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An Lmi–Based Heuristic Algorithm for Vertex Reduction in LPV Systems Cover

An Lmi–Based Heuristic Algorithm for Vertex Reduction in LPV Systems

Open Access
|Dec 2019

References

  1. Apkarian, P., Gahinet, P. and Becker, G. (1995). Self-scheduled ℋ control of linear parameter-varying systems: A design example, Automatica31(9): 1251–1261.10.1016/0005-1098(95)00038-X
  2. Apkarian, P. and Tuan, H.D. (2000). Parameterized LMIs in control theory, SIAM Journal on Control and Optimization38(4): 1241–1264.10.1137/S036301299732612X
  3. Boyd, S., El Ghaoui, L., Feron, E. and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA.10.1137/1.9781611970777
  4. Chilali, M. and Gahinet, P. (1996). ℋ design with pole placement constraints: An LMI approach, IEEE Transactions on Automatic Control41(3): 358–367.10.1109/9.486637
  5. Chitraganti, S., Tóth, R., Meskin, N. and Mohammadpour, J. (2017). Stochastic model predictive tracking of piecewise constant references for LPV systems, IET Control Theory & Applications11(12): 1862–1872.10.1049/iet-cta.2016.0629
  6. Curran, P.F. (2009). On a variation of the Gershgorin circle theorem with applications to stability theory, IET Irish Signals and Systems Conference (ISSC 2009), Dublin, Ireland, pp. 1–5.10.1049/cp.2009.1687
  7. El-Sakkary, A. (1985). The gap metric: Robustness of stabilization of feedback systems, IEEE Transactions on Automatic Control30(3): 240–247.10.1109/TAC.1985.1103926
  8. Fergani, S., Menhour, L., Sename, O., Dugard, L. and D’Andréa-Novel, B. (2017). Integrated vehicle control through the coordination of longitudinal/lateral and vertical dynamics controllers: Flatness and LPV/ℋ-based design, International Journal of Robust and Nonlinear Control27(18): 4992–5007.10.1002/rnc.3846
  9. Fleischmann, S., Theodoulis, S., Laroche, E., Wallner, E. and Harcaut, J.-P. (2016). A systematic LPV/LFR modelling approach optimized for linearised gain scheduling control synthesis, AIAA Modeling and Simulation Technologies Conference, San Diego, CA, USA, p. 1921.10.2514/6.2016-1921
  10. Gahinet, P., Apkarian, P. and Chilali, M. (1996). Affine parameter-dependent Lyapunov functions and real parametric uncertainty, IEEE Transactions on Automatic Control41(3): 436–442.10.1109/9.486646
  11. Ho, W.K., Lee, T.H., Xu, W., Zhou, J.R. and Tay, E.B. (2000). The direct Nyquist array design of PID controllers, IEEE Transactions on Industrial Electronics47(1): 175–185.10.1109/41.824140
  12. Hoffmann, C. and Werner, H. (2015). A survey of linear parameter-varying control applications validated by experiments or high-fidelity simulations, IEEE Transactions on Control Systems Technology23(2): 416–433.10.1109/TCST.2014.2327584
  13. Inthamoussou, F.A., Bianchi, F.D., De Battista, H. and Mantz, R.J. (2014). LPV wind turbine control with anti-windup features covering the complete wind speed range, IEEE Transactions on Energy Conversion29(1): 259–266.10.1109/TEC.2013.2294212
  14. Jabali, M. B.A. and Kazemi, M.H. (2017). A new LPV modeling approach using PCA-based parameter set mapping to design a PSS, Journal of Advanced Research8(1): 23–32.10.1016/j.jare.2016.10.006
  15. Kwiatkowski, A., Boll, M.-T. and Werner, H. (2006). Automated generation and assessment of affine LPV models, 45th IEEE Conference on Decision and Control, San Diego, CA, USA, pp. 6690–6695.10.1109/CDC.2006.377768
  16. Kwiatkowski, A. and Werner, H. (2008). PCA-based parameter set mappings for LPV models with fewer parameters and less overbounding, IEEE Transactions on Control Systems Technology16(4): 781–788.10.1109/TCST.2007.903094
  17. Lofberg, J. (2004). YALMIP: A toolbox for modeling and optimization in MATLAB, IEEE International Symposium on Computer Aided Control Systems Design, New Orleans, LA, USA, pp. 284–289.
  18. López-Estrada, F.-R., Ponsart, J.-C., Astorga-Zaragoza, C.-M., Camas-Anzueto, J.-L. and Theilliol, D. (2015). Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: Application to an anaerobic bioreactor, International Journal of Applied Mathematics and Computer Science25(2): 233–244, DOI: 10.1515/amcs-2015-0018.10.1515/amcs-2015-0018
  19. Luspay, T., Péni, T., Gőzse, I., Szabó, Z. and Vanek, B. (2018). Model reduction for LPV systems based on approximate modal decomposition, International Journal for Numerical Methods in Engineering113(6): 891–909.10.1002/nme.5692
  20. Marcos, A. and Balas, G.J. (2004). Development of linear-parameter-varying models for aircraft, Journal of Guidance, Control, and Dynamics27(2): 218–228.10.2514/1.9165
  21. Mohammadpour, J. and Scherer, C.W. (2012). Control of Linear Parameter Varying Systems with Applications, Springer, New York, NY.10.1007/978-1-4614-1833-7
