Title: U-model-based adaptive control for a class of stochastic non-linear dynamic plants with unknown parameters

Authors: Xueli Wu, Lei Liu, Quanmin Zhu, Wenxia Du, Bin Wang, Jianhua Zhang

Addresses: Department of Electrical Engineering Science and Technology, Hebei University of Science and Technology, Shijiazhuang, Hebei, 050018, China; Department of Electrical Science and Technology, YanShan University, Qinhuangdao, Hebei, 066004, China. ' Department of Electrical Engineering Science and Technology, Hebei University of Science and Technology, Shijiazhuang, Hebei, 050018, China. ' Bristol Institute of Technology, University of the West of England, Coldharbour Lane, Bristol BS16 1QY, UK. ' Department of Electrical Science and Technology, YanShan University, Qinhuangdao, Hebei, 066004, China. ' Department of Electrical Science and Technology, YanShan University, Qinhuangdao, Hebei, 066004, China. ' Department of Electrical Science and Technology, YanShan University, Qinhuangdao, Hebei, 066004, China

Abstract: In this paper, an adaptive control algorithm within a U-model framework is developed for controlling a class of stochastic non-linear discrete-time models with unknown parameters. With the authors| previous justification, the control-oriented model not only represents a wide range of smooth (polynomial) non-linear dynamic plants (without using linearisation approximation at all), but also makes almost all linear control system design techniques directly applicable to non-linear dynamic plants (with a root solver bridging the linear design and calculation of controller output). A new recursive least squares algorithm is derived and its convergence is proved for the online estimation of time-varying parameters. For initial bench test, a pole placement controller for non-linear stochastic polynomial models is designed using the corresponding linear design technique. Accordingly a step by step procedure is listed to implement the adaptive control operation. A number of simulated case studies are conducted to illustrate the efficiency of the claimed insight and design procedure.

Keywords: U-model; online estimation; nonlinear systems; stochastic dynamic systems; pole placement controller; time varying parameters; adaptive control; unknown parameters; discrete-time models; recursive least squares.

DOI: 10.1504/IJMIC.2011.041300

International Journal of Modelling, Identification and Control, 2011 Vol.13 No.3, pp.135 - 143

Published online: 21 Mar 2015 *

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