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Front. Inform. Technol. Electron. Eng.  2011, Vol. 12 Issue (1): 1-16    DOI: 10.1631/jzus.C1000224
    
Direct adaptive regulation of unknown nonlinear systems with analysis of the model order problem
Dimitrios Theodoridis1,2, Yiannis Boutalis*,1,3, Manolis Christodoulou4,5
1 Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi 67100, Greece 2 Department of Industrial Informatics, Technological Education Institute of Kavala, Kavala 65404, Greece 3 Chair of Automatic Control, University of Erlangen-Nuremberg, Erlangen 91058, Germany 4 Department of Electronic and Computer Engineering, Technical University of Crete, Chania 73100, Greece 5 Dipartimento di Automatica et Informatica, Politecnico di Torino, Torino 10129, Italia
Direct adaptive regulation of unknown nonlinear systems with analysis of the model order problem
Dimitrios Theodoridis1,2, Yiannis Boutalis*,1,3, Manolis Christodoulou4,5
1 Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi 67100, Greece 2 Department of Industrial Informatics, Technological Education Institute of Kavala, Kavala 65404, Greece 3 Chair of Automatic Control, University of Erlangen-Nuremberg, Erlangen 91058, Germany 4 Department of Electronic and Computer Engineering, Technical University of Crete, Chania 73100, Greece 5 Dipartimento di Automatica et Informatica, Politecnico di Torino, Torino 10129, Italia
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摘要： 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 neuro-fuzzy (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).
关键词： Neuro-fuzzy systems;  Direct adaptive regulation;  Model order problems;  Parameter hopping    
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 neuro-fuzzy (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).
Key words: Neuro-fuzzy systems    Direct adaptive regulation    Model order problems    Parameter hopping
收稿日期: 2010-06-27 出版日期: 2010-01-10
CLC:  TP183  
通讯作者: Yiannis Boutalis     E-mail: dtheodo@ee.duth.gr
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Dimitrios Theodoridis, Yiannis Boutalis, Manolis Christodoulou. Direct adaptive regulation of unknown nonlinear systems with analysis of the model order problem. Front. Inform. Technol. Electron. Eng., 2011, 12(1): 1-16.

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