Robust dynamic programming approach to aircraft control problems with disturbances

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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.