Koopman Operator for Nonlinear Flight Dynamics

Technical report


Lock, Andrew, Bone, Viv and Jahn, Ingo. 2022. Koopman Operator for Nonlinear Flight Dynamics. Toowoomba, Australia. University of Southern Queensland.
Title

Koopman Operator for Nonlinear Flight Dynamics

Report TypeTechnical report
AuthorsLock, Andrew (Author), Bone, Viv (Author) and Jahn, Ingo (Author)
Institution of OriginUniversity of Southern Queensland
Number of Pages25
Year2022
PublisherUniversity of Southern Queensland
Place of PublicationToowoomba, Australia
Abstract

Dynamical systems representing vehicle flight are inherently nonlinear. Currently there are no generalised frameworks for explicit characterisation and solution of such systems. Conversely, linear systems are well understood, and many efficient algorithms are available for explicit characterisation and prediction.

Koopman operator theory presents a framework for constructing finite linear approximations to nonlinear systems, by projecting the nonlinear dynamics onto a Hilbert space constructed of Koopman operator eigenfunctions. This work summarises the theory underpinning the Galerkin method of constructing Koopman linear approximations of known dynamics using polynomial basis functions. Details of a system-agnostic program for computing the Koopman linear matrix is presented.

Linear approximations are constructed for two nonlinear systems: a simple Duffing oscillator, and a three degree-of-freedom glider trajectory. The ability of linear systems to closely follow the time-integrated nonlinear solution is demonstrated. Furthermore, expansions of the lifted linear model to incorporate variable system parameter, to incorporate bilinear time-varying inputs necessary for optimal control calculations, as well as methods to avoid the inherent linear system limitations are explored.

This work demonstrates feasibility and merit of the lifted linear system approach for analysis of vehicle dynamics and trajectory problems.

KeywordsLifted Systems; Koopman operator; Non-linear dynamic systems; Coordinate transforms; nonlinear control; system linearisation
ANZSRC Field of Research 2020400711. Simulation, modelling, and programming of mechatronics systems
400105. Flight dynamics
Byline AffiliationsInstitute for Advanced Engineering and Space Sciences
University of Melbourne
Permalink -

https://research.usq.edu.au/item/q7v94/koopman-operator-for-nonlinear-flight-dynamics

Download files


Published Version
  • 150
    total views
  • 223
    total downloads
  • 4
    views this month
  • 3
    downloads this month

Export as

Related outputs

Optical aerodynamic measurements of hypersonic free-flight using Bayesian state estimation
Lock, Andrew, Armstrong, Gerard, Hack, Flynn, Birch, Byrenn, Buttsworth, David and Jahn, Ingo. 2023. "Optical aerodynamic measurements of hypersonic free-flight using Bayesian state estimation." AIAA Aviation 2023 Forum . San Diego, United States 12 202 - 16 Jun 2023 United States. American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2023-3713
Model predictive control of the high-pressure side of simple supercritical CO2cycle
Bone, Viv, Kearney, Michael and Jahn, Ingo. 2023. "Model predictive control of the high-pressure side of simple supercritical CO2cycle." 2023 American Control Conference (ACC). San Diego, CA, USA 31 May - 02 Jun 2023 United States. https://doi.org/10.23919/ACC55779.2023.10156234
The effect of collisions on the multi-fluid plasma Richtmyer–Meshkov instability
Tapinou, K. C., Wheatley, V., Bond, D. and Jahn, I.. 2023. "The effect of collisions on the multi-fluid plasma Richtmyer–Meshkov instability." Physics of Plasmas. 30 (2), pp. 1-25. https://doi.org/10.1063/5.0132461
Trajectory Optimization of a Partially Reusable Rocket–Scramjet–Rocket Launch System Including Fly-Back
Forbes-Spyratos, Sholto O., Smart, Michael K., Kearney, Michael P., Ward, Alexander D. T. and Jahn, Ingo H.. 2023. "Trajectory Optimization of a Partially Reusable Rocket–Scramjet–Rocket Launch System Including Fly-Back." Journal of Spacecraft and Rockets. 60 (3), pp. 779-796. https://doi.org/10.2514/1.A35535
Development and validation of a Riemann solver in OpenFOAM® for non-ideal compressible fluid dynamics
Qi, Jianhui, Xu, Jinliang, Han, Kuihua and Jahn, Ingo H. J.. 2022. "Development and validation of a Riemann solver in OpenFOAM® for non-ideal compressible fluid dynamics ." Engineering Applications of Computational Fluid Mechanics. 16 (1), pp. 116-140. https://doi.org/10.1080/19942060.2021.2002723
Development and commissioning of the T6 Stalker Tunnel
Collen, Peter, Doherty, Luke J., Subiah, Suria D., Sopek, Tamara, Jahn, Ingo, Gildfind, David, Geraets, Rowland Penty, Gollan, Rowan, Hambidge, Christopher, Morgan, Richard and McGilvray, Matthew. 2021. "Development and commissioning of the T6 Stalker Tunnel." Experiments in Fluids: experimental methods and their applications to fluid flow. 62, pp. 1-24. https://doi.org/10.1007/s00348-021-03298-1
Hypersonic oscillating shock-wave/boundary-layer interaction on a flat plate
Currao, Gaetano M. D., McQuellin, Liam P., Neely, Andrew J., Gai, Sudhir L., O'Byrne, Sean, Zander, Fabian, Buttsworth, David R., McNamara, Jack J. and Jahn, Ingo. 2021. "Hypersonic oscillating shock-wave/boundary-layer interaction on a flat plate." AIAA Journal: devoted to aerospace research and development. 59 (3), pp. 940-959. https://doi.org/10.2514/1.J059590
A survey of mHealth use from a physician perspective in paediatric emergency care in the UK and Ireland
Jahn, Haiko Kurt, Jahn, Ingo Henry Johannes, Behringer, Wilhelm, Lyttle, Mark D., Roland, Damian and Paediatric Emergency Research in the United Kingdom. 2021. "A survey of mHealth use from a physician perspective in paediatric emergency care in the UK and Ireland ." European Journal of Pediatrics. 180 (8), pp. 2409-2418. https://doi.org/10.1007/s00431-021-04023-0
Letter in response to letter by Diba Behzad-Noori & Gurdas Singh in response to ‘Prescribing in a paediatric emergency’
Jahn, Haiko Kurt, Jahn, Ingo Henry, Roland, Damian, Behringer, Wilhelm, Lyttle, Mark and Paediatric Emergency Research in the United Kingdom and Ireland (PERUKI). 2021. "Letter in response to letter by Diba Behzad-Noori & Gurdas Singh in response to ‘Prescribing in a paediatric emergency’ ." Acta Paediatrica. 110 (3), pp. 1077-1077. https://doi.org/10.1111/apa.15616
Prescribing in a paediatric emergency: A PERUKI survey of prescribing and resuscitation aids
Jahn, Haiko Kurt, Jahn, Ingo Henry Johannes, Roland, Damian, Behringer, Wilhelm, Lyttle, Mark and Paediatric Emergency Research in the United Kingdom. 2021. "Prescribing in a paediatric emergency: A PERUKI survey of prescribing and resuscitation aids." Acta Paediatrica. 110 (3), pp. 1038-1045. https://doi.org/10.1111/apa.15551
Experimental and numerical heat transfer from vortex-injection interaction in scramjet flowfields
Llobet, J.R., Basore, K.D., Gollan, R.J. and Jahn, I.H.. 2020. "Experimental and numerical heat transfer from vortex-injection interaction in scramjet flowfields ." Aeronautical Journal. 124 (1280), pp. 1545-1567. https://doi.org/10.1017/aer.2020.39
Mobile device and app use in paediatric emergency care: a survey of departmental practice in the UK and Ireland
Jahn, Haiko Kurt, Jahn, Ingo H, Roland, Damian, Lyttle, Mark D, Behringer, Wilhelm and Paediatric Emergency Research in the United Kingdom. 2019. "Mobile device and app use in paediatric emergency care: a survey of departmental practice in the UK and Ireland." Archives of Disease in Childhood. 104 (12), pp. 1203-1207. https://doi.org/10.1136/archdischild-2019-316872
Effect of scramjet inlet vortices on fuel plume elongation and mixing rate
Llobet, J.R., Gollan, R.J. and Jahn, I.H.. 2019. "Effect of scramjet inlet vortices on fuel plume elongation and mixing rate ." Aeronautical Journal. 123 (1265), pp. 1032-1052. https://doi.org/10.1017/aer.2019.45
Simulation in the Loop Control of a Planar Hypersonic Wing with a Rigid Control Surface
Jahn, I. H., Zander, F., Stern, N. and Buttsworth, D. R.. 2018. "Simulation in the Loop Control of a Planar Hypersonic Wing with a Rigid Control Surface." 21st Australasian Fluid Mechanics Conference (AFMC 2018). Adelaide, Australia 10 - 13 Dec 2018 Australia.