Robust dynamic programming approach to aircraft control problems with disturbances
Mathematics
Final Report Abstract
A differential game based tracking procedure is investigated which enables tracking of ustable reference trajectories without requiring an explicit measurement of disturbances. The applicability of this tracking procedure to aircraft control problems under wind conditions is demonstrated through the implementation in a realistic flight simulator model. Reference trajectories are generated through the solution of multi-phase optimal control problems. The main concept for the integration of the tracking controller in the flight simulator model is based on the use of a reduced model featuring a first-order reference model for the attitude states of the aircraft. The controls computed from the tracking procedure are translated to actuator command for the primary control surfaces through a nonlinear dynamic inversion controller. The reference model for the attitude loop matches the dynamics of the reduced model used in the tracking procedure and can, as such, be regarded as an interface between the two controllers. The fact that no measurement of the wind disturbance is required and the real-time capability of the differential game based procedure represent favorable properties for its applications in aircraft control. Besides robust control applications, optimal control and differential game based methods are investigated in the context of flight control law clearance problems. For the optimal control based approach the criterion to be tested is introduced in the cost function and state constraints model internal limits of the servomechanism, such as rate and position limits. The main idea behind the considered approaches is to explicitly find disturbances (wind or pilot inputs) that violate the criterion, i.e. to assess the “performance under worst-case conditions”. The differential game based approach takes this idea one step further through a suitable controller parametrization which acts as a second player trying to counteract the disturbances. As such, the value of the game can be interpreted as the “best-case performance under worst-case conditions”. In general, this application requires the solution of nonlinear, state-constrained differential game problems which represents a computationally demanding task. As such, this project was additionally supported by Leibniz Supercomputing Centre (grant pr74lu) which provided computer resources on the SuperMUC / NG grid computer. A solver tailored to this computer architecture was developed during the course of this project based on a mixed MPI/OpenMP strategy. This solver implementation has so far been applied for the solution of project-related nonlinear state-constrained differential games in up to seven dimensions, which can be considered large regarding the current state-of-the-art.
Publications
- Aircraft Guiding in Windshear through Differential Game-Based Overload Control. IFAC-PapersOnLine, Vol. 52, pp. 706-711
N. D. Botkin, A. E. Golubev, V. L. Turova
(See online at https://doi.org/10.1016/j.ifacol.2019.12.045) - Backstepping control of aircraft take-off in windshear. IFAC-PapersOnLine, Vol. 52, pp. 712-717
A. E. Golubev, N. D. Botkin, A. P. Krishchenko
(See online at https://doi.org/10.1016/j.ifacol.2019.12.046) - Optimal Disturbance Generation for Flight Control Law Testing. IFAC-PapersOnLine, Vol. 52, pp. 730-734
J. Diepolder, N. D. Botkin, F. Holzapfel
(See online at https://doi.org/10.1016/j.ifacol.2019.12.049) - Antony Merz and his works. Dynamic Games and Applications. Vol. 10, pp. 157-182, 2020
V. Patsko, V. L. Turova
(See online at https://doi.org/10.1007/s13235-019-00318-y) - Flight Control Law Clearance Using Worst-Case Inputs Under Parameter Uncertainty. Journal of Guidance, Control, and Dynamics, Vol. 43, pp. 1-8
J. Diepolder, J. Z. Ben Asher, F. Holzapfel
(See online at https://doi.org/10.2514/1.G005236) - Implementation of a Robust Differential Game Based Trajectory Tracking Approach on a Realistic Flight Simulator. CEUR Proceedings of the Workshop on Mathematical Modeling and Scientific Computing: Focus on Complex Processes and Systems, Munich, Germany, November 19-20, Vol. 2783, pp. 68-93, 2020
A. Gerdt, J. Diepolder, B. Hosseini, V. L. Turova, F. Holzapfel
- Optimal Control Based Flight Control Law Clearance Using Generalized Polynomial Chaos. IACAS 60th Israel Annual Conference on Aerospace Sciences, Israel, 2020
J. Diepolder, J. Z. Ben Asher, P. Piprek, F. Holzapfel
- Quick construction of dangerous disturbances in conflict control problems. Annals of the International Society of Dynamic Games, Vol. 17, pp. 3-24
K. Martynov, N. D. Botkin, V. L. Turova, J. Diepolder
(See online at https://doi.org/10.1007/978-3-030-56534-3_1) - Viability kernel based control approach for a flight simulator model. CEUR Proceedings of the Workshop on Mathematical Modeling and Scientific Computing: Focus on Complex Processes and Systems, Munich, Germany, November 19-20, Vol. 2783, pp. 94-112, 2020
A. Gerdt, N. D. Botkin, J. Diepolder, V. L. Turova, F. Holzapfel
- Tracking aircraft trajectories in the presence of wind disturbances. Mathematical Control and Related Fields
N. D. Botkin, V. L. Turova, B. Hosseini, J. Diepolder, F. Holzapfel
(See online at https://doi.org/10.3934/mcrf.2021010)