  22. Montagner, V., Oliveira, R., Leite, V.J. and Peres, P.L.D. (2005). LMI approach for ℋ linear parameter-varying state feedback control, IEE Proceedings: Control Theory and Applications152(2): 195–201.10.1049/ip-cta:20045117
  23. Nguyen, A.-T., Chevrel, P. and Claveau, F. (2018). Gain-scheduled static output feedback control for saturated LPV systems with bounded parameter variations, Automatica89: 420–424.10.1016/j.automatica.2017.12.027
  24. Packard, A. (1994). Gain scheduling via linear fractional transformations, Systems & Control Letters22(2): 79–92.10.1016/0167-6911(94)90102-3
  25. Pemmaraju, S. and Skiena, S. (2003). Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica, Cambridge University Press, New York, NY.10.1017/CBO9781139164849
  26. Quarteroni, A., Sacco, R. and Saleri, F. (2010). Numerical Mathematics, Vol. 37, Springer Science & Business Media, New York, NY.
  27. Rahideh, A. and Shaheed, M. (2007). Mathematical dynamic modelling of a twin-rotor multiple input-multiple output system, Proceedings of the Institution of Mechanical Engineers I: Journal of Systems and Control Engineering221(1): 89–101.10.1243/09596518JSCE292
  28. Rizvi, S. Z., Mohammadpour, J., Tóth, R. and Meskin, N. (2016). A kernel-based PCA approach to model reduction of linear parameter-varying systems, IEEE Transactions on Control Systems Technology24(5): 1883–1891.10.1109/TCST.2016.2517126
  29. Rotondo, D. (2017). Advances in Gain-Scheduling and Fault Tolerant Control Techniques, Springer, Cham.10.1007/978-3-319-62902-5
  30. Rotondo, D., Nejjari, F. and Puig, V. (2013). Quasi-LPV modeling, identification and control of a twin rotor MIMO system, Control Engineering Practice21(6): 829–846.10.1016/j.conengprac.2013.02.004
  31. Rotondo, D., Nejjari, F. and Puig, V. (2014). Robust state-feedback control of uncertain LPV systems: An LMI-based approach, Journal of the Franklin Institute351(5): 2781–2803.10.1016/j.jfranklin.2014.01.018
  32. Rotondo, D., Puig, V., Nejjari, F. and Romera, J. (2015a). A fault-hiding approach for the switching quasi-LPV fault-tolerant control of a four-wheeled omnidirectional mobile robot, IEEE Transactions on Industrial Electronics62(6): 3932–3944.10.1109/TIE.2014.2367002
  33. Rotondo, D., Puig, V., Nejjari, F. and Witczak, M. (2015b). Automated generation and comparison of Takagi–Sugeno and polytopic quasi-LPV models, Fuzzy Sets and Systems27(C): 44–64.10.1016/j.fss.2015.02.002
  34. Rugh, W.J. and Shamma, J.S. (2000). Research on gain scheduling, Automatica36(10): 1401–1425.10.1016/S0005-1098(00)00058-3
  35. Sturm, J.F. (1999). Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones, Optimization Methods and Software11(1–4): 625–653.10.1080/10556789908805766
  36. Sun, X.-D. and Postlethwaite, I. (1998). Affine LPV modelling and its use in gain-scheduled helicopter control, UKACC International Conference on Control ‘98, Swansea, UK, Vol. 2, pp. 1504–1509.10.1049/cp:19980452
  37. Theis, J., Seiler, P. and Werner, H. (2017). LPV model order reduction by parameter-varying oblique projection, IEEE Transactions on Control Systems Technology26(3): 773–784.10.1109/TCST.2017.2692744
  38. Theodoulis, S. and Duc, G. (2009). Missile autopilot design: Gain-scheduling and the gap metric, Journal of Guidance, Control, and Dynamics32(3): 986–996.10.2514/1.34756
  39. Tseng, C.-S., Chen, B.-S. and Uang, H.-J. (2001). Fuzzy tracking control design for nonlinear dynamic systems via TS fuzzy model, IEEE Transactions on Fuzzy Systems9(3): 381–392.10.1109/91.928735
  40. Vinnicombe, G. (1996). The robustness of feedback systems with bounded complexity controllers, IEEE Transactions on Automatic Control41(6): 795–803.10.1109/9.506232
  41. White, A.P., Zhu, G. and Choi, J. (2013). Linear Parameter-Varying Control for Engineering Applications, Springer, London.10.1007/978-1-4471-5040-4
  42. Zhao, P. and Nagamune, R. (2017). Switching LPV controller design under uncertain scheduling parameters, Automatica76: 243–250.10.1016/j.automatica.2016.10.026
  43. Zhou, M., Rodrigues, M., Shen, Y. and Theilliol, D. (2018). ℋ _/ℋ fault detection observer design for a polytopic LPV system using the relative degree, International Journal of Applied Mathematics and Computer Science28(1): 83–95, DOI: 10.2478/amcs-2018-0006.10.2478/amcs-2018-0006
  44. Zribi, A., Chtourou, M. and Djemal, M. (2016). A systematic determination approach of model’s base using gap metric for nonlinear systems, Journal of Dynamic Systems, Measurement, and Control138(3): 031008.10.1115/1.4032222
DOI: https://doi.org/10.2478/amcs-2019-0054 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 725 - 737
Submitted on: Nov 9, 2018
Accepted on: May 30, 2019
Published on: Dec 31, 2019
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2019 Adrián Sanjuan, Damiano Rotondo, Fatiha Nejjari, Ramon Sarrate, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.