Nikolay N. Karabutov

Structural-parametrical Design Method of Adaptive Observers for Nonlinear Systems

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Author(s)

Nikolay N. Karabutov ^1,*

1. Moscow Technological University (MIREA), Moscow, Russia

* Corresponding author.

DOI: https://doi.org/10.5815/ijisa.2018.02.01

Received: 2 Jul. 2017 / Revised: 10 Aug. 2017 / Accepted: 11 Sep. 2017 / Published: 8 Feb. 2018

Index Terms

Adaptive observer, Structural identifiabil-ity, Nonlinear system, Lyapunov vector function, Frame-work, Saturation

Abstract

The structural-parametrical method for design of adaptive observers (AO) for nonlinear dynamic sys-tems under uncertainty is proposed. The design of AO is consisting of two stages. The structural stage allowed identifying a class of nonlinearity and its structural pa-rameters. The solution of this task is based on an estima-tion of the system structural identifiability (SI). The method and criteria of the system structural identi-fiability are proposed. Effect of an input on the SI is showed. We believe that the excitation constancy condition is satisfied for system variables. Requirements to the input at stages of structural and parametrical design of AO differ. The parametrical design stage AO uses the results obtained at the first stage of the adaptive observer construction. Two cases of the structural information application are considered. The main attention is focused on the case of the insufficient structural information. Adaptive algorithms for tuning of parameters AO are proposed. The uncertainty estimation procedure is proposed. Stability of the adaptive system is proved. Simulation results confirmed the performance of the proposed approach.

Cite This Paper

Nikolay Karabutov, "Structural-parametrical Design Method of Adap-tive Observers for Nonlinear Systems", International Journal of Intelligent Systems and Applications(IJISA), Vol.10, No.2, pp.1-16, 2018. DOI:10.5815/ijisa.2018.02.01

Reference

[1]R. L. Carrol , D. P. Lindorff, “An adaptive observer for single-input single-output linear systems,” IEEE Trans. Automat. Control, 1973, vol. AC-18, no. 5, pp. 428–435.

[2]R. L. Carrol, R. V. Monopoli, “Model reference adaptive control estimation and identification using only and output signals,” Processings of IFAC 6th Word congress. Boston, Cembridge, 1975, part 1, pp. 58.3/1-58.3/10.

[3]G.Kreisselmeier, “A robust indirect adaptive control approach,” Int. J. Control, 1986, vol. 43, no. 1, pp. 161–175.

[4]P. Kudva, K.S. Narendra, “Synthesis of a adaptive ob-server using Lyapunov direct method,” Jnt. J. Control, 1973, vol. 18, no.4, pp. 1201–1216.

[5]K.S. Narendra , B. Kudva, “Stable adaptive schemes for system: identification and control,” IEEE Trans. on Syst., Man and Cybern., 1974, vol. SMC-4, no. 6, pp. 542–560.

[6]G. Bastin, R. Gevers, “Stable adaptive observers for nonlinear time-varying systems,” IEEE Transactions on automatic control, 1988, vol. 33, no. 7, pp. 650-658.

[7]R. Marino, P. Tomei, “Global adaptive observers for nonlinear systems via filteres transformations,” IEEE Transactions on Automatic Control, 1992, vol. 37, no. 8, pp. 1239–1245.

[8]R. Marino, P. Tomei, Nonlinear control design: Geo-metric, Adaptive & Robust. London: Prentice Hall, 1995

[9]M. Krstić, P.V. Kokotović, “Adaptive Nonlinear Output-Feedback Schemes with Marino-Tomei Controller,” IEEE Transactions on automatic control, 1996, vol. 41, no. 2, pp. 274-280.

[10] N.E. Kahveci, P.A. Ioannou, “Indirect Adaptive Control for Systems with Input Rate Saturation,” 2008 American Control Conference, Westin Seattle Hotel, Seattle, Washington, USA June 11-13, 2008, pp. 3396-3401.

[11]А.М. Аnnaswamy, А.-Р. Loh, “Stale adaptive systems in the presence of nonlinear parameterization,” In Adaptive Control Systems, Ed. G. Feng and R. Lozano. Newnes, 1999, pp. 215-259.

