399
Views
14
CrossRef citations to date
0
Altmetric
Articles

Polynomial LPV approach to robust H control of nonlinear sampled-data systems

ORCID Icon, ORCID Icon, &
Pages 2145-2160 | Received 08 Oct 2017, Accepted 02 Nov 2018, Published online: 19 Nov 2018

References

  • Abbas, H. S., Tóth, R., Petreczky, M., Meskin, N., & Mohammadpour, J. (2014). Embedding of nonlinear systems in a linear parameter-varying representation. IFAC Proceedings Volumes, 47(3), 6907–6913. doi: 10.3182/20140824-6-ZA-1003.02506
  • Agulhari, C. M., De Oliveira, R., & Peres, P. L. (2012). Robust lmi parser: A computational package to construct lmi conditions for uncertain systems. Xix brazilian conference on automation (CBA 2012) (pp. 2298–2305). Campina Grande, Paraíba, Brazil.
  • Agulhari, C. M., Tognetti, E. S., Oliveira, R. C., & Peres, P. L. (2013). H∞ dynamic output feedback for lpv systems subject to inexactly measured scheduling parameters. American control conference (ACC), 2013 (pp. 6060–6065). Washington, DC, USA.
  • Apkarian, P., & Gahinet, P. (1995). A convex characterization of gain-scheduled h∞ controllers. IEEE Transactions on Automatic Control, 40(5), 853–864. doi: 10.1109/9.384219
  • Belikov, J., Kotta, Ü., & Tõnso, M. (2014). Comparison of LPV and nonlinear system theory: A realization problem. Systems & Control Letters, 64, 72–78. doi: 10.1016/j.sysconle.2013.10.009
  • Bos, R., Bombois, X., & Van den Hof, P. M. (2009). Accelerating simulations of computationally intensive first principle models using accurate quasi-linear parameter varying models. Journal of Process Control, 19(10), 1601–1609. doi: 10.1016/j.jprocont.2009.09.004
  • Braga, M. F., Morais, C. F., Tognetti, E. S., Oliveira, R. C., & Peres, P. L. (2015). Discretization and event triggered digital output feedback control of LPV systems. Systems & Control Letters, 86, 54–65. doi: 10.1016/j.sysconle.2015.10.002
  • Briat, C. (2011). Convergence and equivalence results for the Jensen's inequality-application to time-delay and sampled-data systems. IEEE Transactions on Automatic Control, 56(7), 1660–1665. doi: 10.1109/TAC.2011.2121410
  • Briat, C. (2014). Linear parameter-varying and time-delay systems: Analysis, observation, filtering & control (Vol. 3). Berlin, Heidelberg: Springer.
  • Briat, C., Sename, O., & Lafay, J. F. (2008). Parameter dependent state-feedback control of LPV time delay systems with time varying delays using a projection approach. IFAC Proceedings Volumes, 41(2), 4946–4951. doi: 10.3182/20080706-5-KR-1001.00831
  • Cauet, S., Coirault, P., & Njeh, M. (2013). Diesel engine torque ripple reduction through LPV control in hybrid electric vehicle powertrain: Experimental results. Control Engineering Practice, 21(12), 1830–1840. doi: 10.1016/j.conengprac.2013.03.005
  • Chen, W. H., & Zheng, W. X. (2006). On improved robust stabilization of uncertain systems with unknown input delay. Automatica, 42(6), 1067–1072. doi: 10.1016/j.automatica.2006.02.015
  • Chesi, G. (2010). Lmi techniques for optimization over polynomials in control: A survey. IEEE Transactions on Automatic Control, 55(11), 2500–2510. doi: 10.1109/TAC.2010.2046926
  • Daafouz, J., Bernussou, J., & Geromel, J. C. (2008). On inexact LPV control design of continuous–time polytopic systems. IEEE transactions on Automatic Control, 53(7), 1674–1678. doi: 10.1109/TAC.2008.928119
  • da Silva, J. G., Moraes, V., Flores, J., & Palmeira, A. (2015). Sampled-data LPV control: A looped functional approach. IFAC-PapersOnLine, 48(26), 19–24. doi: 10.1016/j.ifacol.2015.11.107
  • De Caigny, J., Camino, J. F., Oliveira, R. C., Peres, P. L., & Swevers, J. (2012). Gain-scheduled dynamic output feedback control for discrete-time LPV systems. International Journal of Robust and Nonlinear Control, 22(5), 535–558. doi: 10.1002/rnc.1711
  • El Ghaoui, L., Oustry, F., & AitRami, M. (1997). A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Transactions on Automatic Control, 42(8), 1171–1176. doi: 10.1109/9.618250
  • Fridman, E. (2010). A refined input delay approach to sampled-data control. Automatica, 46(2), 421–427. doi: 10.1016/j.automatica.2009.11.017
  • Gaspar, P., Szabo, Z., Bokor, J., & Nemeth, B. (2017). Modeling of lpv systems. In Robust control design for active driver assistance systems (pp. 11–70). Springer: Springer, Cham.
