1. bookVolume 67 (2016): Issue 2 (April 2016)
Journal Details
License
Format
Journal
First Published
07 Jun 2011
Publication timeframe
6 times per year
Languages
English
access type Open Access

Output Feedback Control of Switched Nonlinear Systems: A Gain Scheduling Approach

Published Online: 14 May 2016
Page range: 87 - 94
Received: 15 Dec 2015
Journal Details
License
Format
Journal
First Published
07 Jun 2011
Publication timeframe
6 times per year
Languages
English

Switched controller design for nonlinear continuous and discrete-time systems under an arbitrary switching signal using the gain scheduling approach is addressed in this paper. The obtained controller design procedures for continuous and discrete-time systems are in the bilinear matrix inequality form. The proposed design procedure ensures multi parameter-dependent quadratic stability of the switched gain scheduled plant which is associative to a nonlinear plant model and optimal performance defined by quadratic gain scheduled parameters weighting cost function. Example demonstrates the effectiveness of the proposed approaches.

Keywords

[1] ADEGAS, F. D.-STOUSTRUP, J. : Structured Control of Affine Linear Parametric Varying Systems, In: ACC San Fran- cisco, June 2011, pp. 739-744.Search in Google Scholar

[2] ALEKSANDROV, A. Yu.-CHEN, Y.-PLATONOV, A. V.-ZHANG, L. : Stability Analysis for a Class of Switched Nonlin- ear Systems, Automatica 47 (2011), 2286-2291.Search in Google Scholar

[3] ALLEWRHAND, L. I.-SHAKED, U. : Robust Stability and Stabilization of Linear Switched Systems with Dwell Time, IEEE Trans on AC 56 (2011), 381-386.Search in Google Scholar

[4] BRANICKY, M. S.-BORKAR, V. S.-MITTER, S. K. : A Unified Framework for Hybrid Control: Model and Optimal Con- trol Theory, IEEE Transactions on Automatic Control 43 No. 1 (1998), 31-45.Search in Google Scholar

[5] GAHINET, P.-APKARIAN, P.-CHILALI, M. : Affine Pa- rameter-Dependent Lyapunov Functions and Real Parametric Uncertainty, IEEE Trans on AC 41 No. 3 (1996), 436-442.Search in Google Scholar

[6] GEROMEL, J. C.-COLONERI, P. : Stability and Stabiliza- tion of Continuous Time Switched Linear Systems, SIAM J. Control Optim. 45 No. 5 (2006), 1915-1930.Search in Google Scholar

[7] GOEBEL, R.-TEEL, A. R. : Solutions to Hybrid Inclusions via Set and Graphical Convergence with Stability Theory Ap- plications, Automatica 42 No. 4 (2006), 573-587.Search in Google Scholar

[8] GUOLIANG WEI-ZIDONG WANG-WANGYAN LI-LI- FENG MA: A Survey on Gain-Scheduled Control and Filtering for Parameter-Varying Systems, Discrete Dynamics in Nature and Sociaty, vol. 2014, Article ID 105815.Search in Google Scholar

[9] SHAKER, H. R.-HOW, J. P. : Stability Analysis for a Class of Switched Nonlinear Systems, In: ACC, 2010, pp. 2517-2520.Search in Google Scholar

[10] HANIFZADEGAN, M.-NAGAMUNE, R. : Switching Gain Scheduled Control Design for Flexible Ball-Srew Drives, Journal of dynamic systems, measurement and control 136 No. 1 (2013).Search in Google Scholar

[11] HORRI, N.-PALMER, P.-ROBERTS, M. : Gain Sched- uled Inverse Optimal Satelit Attitude Control, IEEE trans. on Aerospace and Electronic Systems 48 No. 3 (2012), 2437-2457.Search in Google Scholar

[12] KUNCEVIC, V. M.-LYCAK, M. M. : Control Systems Design using Lyapunov Function Approach, Nauka, Moscow, 1977. (in Russian)Search in Google Scholar

