Open Access Open Access  Restricted Access Subscription or Fee Access

Robust Switched Control of Nonlinear Continuous-Time Systems


(*) Corresponding author


Authors' affiliations


DOI: https://doi.org/10.15866/ireaco.v10i2.9796

Abstract


This paper presents a novel approach to robust switched controller design developed for continuous-time nonlinear systems with arbitrary switching signal. As a basis of our controller design we have applied the gain-scheduling approach. It ensures the robust multi parameter-dependent quadratic stability and guaranteed cost. The obtained requirements for robust stability and performance are translated to an optimization problem in light of bilinear matrix inequality (BMI) constraints. Finally, the obtained controller design properties are validated on simulation examples.
Copyright © 2017 Praise Worthy Prize - All rights reserved.

Keywords


Switched Control; Robust Control; Gain Scheduling; Lyapunov Function; Continuous-Time Nonlinear Systems

Full Text:

PDF


References


N. H. El-Farra, P. Mhaskar, P. D. Christofides, Output feedback control of switched nonlinear systems using multiple Lyapunov functions, Systems & Control Letters, Vol. 54(Issue 12):1163-1182, 2005.
http://dx.doi.org/10.1016/j.sysconle.2005.04.005

L. Long, J. Zhao, Global stabilization for a class of switched nonlinear feedforward systems, Systems & Control Letters, Vol. 60(Issue 9):734-738, 2011.
http://dx.doi.org/10.1016/j.sysconle.2011.05.011

Y. Sun, L. Wang, On stability of a class of switched nonlinear systems, Automatica Vol. 49(Issue 1):305-307, 2013.
http://dx.doi.org/10.1016/j.automatica.2012.10.011

J. Lunze, F. Lagarrigue (Eds.), Handbook of Hybrid Systems Control, Theory, Tools, Applications (Cambridge University Press, 2009).
http://dx.doi.org/10.1017/cbo9780511807930

H. R. Shaker, J. P. How, Stability analysis for class of switched nonlinear systems, American Control Conference (ACC), pp. 2517-2520, 2010.
http://dx.doi.org/10.1109/acc.2010.5530585

H. Lin, P. Antsaklis, Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results, IEEE Transactions on Automatic Control Vol. 54(Issue 2):308-322, 2009.
http://dx.doi.org/10.1109/tac.2008.2012009

A. Aleksandrov, Y. Chen, A. V. Platonov, L. Zhang, Stability analysis for a class of switched nonlinear systems, Automatica Vol. 47(Issue 10):2286-2291, 2011.
http://dx.doi.org/10.1016/j.automatica.2011.08.016

V. Montagner, P. Peres, State feedback gain scheduling for linear systems with time-varying parameters, American Control Conference (ACC), pp. 2004-2009, 2004.
http://dx.doi.org/10.1115/1.2194074

M. Sato, D. Peaucelle, Gain-scheduled output-feedback controllers using inexact scheduling parameters for continuous-time LPV systems, Automatica Vol. 49(Issue 4):1019-1025, 2013.
http://dx.doi.org/10.1016/j.automatica.2013.01.034

V. Veselý, A. Ilka, Gain-scheduled PID controller design, Journal of Process Control Vol. 23(Issue 8):1141-1148., 2013.
http://dx.doi.org/10.1016/j.jprocont.2013.07.002

F. Adegas, J. Stoustrup, Structured control of affine linear parameter varying systems, American Control Conference (ACC), pp. 739-744, 2011.
http://dx.doi.org/10.1109/acc.2011.5991517

W. J. Rugh, J. S. Shamma, Survey Research on gain scheduling, Automatica Vol. 36(Issue 10):1401-1425, 2000.
http://dx.doi.org/10.1016/s0005-1098(00)00058-3

D. J. Leith, W. E. Leithead, Survey of gain-scheduling analysis and design, International Journal of Control, Vol. 73(Issue 11):1001-1025, 2000.
http://dx.doi.org/10.1080/002071700411304

