International Journal of Intelligent Systems and Applications (IJISA)
IJISA Vol. 9, No. 6, 8 Jun. 2017
Cover page and Table of Contents: PDF (size: 900KB)
Adaptive Observers for Linear Time-Varying Dynamic Objects with Uncertainty Estimation
Full Text (PDF, 900KB), PP.1-14
Views: 0 Downloads: 0
Author(s)
Index Terms
Adaptive observer, identification, uncer-tainty, time-varying system, exponential dissipativity, Lyapunov vector function
Abstract
The method for construction adaptive observ-ers (AO) time-varying linear dynamic objects at non-fulfillment of condition excitation constancy (EC) is pro-posed. Synthesis of the adaptive observer is given as the solution of two tasks. The solution first a problem is a choice of the constant matrix decreasing the effect of EC condition. Procedures for obtaining of this matrix are proposed. The matrix specifies restrictions for a vector of parameters AO. The solution of the second problem gives a method of design adaptive multiplicative algorithms in the presence of the obtained restrictions. Procedures for an estimation uncertainty in an object are proposed. They are based on obtaining of static models giving the forecast change of uncertainty. Optimum estimations of the uncertainty are obtained which minimize an error between outputs of the object and AO. An exponential dissipativity of adaptive system is proved. The results of the modeling confirming the effectiveness of designed methods and procedures are presented.
Cite This Paper
Nikolay Karabutov, "Adaptive Observers for Linear Time-Varying Dynamic Objects with Uncertainty Estimation", International Journal of Intelligent Systems and Applications(IJISA), Vol.9, No.6, pp.1-14, 2017. DOI:10.5815/ijisa.2017.06.01
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," In Processings of IFAC 6th Word congress. Bos-ton, Cembridge, 1975, part 1, pp. 58.3/1-58.3/10.
[3]G. Kreisselmeier, "A robust indirect adaptive control ap-proach," 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, P. 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]S. Nuyan, R. L. Carrol, "Minimal order arbitrarily fast adaptive observer and identifies," IEEE Trans. Automat. Control, 1979, vol. AC-24, no. 2, pp. 496–499.
[7]M. J. Feiler, K. S. Narendra, "Simultaneous identification and control of time–varying systems," In Proceedings of the 45th IEEE Conference on Decision and Control, San Diego CA, U.S.A., 2006, pp. 1-7.
[8]N. Jing, Y. Juan, R. Xuemei and Gu. Yu, "Robust adaptive estimation of nonlinear system with time-varying pa-rameters," International journal of adaptive control and signal processing, 2014, vol. 29, no. 8, pp. 1055–1072.
[9]G. Bastin, and M. R. Gevers, "Stable adaptive observers for nonlinear time-varying systems. IEEE Trans. Automat. Control, vol. AC-33, no. 7, 1988, pp. 650-658.
[10]Y. Zhang, B. Fidan, and P.A. Ioannou, "Backstepping control of linear time-varying systems with known and unknown parameters," IEEE Trans. Automat. Contr., 2003, vol. AC-38, no. 11, pp. 1908–1925.
[11]Q. Zhang, and A. Clavel, "Adaptive observer with expo-nential forgetting factor for linear time varying systems," In Proceedings of the 40th IEEE Conference on Decision and Control (CDC ’01), 2001, vol. 4, pp. 3886–3891.
[12]V.Ja. Katkovnik, V.Е. Heysin, "Adaptive control static essentially time-varying object," Automation and Remote Control, 1988, vol. 49, no. 4, pp. 465–474.
[13]I. I. Perel'man, "Methods for sound estimation of linear dynamic plant parameters and feasibility of their imple-mentation on finite samples," Automation and Remote Control, 1981, vol.42, no. 3, pp. 309–313.
[14]D. Bestle, M. Zeitz, "Canonical form observer design for nonlinear time-variable systems," Int. J. Control, 1983. vol. 38, no. 2, pp. 419–431.
[15]N.N. Karabutov, Adaptive identification of systems: in-formation synthesis. Moscow: URSS, 2007.
[16]N.N. Karabutov, "Methods of -algorithms control," In Mathematical models of non-linear phenomena, processes, and systems: from molecular scale to planetary atmos-phere, Ed. Alexey B. Nadykto, Ludmila Uvarova, Anatolii V. Latyshev. Nova Science Publishers Inc, 2013, pp. 359-396.
[17]N.N. Karabutov, "Construction of adaptive observers of time-varying objects with specified quality of adaptation," In Microprocessor systems of automation: Theses of re-ports of II All-Union scientific and technical conference. Novosibirsk, 1990, pp. 10-11.
[18]N.N. Karabutov, "Influence of measurement information on the properties of adaptive systems," Measurement Techniques, 2010, vol. 53, no. 9, pp. 956-963.
[19]F.R. Gantmacher, The Theory of Matrices. AMS Chelsea Publishing: Reprinted by American Mathematical Society, 2000.
[20]P. V. Pakshin, "Exponential dissipativeness of the random-structure diffusion processes and problems of robust stabi-lization," Automation and Remote Control, 2007, vol. 68, is. 10, pp. 1852–1870.
[21]E.A. Barbashin, Lyapunov function. Moscow: Nauka, 1970.