[12]D. Baang, J. Stoev, J.Y. Choi, “Adaptive observer using auto-generating B-splines,” International Journal of Control, Automation, and Systems, 2007, vol. 5, no. 5, pp. 479-491.

[13]P. Garimella, B. Yao, “Nonlinear adaptive robust ob-server design for a class of nonlinear systems,” Pro-ceedings of the American Control Conference Denver, Colorado June 4-6, 2003, 2003, pp. 4391-4396.

[14]N. Oucief, M. Tadjine, S. Labiod, “Adaptive observer-based fault estimation for a class of Lipschitz nonlinear systems,” Archives of control sciences, 2016, vol. 26(LXII), no. 2, pp. 245–259.

[15]G. Besançon, “An Overview on Observer Tools for Nonlinear Systems,” In Lecture Notes in Control and Information Sciences 363, Ed. M. Thoma, M. Morari. Springer, 2007, pp. 10-42.

[16]N. Boizot, and E. Busvelle, “Adaptive-Gain Observers and Applications,” In Lecture Notes in Control and In-formation Sciences 363, Ed. G. Besançon. Springer, 2007, pp. 10-42.

[17]N. Boizot, E. Busvelle, J-P. Gauthier, “An adaptive high-gain observer for nonlinear systems,” Automatica, 2010, vol. 46, is. 9, pp. 1483–1488.

[18]N. Hovakimyan, A.J. Calise, and V.K. Madyastha, “An adaptive observer design methodology for bounded nonlinea r processes,” In Proc. 41st IEEE Conference on Decision and Control, Las Vegas, NV , Dec. 2002, pp. 4700-4705.

[19]K.S. Narendra, and K. Parthasarathy, “Identification and control of dynamical systems using neural networks,” IEEE Transactions on Neural Networks, 1990, vol. 1, pp. 4 27.

[20]J. Zhu, K. Khayati, “LMI-based adaptive observers for nonlinear systems,” International journal of mechanical engineering and mechatronics, vol. 1, is. 2, 2012, pp. 50-60.

[21]N. Karabutov, “Structural identification of dynamic systems with hysteresis,” International Journal of Intelligent Systems and Applications, 2016, vol. 8, no. 7, pp. 1-13.

[22]N. Karabutov, Frameworks in problems of structural identification systems,” International Journal of Intelligent Systems and Applications, 2017, vol. 9, no. 1, pp. 1-19.

[23]N.N. Karabutov, Structural identification of static objects: Fields, structures, methods. Moscow: Librokom, 2011.

[24]N. Karabutov, “Structural identification of nonlinear dynamic systems,” International journal intelligent systems and applications, 2015, vol. 7, no.9, pp. 1-11.

[25]N.N. Karabutov, Adaptive identification of systems: Informational synthesis. Moscow: URSS, 2006.

[26]N. Karabutov, "Structures, fields and methods of identification of nonlinear static systems in the conditions of uncertainty," Intelligent Control and Automation, 2010, vol.1 no.2, pp. 59-67.

[27]G. Choquet, L'enseignement de la geometrie. Paris: Hermann, 1964.

[28]N. Karabutov, “Structural identification of nonlinear static system on basis of analysis sector sets,” International journal intelligent systems and applications, 2013, vol. 6, no. 1, pp. 1-10.

[29]N. Karabutov, “Adaptive observers for linear time-varying dynamic objects with uncertainty estimation,” International journal intelligent systems and applica-tions, 2017, vol. 9, no. 6, pp. 1-14.

[30]N. Karabutov, "Adaptive observers with uncertainty in loop tuning for linear time-varying dynamical systems," International journal intelligent systems and applica-tions, 2017, vol. 9, no. 4, pp. 1-13.

[31]E.A. Barbashin, Lyapunov function. Moscow: Nauka, 1970.

[32]F.R. Gantmacher, The Theory of Matrices. AMS Chel-sea Publishing: Reprinted by American Mathematical Society, 2000.

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