Volume 13, Issue 3 (Journal of Control, V.13, N.3 Fall 2019)                   JoC 2019, 13(3): 85-94 | Back to browse issues page


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Abstract:   (1906 Views)
The aim of this paper is to propose a novel method for controlling a class of parameter-varying systems by controlling interval observer. The interval observers, that are applicable for the systems with uncertainty, estimate bounds on the states instead of estimating the states. It has been shown that by designing appropriate control inputs for controlling the bounds of the interval observer, the states of the system can be also controlled using the same control inputs. For this purpose, a suitable interval observer is firstly designed for the parameter-varying system and the required conditions, for which the dynamical system consisting of lower and upper bounds on error is monotone, are presented. Then, a novel controller is designed for stabilizing the interval observer such that the bounds on the states are stabilized and thereby the states are also stabilized. The proposed controller is based on adaptive sliding mode control method that is utilized to tackle the effects of variations in some parameters of the interval observers as well as the existing disturbances in the system. By choosing an appropriate Lyapunov function, the conditions and areas for the stability of the observer are determined. Simulation results, obtained by applying the method to a sample system, show the effectiveness of the proposed method.
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Type of Article: Research paper | Subject: Special
Received: 2018/01/14 | Accepted: 2018/06/11 | Published: 2019/12/31

1. [1] Mohd Ali, J., et al.,'Review and classification of recent observers applied in chemical process systems'. Computers & Chemical Engineering, 2015. 76(0): p. 27-41. [DOI:10.1016/j.compchemeng.2015.01.019]
2. [2] Luenberger, D.,'An introduction to observers'. Automatic Control, IEEE Transactions on, 1971. 16(6): p. 596-602. [DOI:10.1109/TAC.1971.1099826]
3. [3] Postoyan, R. and D. Nešić,'On emulated nonlinear reduced-order observers for networked control systems'. Automatica, 2012. 48(4): p. 645-652. [DOI:10.1016/j.automatica.2012.01.017]
4. [4] Chen, T., J. Morris, and E. Martin,'Particle filters for state and parameter estimation in batch processes'. Journal of Process Control, 2005. 15(6): p. 665-673. [DOI:10.1016/j.jprocont.2005.01.001]
5. [5] Li, S., et al.,'Disturbance observer-based control: methods and applications'. 2014: CRC press.
6. [6] Theocharis, J. and V. Petridis,'Neural Network Observer'. vectors, 1994. 27.
7. [7] Gao, Z., X. Shi, and S.X. Ding,'Fuzzy state/disturbance observer design for T-S fuzzy systems with application to sensor fault estimation'. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2008. 38(3): p. 875-880. [DOI:10.1109/TSMCB.2008.917185]
8. [8] Gouzé, J.L., A. Rapaport, and M.Z. Hadj-Sadok,'Interval observers for uncertain biological systems'. Ecological Modelling, 2000. 133(1-2): p. 45-56. [DOI:10.1016/S0304-3800(00)00279-9]
9. [9] Rapaport, A. and D. Dochain,'Interval observers for biochemical processes with uncertain kinetics and inputs'. Mathematical Biosciences, 2005. 193(2): p. 235-253. [DOI:10.1016/j.mbs.2004.07.004]
10. [10] Moisan, M. and O. Bernard.'Robust interval observers for uncertain chaotic systems'. in 45th IEEE Conference on Decision and Control, San Diego, CA, USA. 2006. [DOI:10.1109/CDC.2006.377682]
11. [11] Rami, M.A., C.H. Cheng, and C. de Prada.'Tight robust interval observers: An LP approach'. in Decision and Control, 2008. CDC 2008. 47th IEEE Conference on. 2008. [DOI:10.1109/CDC.2008.4739280]
12. [12] McCarthy, P.J., C. Nielsen, and S.L. Smith,'Cardinality constrained robust optimization applied to a class of interval observers', in American Control Conference (ACC), 2014. 2014, IEEE. p. 5337-5342. [DOI:10.1109/ACC.2014.6859149]
13. [13] Chebotarev, S., et al.,'Interval observers for continuous-time LPV systems with L1/L2 performance'. Automatica, 2015. 58: p. 82-89. [DOI:10.1016/j.automatica.2015.05.009]
14. [14] Mazenc, F. and O. Bernard,'Interval observers for linear time-invariant systems with disturbances'. Automatica, 2011. 47(1): p. 140-147. [DOI:10.1016/j.automatica.2010.10.019]
15. [15] Efimov, D., et al.,'Interval estimation for lpv systems applying high order sliding mode techniques'. Automatica, 2012. 48(9): p. 2365-2371. [DOI:10.1016/j.automatica.2012.06.073]
16. [16] Atassi, A.N. and H.K. Khalil,'A separation principle for the stabilization of a class of nonlinear systems'. IEEE Transactions on Automatic Control, 1999. 44(9): p. 1672-1687. [DOI:10.1109/9.788534]
17. [17] Efimov, D., T. Raissi, and A. Zolghadri,'Control of Nonlinear and LPV Systems: Interval Observer-Based Framework'. Automatic Control, IEEE Transactions on, 2013. 58(3): p. 773-778. [DOI:10.1109/TAC.2013.2241476]
18. [18] Efimov, D., T. Raissi, and A. Zolghadri.'Stabilization of nonlinear uncertain systems based on interval observers'. in Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on. 2011. [DOI:10.1109/CDC.2011.6160573]
19. [19] Cai, X., G. Lv, and W. Zhang,'Stabilisation for a class of non-linear uncertain systems based on interval observers'. IET Control Theory & Applications, 2012. 6(13): p. 2057-2062. [DOI:10.1049/iet-cta.2011.0493]
20. [20] Zhongwei, H. and X. Wei,'Control of non-linear switched systems with average dwell time: interval observer-based framework'. Control Theory & Applications, IET, 2016. 10(1): p. 10-16. [DOI:10.1049/iet-cta.2015.0285]
21. [21] Smith, H.L.,'Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems'. 2008: American Mathematical Soc. [DOI:10.1090/surv/041]
22. [22] Polycarpou, M.M. and P.A. Ioannou,'A robust adaptive nonlinear control design'. Automatica, 1996. 32(3): p. 423-427. [DOI:10.1016/0005-1098(95)00147-6]
23. [23] Liu, J.,'Sliding Mode Control Using MATLAB '. 1st ed. 2017: Academic Press. [DOI:10.1016/B978-0-12-802575-8.00001-1]