V. Veselý, A. Ilka, Novel Approach to Switched Controller Design for Linear Continuous-Time Systems, Asian Journal of Control, Vol. 18(Issue 4):1-11, 2016.
http://dx.doi.org/10.1002/asjc.1240

M. Hanifzadegan, R. Nagamune, Switching Gain-Scheduled Control Design for Flexible Ball-Screw Drives, Journal of Dynamic Systems, Measurement, and Control, Vol. 136(Issue 1):6 pages, 2013.
http://dx.doi.org/10.1115/1.4025154

C. Olalla, R. Leyva, I. Queinnec, D. Maksimovic, Robust Gain-Scheduled Control of Switched-Mode DC-DC Converters, IEEE Transactions on Power Electronics, Vol. 27(Issue 6):3006-3019, 2012.
http://dx.doi.org/10.1109/tpel.2011.2178271

N. M. Horri, P. Palmer, M. Roberts, Gain-Scheduled Inverse Optimal Satellite Attitude Control, IEEE Transactions on Aerospace and Electronic Systems, Vol. 48(Issue 3):2437-2457, 2012.
http://dx.doi.org/10.1109/taes.2012.6237602

J. Geromel, P. Colaneri, Stability and Stabilization of Continuous Time Switched Linear Systems, SIAM Journal on Control and Optimization, Vol. 45(Issue 5):1915-1930, 2006.
http://dx.doi.org/10.1137/050646366

L. Allerhand, U. Shaked, Robust Stability and Stabilization of Linear Switched Systems With Dwell Time, IEEE Transactions on Automatic Control, Vol. 56(Issue 2):381-386, 2011.
http://dx.doi.org/10.1109/tac.2010.2097351

V. Montagner, P. Peres, A new LMI condition for the robust stability of linear time-varying systems, 42nd IEEE Conference on Decision and Control, Vol. 6, pp. 6133-6138, 2003.
http://dx.doi.org/10.1109/cdc.2003.1272249

V. Veselý, A. Ilka. Robust Switched Controller Design for Nonlinear Continuous Systems. 1st IFAC Conference on Modeling, Identification and Control of Nonlinear Systems – MICNON 2015, Saint Petersburg, Russia, June 24-26, 2015, p. 1079-1084.
http://dx.doi.org/10.1515/acsc-2015-0026

M. Müller, D. Liberzon, Input/output-to-state stability of switched nonlinear systems, American Control Conference (ACC), pp. 1708-1712, 2010.
http://dx.doi.org/10.1109/acc.2010.5531504

V. Veselý, D. Rosinová, Robust PID-PSD Controller Design: BMI Approach, Asian Journal of Control, Vol. 15(Issue 2):469-478, 2013.
http://dx.doi.org/10.1002/asjc.559

V. M. Kuncevic, M. M. Lycak, Control systems design using Lyapunov function approach in Russian (Nauka, Moscow, 1977).
http://dx.doi.org/10.1109/icces.2007.4447018

A. Ilka , V. Veselý, Robust switched controller design for linear continuous-time systems, Archives of Control Sciences, Vol. 25(Issue 4):401-416.
http://dx.doi.org/10.1515/acsc-2015-0026

P. Gahinet, P. Apkarian, M. Chilali, Affine parameter-dependent Lyapunov functions and real parametric uncertainty, IEEE Transactions on Automatic Control, Vol. 41(Issue 3):436-442, 1996.
http://dx.doi.org/10.1109/9.486646

D. Henrion, J. Löfberg, M. Koc ̆vara, M. Stingl, Solving polynomial static output feedback problems with PENBMI, 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC ’05., pp. 7581–7586, 2005.
http://dx.doi.org/10.1109/cdc.2005.1583385

J. Löfberg, YALMIP : A Toolbox for Modeling and Optimization in MATLAB, Proceedings of the CACSD Conference, Taipei, Taiwan, 2004.
http://dx.doi.org/10.1109/cacsd.2004.1393890


Refbacks

  • There are currently no refbacks.



Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize