Abstract
A new method for the direct adaptive regulation of unknown nonlinear dynamical systems is proposed in this paper, paying special attention to the analysis of the model order problem. The method uses a neurofuzzy (NF) modeling of the unknown system, which combines fuzzy systems (FSs) with high order neural networks (HONNs). We propose the approximation of the unknown system by a special form of an NF-dynamical system (NFDS), which, however, may assume a smaller number of states than the original unknown model. The omission of states, referred to as a model order problem, is modeled by introducing a disturbance term in the approximating equations. The development is combined with a sensitivity analysis of the closed loop and provides a comprehensive and rigorous analysis of the stability properties. An adaptive modification method, termed ‘parameter hopping’, is incorporated into the weight estimation algorithm so that the existence and boundedness of the control signal are always assured. The applicability and potency of the method are tested by simulations on well known benchmarks such as ‘DC motor’ and ‘Lorenz system’, where it is shown that it performs quite well under a reduced model order assumption. Moreover, the proposed NF approach is shown to outperform simple recurrent high order neural networks (RHONNs).
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Introducing editorial board member: Yiannis Boutalis, the corresponding author, is an editorial board member of Journal of Zhejiang University-SCIENCE C (Computers & Electronics). He received the diploma of Electrical Engineer in 1983 from Democritus University of Thrace (DUTH), Greece and the PhD degree in Electrical and Computer Engineering (topic image processing) in 1988 from the Computer Science Division of National Technical University of Athens, Greece. Since 1996, he serves as a faculty member, at the Department of Electrical and Computer Engineering, DUTH, Greece, where he is currently an associate professor and director of the Automatic Control Systems Lab. Currently, he is also a visiting professor for research cooperation at Friedrich-Alexander University of Erlangen-Nuremberg, Germany, chair of automatic control. His current research interests are focused in the development of computational intelligence techniques with applications in control, pattern recognition, signal and image processing problems.
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Theodoridis, D., Boutalis, Y. & Christodoulou, M. Direct adaptive regulation of unknownnonlinear systems with analysis of themodel order problem. J. Zhejiang Univ. - Sci. C 12, 1–16 (2011). https://doi.org/10.1631/jzus.C1000224
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DOI: https://doi.org/10.1631/jzus.C1000224