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On-line Access: 2010-01-10

Received: 2010-06-27

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Journal of Zhejiang University SCIENCE C 2011 Vol.12 No.1 P.1-16

10.1631/jzus.C1000224


Direct adaptive regulation of unknown nonlinear systems with analysis of the model order problem


Author(s):  Dimitrios Theodoridis, Yiannis Boutalis, Manolis Christodoulou

Affiliation(s):  Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi 67100, Greece, Department of Industrial Informatics, Technological Education Institute of Kavala, Kavala 65404, Greece, Chair of Automatic Control, University of Erlangen-Nuremberg, Erlangen 91058, Germany, Department of Electronic and Computer Engineering, Technical University of Crete, Chania 73100, Greece, Dipartimento di Automatica et Informatica, Politecnico di Torino, Torino 10129, Italia

Corresponding email(s):   ybout@ee.duth.gr, dtheodo@ee.duth.gr

Key Words:  Neuro-fuzzy systems, Direct adaptive regulation, Model order problems, Parameter hopping


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Dimitrios Theodoridis, Yiannis Boutalis, Manolis Christodoulou. Direct adaptive regulation of unknown nonlinear systems with analysis of the model order problem[J]. Journal of Zhejiang University Science C, 2011, 12(1): 1-16.

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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).

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Reference

[1]Boutalis, Y.S., Theodoridis, D.C., Christodoulou, M.A., 2009. A new neuro FDS definition for indirect adaptive control of unknown nonlinear systems using a method of parameter hopping. IEEE Trans. Neur. Networks, 20(4):609-625.

[2]Chemachema, M., Belarbi, K., 2007. Robust direct adaptive controller for a class of nonlinear systems based on neural networks and fuzzy logic system. Int. J. Artif. Intell. Tools, 16(3):553-560.

[3]Christodoulou, M.A., Theodoridis, D.C., Boutalis, Y.S., 2007. Building Optimal Fuzzy Dynamical Systems Description Based on Recurrent Neural Network Approximation. Conf. of Networked Distributed Systems for Intelligent Sensing and Control, p.82-93.

[4]Diao, Y., Passino, K.M., 2002. Adaptive neural/fuzzy control for interpolated nonlinear systems. IEEE Trans. Fuzzy Syst., 10(5):583-595.

[5]Ge, S.S., Jing, W., 2002. Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems. IEEE Trans. Neur. Networks, 13(6):1409-1419.

[6]Haddad, W., Hayakawaa, T., Chellaboina, V., 2003. Robust adaptive control for nonlinear uncertain systems. Automatica, 39(3):551-556.

[7]Hornik, K., Stinchcombe, M., White, H., 1989. Multilayer feedforward networks are universal approximators. Neur. Networks, 2(5):359-366.

[8]Ioannou, P., Fidan, B., 2006. Adaptive Control Tutorial. SIAM.

[9]Kim, Y.T., Bien, Z.Z., 2004. Robust adaptive fuzzy control in the presence of external disturbance and approximation error. Fuzzy Sets Syst., 148(3):377-393.

[10]Li, C.H., Zhu, X.J., Cao, G.Y., Hu, W.Q., Sui, S., Hu, M.R., 2009. A maximum power point tracker for photovoltaic energy systems based on fuzzy neural networks. J. Zhejiang Univ.-Sci. A, 10(2):263-270.

[11]Lin, C.T., 1995. A neural fuzzy control system with structure and parameter learning. Fuzzy Sets Syst., 70(2-3):183-212.

[12]Mamdani, E., 1976. Advances in the linguistic synthesis of fuzzy controllers. Int. J. Man-Mach. Stud., 8(6):669-678.

[13]Michel, A.N., Miller, R.K., 1977. Qualitative Analysis of Large Scale Dynamic Systems. Academic Press, New York.

[14]Nounou, H.N., Passino, K.M., 2004. Stable auto-tuning of adaptive fuzzy/neural controllers for nonlinear discrete-time systems. IEEE Trans. Fuzzy Syst., 12(1):70-83.

[15]Ordonez, R., Passino, K.M., 2001. Adaptive control for a class of nonlinear systems with time-varying structure. IEEE Trans. Autom. Control, 46(1):152-155.

[16]Passino, K.M., Yurkovich, S., 1998. Fuzzy Control. Addison-Wesley, Menlo Park, CA.

[17]Rovithakis, G.A., Christodoulou, M.A., 2000. Adaptive Control with Recurrent High Order Neural Networks (Theory and Industrial Applications). In: Grimble, M. (Ed.), Advances in Industrial Control. Springer Verlag London Limited.

[18]Theodoridis, D.C., Boutalis, Y.S., Christodoulou, M.A., 2009a. Direct adaptive control of unknown nonlinear systems using a new neuro-fuzzy method together with a novel approach of parameter hopping. Kybernetica, 45(3):349-386.

[19]Theodoridis, D.C., Boutalis, Y.S., Christodoulou, M.A., 2009b. A New Neuro-Fuzzy Dynamical System Definition Based on High Order Neural Network Function Approximators. European Control Conf., p.3305-3310.

[20]Tong, S., Chai, T., 1999. Direct adaptive control and robust analysis for unknown multivariable nonlinear systems with fuzzy logic systems. Fuzzy Sets Syst., 106(3):309-319.

[21]Wang, L., 1994. Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Prentice Hall, NJ.

[22]Yang, Y., 2004. Direct robust adaptive fuzzy control (DRAFC) for uncertain nonlinear systems using small gain theorem. Fuzzy Sets Syst., 151(1):79-97.

[23]Yeap, T.H., Ahmed, N.U., 1994. Feedback control of chaotic systems. Dyn. Control, 4(1):97-114.

[24]Zhang, J.H., Zhang, S.L., Liu, M.Q., 2007. Robust exponential stability analysis of a larger class of discrete-time recurrent neural networks. J. Zhejiang Univ.-Sci. A, 8(12):1912-1920.

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