Journal of Zhejiang University SCIENCE C

, Volume 12, Issue 1, pp 1–16 | Cite as

Direct adaptive regulation of unknownnonlinear systems with analysis of themodel order problem

  • Dimitrios Theodoridis
  • Yiannis Boutalis
  • Manolis Christodoulou


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).

Key words

Neuro-fuzzy systems Direct adaptive regulation Model order problems Parameter hopping 

CLC number



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Copyright information

© Journal of Zhejiang University Science Editorial Office and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dimitrios Theodoridis
    • 1
    • 2
  • Yiannis Boutalis
    • 1
    • 3
  • Manolis Christodoulou
    • 4
    • 5
  1. 1.Department of Electrical and Computer EngineeringDemocritus University of ThraceXanthiGreece
  2. 2.Department of Industrial InformaticsTechnological Education Institute of KavalaKavalaGreece
  3. 3.Chair of Automatic ControlUniversity of Erlangen-NurembergErlangenGermany
  4. 4.Department of Electronic and Computer EngineeringTechnical University of CreteChaniaGreece
  5. 5.Dipartimento di Automatica et InformaticaPolitecnico di TorinoTorinoItalia

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