Robust dynamic programming approach to aircraft control problems with disturbances

该项目提案旨在继续DFG正在进行的赠款“鲁棒动态规划方法，飞机控制问题的干扰”涉及数学建模组（M6）和飞行系统动力学研究所在慕尼黑技术大学。本计画探讨对策论方法在飞机强健控制上的应用。这种控制方法的基础是飞机控制和干扰（风）之间的冲突控制问题的制定，它产生一个强大的状态反馈控制律。正在进行的项目的主要部分是一方面实施一个高度并行化的差分游戏求解器，为“莱布尼茨超级计算中心”的大型网格计算机SuperMUC量身定制。该求解器可以离线求解多达七个维度的非线性微分博弈。在飞行系统动力学研究所完成了为一个真实的飞行模拟器集成到一个在线控制概念。另一方面，基于微分对策和最优控制理论的连续干扰的新测试程序正在开发中。继续该项目的建议侧重于增强所开发方法的两个具体方面：首先，将研究微分对策理论在鲁棒轨迹控制中的新应用。本申请的目的在于通过微分对策解决方案通过控制器参数（例如增益）的真实的时间适配来实现现有控制概念的鲁棒化。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综合和测试，在起飞和着陆等关键飞行阶段使用真实的参考轨迹。此外，除了已经考虑的干扰（风），我们还将包括传感器测量误差作为干扰的制定。第二，测试程序的基础上，非线性和线性微分对策方法和直接最优控制方法将得到扩展。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态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，产生最佳的最坏情况下的干扰的子部分的模型与减少的状态空间。另一方面，线性微分对策方法被用来测试线性化模型与高维。这两种方法都需要在SuperMUC系统上扩展求解器，以便计算最多9维非线性和24维线性情况下的微分博弈问题的解决方案。

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.