  • Heuberger, P., Van den Hof, P., & Tóth, R. (2010). Discretisation of linear parameter-varying state-space representations. IET Control Theory & Applications, 4(10), 2082–2096. doi: 10.1049/iet-cta.2009.0572
  • Hoffmann, C., & Werner, H. (2015). A survey of linear parameter-varying control applications validated by experiments or high-fidelity simulations. IEEE Transactions on Control Systems Technology, 23(2), 416–433. doi: 10.1109/TCST.2014.2327584
  • Hooshmandi, K., Bayat, F., Jahed-Motlagh, M. R., & Jalali, A. (2018a). Robust sampled-data control of non-linear lpv systems: Time-dependent functional approach. IET Control Theory & Applications, 12(9), 1318–1331. doi: 10.1049/iet-cta.2017.0980
  • Hooshmandi, K., Bayat, F., Jahed-Motlagh, M. R., & Jalali, A. (2018b). Stability analysis and design of nonlinear sampled-data systems under aperiodic samplings. International Journal of Robust and Nonlinear Control, 28(7), 2679–2699. doi: 10.1002/rnc.4043
  • Karafyllis, I., & Kravaris, C. (2009). Global stability results for systems under sampled-data control. International Journal of Robust and Nonlinear Control, 19(10), 1105–1128. doi: 10.1002/rnc.1364
  • Kwiatkowski, A., Boll, M. T., & Werner, H. (2006). Automated generation and assessment of affine lpv models. 2006 45th IEEE conference on decision and control (pp. 6690–6695). San Diego, California, USA.
  • Labit, Y., Peaucelle, D., & Henrion, D. (2002). Sedumi interface 1.02: a tool for solving lmi problems with sedumi. 2002 IEEE international symposium on Computer aided control system design, 2002. Proceedings (pp. 272–277). Anchorage, AK, USA.
  • Lam, J., & Zhou, S. (2008). Gain-scheduled H∞ controller design for discrete-time systems via parameter-dependent lyapunov functions. International Journal of information and science, 4(2), 191–203.
  • Lee, S., Park, M., Kwon, O., & Sakthivel, R. (2017a). Advanced sampled-data synchronization control for complex dynamical networks with coupling time-varying delays. Information Sciences, 420, 454–465. doi: 10.1016/j.ins.2017.08.071
  • Lee, S., Park, M., Kwon, O., & Sakthivel, R. (2017b). Synchronization of lur'e systems via stochastic reliable sampled-data controller. Journal of the Franklin Institute, 354(5), 2437–2460. doi: 10.1016/j.jfranklin.2017.01.003
  • Leith, D. J., & Leithead, W. (1998). Gain-scheduled controller design: An analytic framework directly incorporating non-equilibrium plant dynamics. International Journal of Control, 70(2), 249–269. doi: 10.1080/002071798222398
  • Leith, D. J., & Leithead, W. E. (2000). Survey of gain-scheduling analysis and design. International Journal of Control, 73(11), 1001–1025. doi: 10.1080/002071700411304
  • Liu, Y., & Li, M. (2015). Improved robust stabilization method for linear systems with interval time-varying input delays by using wirtinger inequality. ISA Transactions, 56, 111–122. doi: 10.1016/j.isatra.2014.12.008
  • Lofberg, J. (2004). Yalmip: A toolbox for modeling and optimization in matlab. 2004 IEEE international symposium on Computer aided control systems design (pp. 284–289). Taipei, Taiwan.
  • Luspay, T., & Grigoriadis, K. (2015). Robust linear parameter-varying control of blood pressure using vasoactive drugs. International Journal of Control, 88(10), 2013–2029. doi: 10.1080/00207179.2015.1027953
  • Mazenc, F., Malisoff, M., & Dinh, T. N. (2013). Robustness of nonlinear systems with respect to delay and sampling of the controls. Automatica, 49(6), 1925–1931. doi: 10.1016/j.automatica.2013.02.064
  • Moarref, M., & Rodrigues, L. (2015). Sampled-data piecewise affine differential inclusions. IEEE Transactions on Automatic Control, 60(3), 850–856. doi: 10.1109/TAC.2014.2342051
  • Narendra, K. S., & Tripathi, S. (1973). Identification and optimization of aircraft dynamics. Journal of Aircraft, 10(4), 193–199. doi: 10.2514/3.44364
  • Németh, B., Varga, B., & Gáspár, P. (2015). Hierarchical design of an electro-hydraulic actuator based on robust LPV methods. International Journal of Control, 88(8), 1429–1440. doi: 10.1080/00207179.2014.1002427
  • Nesic, D., Teel, A. R., & Carnevale, D. (2009). Explicit computation of the sampling period in emulation of controllers for nonlinear sampled-data systems. IEEE Transactions on Automatic Control, 54(3), 619–624. doi: 10.1109/TAC.2008.2009597
  • Oliveira, R. C., & Peres, P. L. (2007). Parameter-dependent lmis in robust analysis: Characterization of homogeneous polynomially parameter-dependent solutions via lmi relaxations. IEEE Transactions on Automatic Control, 52(7), 1334–1340. doi: 10.1109/TAC.2007.900848
  • Papachristodoulou, A., Anderson, J., Valmorbida, G., Prajna, S., Seiler, P., & Parrilo, P. (2013). Sostools version 3.00 sum of squares optimization toolbox for matlab. arXiv preprint arXiv:1310.4716.
  • Papachristodoulou, A., & Prajna, S. (2005a). Analysis of non-polynomial systems using the sum of squares decomposition. In Positive polynomials in control (pp. 580–580). Berlin, Heidelberg: Springer.
  • Papachristodoulou, A., & Prajna, S. (2005b). A tutorial on sum of squares techniques for systems analysis. American control conference, 2005. Proceedings of the 2005 (pp. 2686–2700). Portland, OR, USA.
  • Pfifer, H., & Hecker, S. (2011). Generation of optimal linear parametric models for lft-based robust stability analysis and control design. IEEE Transactions on Control Systems Technology, 19(1), 118–131. doi: 10.1109/TCST.2010.2076329
  • Putinar, M. (1993). Positive polynomials on compact semi-algebraic sets. Indiana University Mathematics Journal, 42(3), 969–984. doi: 10.1512/iumj.1993.42.42045
  • Ramezanifar, A., Mohammadpour, J., & Grigoriadis, K. (2012). Sampled-data control of LPV systems using input delay approach. IEEE 51st annual conference on decision and control (CDC) (pp. 6303–6308). Maui, Hawaii.
  • Ramezanifar, A., Mohammadpour, J., & Grigoriadis, K. M. (2013). Sampled-data control of linear parameter varying time-delay systems using state feedback. American control conference (ACC) (pp. 6847–6852). Washington, DC, USA.
  • Ramezanifar, A., Mohammadpour, J., & Grigoriadis, K. M. (2014). Output-feedback sampled-data control design for linear parameter-varying systems with delay. International Journal of Control, 87(12), 2431–2445. doi: 10.1080/00207179.2014.926394
  • Rotondo, D., Puig, V., Nejjari, F., & Witczak, M. (2015). Automated generation and comparison of takagi–sugeno and polytopic quasi-lpv models. Fuzzy Sets and Systems, 277, 44–64. doi: 10.1016/j.fss.2015.02.002
  • Rugh, W. J. (1991). Analytical framework for gain scheduling. IEEE control systems, 11(1), 79–84. doi: 10.1109/37.103361
  • Sato, M., Ebihara, Y., & Peaucelle, D. (2010). Gain-scheduled state-feedback controllers using inexactly measured scheduling parameters: h2 and h∞ problems. American control conference (ACC), 2010 (pp. 3094–3099). Baltimore, Maryland, USA.
