An adaptive observer design approach for a class of discrete-time nonlinear systems

• Autorzy: Srinivasarengan K. , Ragot J. , Aubrun C. , Maquin D.

Identyfikatory

DOI

10.2478/amcs-2018-0004

• Języki publikacji: EN

Abstrakty

EN

We consider the problem of joint estimation of states and some constant parameters for a class of nonlinear discrete-time systems. This class contains systems that could be transformed into a quasi-LPV (linear parameter varying) polytopic model in the Takagi–Sugeno (T–S) form. Such systems could have unmeasured premise variables, a case usually overlooked in the observer design literature. We assert that, for such systems in discrete-time, the current literature lacks design strategies for joint state and parameter estimation. To this end, we adapt the existing literature on continuous-time linear systems for joint state and time-varying parameter estimation. We first develop the discrete-time version of this result for linear systems. A Lyapunov approach is used to illustrate stability, and bounds for the estimation error are obtained via the bounded real lemma. We use this result to achieve our objective for a design procedure for a class of nonlinear systems with constant parameters. This results in less conservative conditions and a simplified design procedure. A basic waste water treatment plant simulation example is discussed to illustrate the design procedure.

Słowa kluczowe

EN

adaptive observer; joint state estimation; parameter estimation; Takagi-Sugeno model; time-varying parameter estimation; sector nonlinearity transformation; discrete-time nonlinear systems

PL

obserwator adaptacyjny; identyfikacja parametrów; model Takagi-Sugeno; transformacja nieliniowa; dyskretny układ nieliniowy

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2018
• Tom: Vol. 28, no. 1
• Strony: 55--67
• Opis fizyczny: Bibliogr. 22 poz., tab., wykr.

Twórcy

autor

Srinivasarengan K.

• CRAN UMR 7039, CNRS, University of Lorraine, F-54000 Vandoeuvre-lès-Nancy, France

autor

Ragot J.

• CRAN UMR 7039, CNRS, University of Lorraine, F-54000 Vandoeuvre-lès-Nancy, France

autor

Aubrun C.

• CRAN UMR 7039, CNRS, University of Lorraine, F-54000 Vandoeuvre-lès-Nancy, France

autor

Maquin D.

• CRAN UMR 7039, CNRS, University of Lorraine, F-54000 Vandoeuvre-lès-Nancy, France

Bibliografia

• [1] Bezzaoucha, S., Marx, B., Maquin, D. and Ragot, J. (2013a). State and parameter estimation for nonlinear systems: A Takagi–Sugeno approach, American Control Conference, ACC’2013, Washington, DC, USA, pp. 1050–1055.
• [2] Bezzaoucha, S., Marx, B., Maquin, D. and Ragot, J. (2013b). State and parameter estimation for time-varying systems: A Takagi–Sugeno approach, 5th Symposium on System Structure and Control/IFAC Joint Conference 2013 SSSC, Grenoble, France.
• [3] Blanco, Y. (2001). Stabilisation des Modeles Takagi-Sugeno et leur usage pour la commande des systemes non lineaires, PhD thesis, Université des Sciences et Technologies de Lille, Lille.
• [4] Boyd, S.P., El Ghaoui, L., Feron, E. and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM, NewYork, NY.
• [5] Caccavale, F., Pierri, F. and Villani, L. (2008). Adaptive observer for fault diagnosis in nonlinear discrete-time systems, Journal of Dynamic Systems, Measurement, and Control 130(2): 021005.
• [6] Cho, Y.M. and Rajamani, R. (1997). A systematic approach to adaptive observer synthesis for nonlinear systems, IEEE Transactions on Automatic Control 42(4): 534–537.
• [7] Ţiclea, A. and Besançon, G. (2016). Adaptive observer design for discrete time LTV systems, International Journal of Control 89(12): 2385–2395.
• [8] de Souza, C.E. and Xie, L. (1992). On the discrete-time bounded real lemma with application in the characterization of static state feedback H∞ controllers, Systems & Control Letters 18(1): 61–71.
• [9] Guyader, A. and Zhang, Q. (2003). Adaptive observer for discrete time linear time varying systems, 13th IFAC/IFORS Symposium on System Identification, SYSID’2003, Rotterdam, The Netherlands, pp. 1705–1710.
• [10] Ichalal, D., Mammar, S., Dabladji, M. E.-H. and Ragot, J. (2015). Observer design for a class of discrete-time quasi-LPV systems with unknown parameters: Algebraic approach, 2015 European Control Conference (ECC), Linz, Austria, pp. 915–920.
• [11] Ichalal, D., Marx, B., Maquin, D. and Ragot, J. (2016). A method to avoid the unmeasurable premise variables in observer design for discrete time TS systems, International Conference on Fuzzy Systems, FUZZ-IEEE’2016, Vancouver, Canada, pp. 2343–2348.
• [12] Ichalal, D., Marx, B., Ragot, J. and Maquin, D. (2009). State and unknown input estimation for nonlinear systems described by Takagi–Sugeno models with unmeasurable premise variables, 17th Mediterranean Conference on Control and Automation, MED’09, Thessaloniki, Greece, pp. 217–222.
• [13] Kwiatkowski, A., Boll, M.T. and Werner, H. (2006). Automated generation and assessment of affine LPV models, Proceedings of the 45th IEEE Conference on Decision and Control CDC’06, San Diego, CA, USA, pp. 6690–6695.
• [14] Lendek, Z., Guerra, T.M. and De Schutter, B. (2010). Stability analysis and nonlinear observer design using Takagi–Sugeno fuzzy models, Fuzzy Sets and Systems 161(15): 2043–2065.
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• [16] Nagy, A.M., Mourot, G., Marx, B., Ragot, J. and Schutz, G. (2010). Systematic multimodeling methodology applied to an activated sludge reactor model, Industrial & Engineering Chemistry Research 49(6): 2790–2799.
• [17] Ohtake, H., Tanaka, K. and Wang, H.O. (2003). Fuzzy modeling via sector nonlinearity concept, Integrated Computer-Aided Engineering 10(4): 333–341.
• [18] Srinivasarengan, K., Ragot, J., Maquin, D. and Aubrun, C. (2016a). Joint state and parameter estimation for discrete-time Takagi–Sugeno model, 13th European Workshop on Advanced Control and Diagnosis, ACD 2016, Lille, France, pp. 012016.
• [19] Srinivasarengan, K., Ragot, J., Maquin, D. and Aubrun, C. (2016b). Nonlinear joint state-parameter observer for VAV damper position estimation, 3rd Conference on Control and Fault-Tolerant Systems, SysTol 2016, Barcelona, Spain, pp. 164–169.
• [20] Tanaka, K. and Wang, H.O. (2004). Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, John Wiley & Sons, New York, NY.
• [21] Thumati, B.T. and Sarangapani, J. (2008). A model based fault detection scheme for nonlinear multivariable discrete-time systems, 2008 IEEE International Conference on Systems, Man and Cybernetics, Singapore, pp. 1978–1983.
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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).