields a robust state feedback control law. The main part of the ongoing project is on the one side the implementation of a highly parallelized differential game solver tailored to the large-scale grid computer SuperMUC at the “Leibniz Supercomputing Centre”. This solver enables the offline solution of nonlinear differential games in up to seven dimensions. The integration into an online control concept for a realistic flight simulator is accomplished at the Institute of Flight System Dynamics. On the other side, novel testing procedures with respect to continuous disturbances based on differential games and optimal control theory are under development.The proposal for the continuation of the project focuses on the enhancement of two specific aspects of the developed methods: First, a novel application of differential game theory to robust trajectory control will be investigated. This application aims towards a robustification of existing control concepts by a real time adaptation of controller parameters (e.g. gains) via a differential game solution. This concept will be integrated and tested in the flight simulator at the Institute of Flight System Dynamics using realistic reference trajectories for critical flight phases such as departure and landing. Furthermore, besides the already considered disturbance (wind) we will additionally include sensor measurement errors as disturbance in the formulation.Second, the testing procedures based on nonlinear and linear differential game approaches and direct optimal control methods will be extended. For the direct optimal control methods, the efficient exploitation of sparse structures and the treatment of highly nonlinear elements within the dynamics need to be addressed. On the one hand the differential game approach is based on nonlinear models which yield optimal worst-case disturbances for subparts of the model with a reduced state space. On the other hand, a linear differential game approach is used to test linearized models with higher dimensionality. Both approaches require an extension of the solver on the SuperMUC system, in order to compute solutions to differential game problems for up to nine dimensions in the non-linear, and 24 dimensions in the linear case.