  • Sato, M., & Peaucelle, D. (2013). Gain-scheduled output-feedback controllers using inexact scheduling parameters for continuous-time LPV systems. Automatica, 49(4), 1019–1025. doi: 10.1016/j.automatica.2013.01.034
  • Scherer, C. W. (2006). Lmi relaxations in robust control. European Journal of Control, 12(1), 3–29. doi: 10.3166/ejc.12.3-29
  • Seiler, P. (2013). Sosopt: A toolbox for polynomial optimization. arXiv preprint arXiv:1308.1889.
  • Seuret, A. (2012). A novel stability analysis of linear systems under asynchronous samplings. Automatica, 48(1), 177–182. doi: 10.1016/j.automatica.2011.09.033
  • Shamma, J. S., & Athans, M. (1992). Gain scheduling: Potential hazards and possible remedies. IEEE Control Systems, 12(3), 101–107. doi: 10.1109/37.165527
  • Shamma, J. S., & Cloutier, J. R. (1993). Gain-scheduled missile autopilot design using linear parameter varying transformations. Journal of guidance, Control, and dynamics, 16(2), 256–263. doi: 10.2514/3.20997
  • Shirazi, F. A., Grigoriadis, K. M., & Viassolo, D. (2012). Wind turbine integrated structural and LPV control design for improved closed-loop performance. International Journal of Control, 85(8), 1178–1196. doi: 10.1080/00207179.2012.679973
  • Tan, W. (1997). Applications of linear parameter-varying control theory (Tech. Rep). University of California at Berkeley.
  • Tan, K., & Grigoriadis, K. M. (2000). State-feedback control of LPV sampled-data systems. Mathematical Problems in Engineering, 6(2–3), 145–170. doi: 10.1155/S1024123X00001307
  • Tan, K., Grigoriadis, K. M., & Wu, F. (2002). Output-feedback control of LPV sampled-data systems. International Journal of Control, 75(4), 252–264. doi: 10.1080/00207170110101775
  • Tóth, R. (2010). Lecture notes in control and information sciences: Vol. 403. Identification and modeling of linear parameter-varying systems. Springer verlag, Berlin.
  • Tóth, R., Heuberger, P. S., & Van den Hof, P. M. (2012). Prediction-error identification of lpv systems: Present and beyond. In Control of linear parameter varying systems with applications (pp. 27–58). Boston, MA: Springer.
  • Tóth, R., Lovera, M., Heuberger, P. S., Corno, M., & Van den Hof, P. M. (2012). On the discretization of linear fractional representations of LPV systems. IEEE Transactions on Control Systems Technology, 20(6), 1473–1489. doi: 10.1109/TCST.2011.2164921
  • van Wingerden, J. W., & Verhaegen, M. (2009). Subspace identification of bilinear and LPV systems for open-and closed-loop data. Automatica, 45(2), 372–381. doi: 10.1016/j.automatica.2008.08.015
  • Vízer, D., Mercère, G., Prot, O., & Laroche, E. (2014). Combining analytic and experimental information for linear parameter-varying model identification: application to a flexible robotic manipulator. Periodica Polytechnica. Electrical Engineering and Computer Science, 58(4), 133–148. doi: 10.3311/PPee.7503
  • Wu, F., & Prajna, S. (2005). Sos-based solution approach to polynomial LPV system analysis and synthesis problems. International Journal of Control, 78(8), 600–611. doi: 10.1080/00207170500114865
  • Xiaodong, L., & Qingling, Z. (2003). New approaches to H∞ controller designs based on fuzzy observers for TS fuzzy systems via LMI. Automatica, 39(9), 1571–1582. doi: 10.1016/S0005-1098(03)00172-9
  • Zhang, C. K., Jiang, L., He, Y., Wu, H., & Wu, M. (2013). Stability analysis for control systems with aperiodically sampled data using an augmented lyapunov functional method. IET Control Theory & Applications, 7(9), 1219–1226. doi: 10.1049/iet-cta.2012.0814

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.