[13] LEITH, D. J.-LEITHEAD, W. E. : Survey of Gain Scheduling Analysis and Design, Inter. Journal of Control 73 No. 11 (2000), 1001-1025.Search in Google Scholar

[14] LIJUN LONG-JUN ZHAO: Global Stabilization for a Class of Switched Nonlinear Feedforward Systems, Systems and Control Letters 60 (2011), 734-738.Search in Google Scholar

[15] LIBERZON, D. : Switching in Systems and Control, Birkhauser, Boston, 2003.Search in Google Scholar

[16] LUNZE, J.-LAGARRIGUE, F. L. Editors : Hanbook of Hy- brid Systems Control, Theory, Tools, Applications, Cambridge University Press, 2009.Search in Google Scholar

[17] LYGEROS, J. : On Overview of Research Areas in Hybrid Systems Control, In: Proc. of the 44 IEEE Conf. on Decission and Control and the European Control Conf., Spain, 2005.Search in Google Scholar

[18] MASAYUKI SATO-DIMITRI PEAUCELLE : Gain Sched- uled Output Feedback Controllers using Inexat Scheduling Pa- rameters for Continuous-Time Varying Systems, Automatica 49 (2013), 1019-1025.Search in Google Scholar

[19] MASIH HAMIFZADEGAN-RYOZO NAGAMUNE: Switch- ing Gain scheduled Control Design for Flexible Ball-Screw Drives, J. Dyn. Sys. Meas. Control 136 No. 1 (2013).Search in Google Scholar

[20] MULLER, M. A.-LIBERZON, D. : Input/Output-to State Stability of Switched Nonlinear Systems, In: ACC, June 2010, pp. 1708-1712.Search in Google Scholar

[21] MONTAGNER, V. F.-PERES, P. L. D. : State Feedback Gain Scheduling for Linear Systems with Time-Varying Parameters, In: ACC Boston, 2004, pp. 2004-2009.Search in Google Scholar

[22] MONTAGNER, V.-PERES, P. L. D. : A New LMI Condition for the Robust Stability of Linear Time-Varying Systems, In: Proceedings of CDC, 2003, pp. 6133-6138.Search in Google Scholar

[23] HORRI, N. M.-PALMER, P.-ROBERTS, M. : Gain-Sched- uled Inverse Optimal Satellite Attitude Control, Trans. on Aerospace and Electronic Systems 48 (2011), 2437-2457.Search in Google Scholar

[24] El-FARR, N. H.-PRASHANT MHASKAR-CHRISTOFI- DES, P. D. : Output Feedback Control of Switched Nonlin- ear Systems using Multiple Lyapunov Functions, Systems and Control Letters 54 (2005), 1163-1182.Search in Google Scholar

[25] OLALLA, C.-LEYVE, R.-QUEINNEC, I.-MAKSIMOVIC, D. : Robust Gain-Scheduled Control of Switched-Mode DC-DC Convertors, IEEE Trans on Power Elecrtonics 27 No. 6 (2012), 3006-3019.Search in Google Scholar

[26] RUGH, W. J.-SHAMMA, J. S. : Survey Research on Gain Scheduling, Automatica 36 No. 10, 1401-1425.Search in Google Scholar

[27] VESELÝ, V.-ILKA, A. : PID Robust Gain-Scheduled Con- troller Designinbook In: ECC’2014, June 24-25, 2014, Stras- bourg, France, CD-ROM.Search in Google Scholar

[28] VESELÝ, V.-ILKA, A. : Gain-Scheduled PID Controller De- sign, Journal of Proces Control 23 (2013), 1141-1148.Search in Google Scholar

[29] YUANGONG SUN-LONG WANG: On Stability of Switched Nonlinear Systems, Automatica 49 (2013), 305-307.Search in Google Scholar

[30] WADA, N.-SAEKI, M. : An LMI based Scheduling Algorithm for Constrained Stabilization Problem, Systems and Control Letters 57 (2008), 255-261.Search in Google Scholar

[31] VESELÝ, V.-ROSINOVÁ, D. : Robust PID-PSD Controller Design: BMI Approach, Asian Journal of Control 15 No. 2 (2013), 469-478.Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo