Abstract
The paper presents a general approach to approximate a nonlinear system by a linear fractional representation (LFR), which is suitable for LFT-based robust stability analysis and control design. In a first step, the nonlinear system will be transformed into a quasi linear parameter varying (LPV) system. In the second step, the nonlinear dependencies in the quasi-LPV, which are not rational in the parameters, are approximated using polynomial fitting based on ℓ1-regularized least squares. Using this approach an almost Pareto front between the accuracy and complexity of the resulting LFR can be efficiently obtained. The effectiveness of the proposed method is demonstrated by applying it to a nonlinear missile model of industrial complexity.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Zhou, K., Doyle, J.C.: Essentials of Robust Control. Prentice Hall, New Jersey (1998)
Leith, D.J., Leithead, W.E.: Survey of gain-scheduling analysis and design. International Journal of Control 73(11), 1001–1025 (2000)
Tan, W.: Applications of linear parameter varying control theory. Master’s thesis, University of California at Berkeley (1997)
Marcos, A., Balas, G.: Development of linear-parameter-varying models for aircraft. Journal of Guidance, Control and Dynamics 27, 218–228 (2004)
Hecker, S.: Generation of low order LFT Representations for Robust Control Applications. VDI Verlag (2007)
Pfifer, H., Hecker, S.: Generation of optimal linear parametric models for LFT-based robust stability analysis and control design. In: Proceedings of IEEE Conference on Decision and Control (2008)
Pfifer, H., Hecker, S., Michalka, G.: Lft-based stability analysis of generic guided missile. In: Proceedings of the AIAA Guidance, Navigation and Control Conference (2009)
Hecker, S., Pfifer, H.: Generation of LPV Models and LFRs for a Nonlinear Aircraft Model. In: Varga, A., Hansson, A., Puyou, G. (eds.) Optimization Based Clearance of Flight Control Laws. LNCIS, vol. 416, pp. 39–57. Springer, Heidelberg (2012)
Vinnicombe, G.: Frequency domain uncertainty and the graph topology. IEEE Transactions on Automatic Control 38 (1993)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press (2004)
Kim, S., Koh, K., Lustig, M., Boyd, S., Gorinevsky, G.: An interior-point method for large scale ℓ1-regularized least squares. IEEE Journal on Selected Topics in Signal Processing (2007)
Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least angle regression. The Annals of Statistics 32 (2004)
Peter, F., Leitao, M., Holzapfel, F.: Adaptive augmentation of a new baseline control architecture for tail-controlled missiles using a nonlinear reference model. In: Proceedings of the AIAA Guidance, Navigation and Control Conference (2012)
Hecker, S., Varga, A., Magni, J.: Enhanced LFR-toolbox for Matlab. Aerospace Science and Technology 9 (2005)
Hindi, H., Seong, C.-Y., Boyd, S.: Computing optimal uncertainty models from frequency domain data. In: Proceedings of Conference on Decision and Control (2002)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pfifer, H., Hecker, S. (2013). LFT Model Generation via ℓ1-Regularized Least Squares. In: Chu, Q., Mulder, B., Choukroun, D., van Kampen, EJ., de Visser, C., Looye, G. (eds) Advances in Aerospace Guidance, Navigation and Control. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38253-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-38253-6_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38252-9
Online ISBN: 978-3-642-38253-6
eBook Packages: EngineeringEngineering (R0)