Publication Cover
Mathematical and Computer Modelling of Dynamical Systems
Methods, Tools and Applications in Engineering and Related Sciences
Volume 20, 2014 - Issue 3
335
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Stability analysis of data-driven local model networks

, , &
Pages 224-247 | Received 06 Jan 2013, Accepted 28 Jun 2013, Published online: 26 Jul 2013

References

  • R. Gao, Local model network application in control, Thesis, Dublin Institute of Technology, 2004.
  • G. Gregorcic and G. Lightbody, Local model network identification with Gaussian processes, IEEE Trans. Neural Netw. 18 (2007), pp. 1404–1423.
  • J. Novak and V. Bobal, Predictive Control of the Heat Exchanger Using Local Model Network, Proceedings of the 17th Mediterranean Conference on Control & Automation, IEEE, 2009, pp. 657–662.
  • S. Jakubek and C. Hametner, Identification of neurofuzzy models using GTLS parameter estimation, IEEE Trans. Syst. Man Cybern. B Cybern. 39 (2009), pp. 1121–1133.
  • R. Murray-Smith and T.A. Johansen, Multiple Model Approaches to Modelling and Control, Taylor & Francis, London, 1997.
  • C. Hametner, C. Mayr, and S. Jakubek, Dynamic NOx emission modelling using local model networks [in revision], Int. J. Engine Res.
  • K. Tanaka and M. Sugeno, Stability analysis and design of fuzzy control systems, Fuzzy Sets Syst. 45 (1992), pp. 135–156.
  • A. Lyapunov, The general problem of the stability of motion, Int. J. Control. 55 (1992), pp. 531–773.
  • G. Feng, A survey on analysis and design of model-based fuzzy control systems, IEEE Trans. Fuzzy Syst. 14 (2006), pp. 676–697.
  • G. Feng, Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions, IEEE Trans. Fuzzy Syst. 12 (2004), pp. 22–28.
  • G. Feng, Analysis and Synthesis of Fuzzy Control Systems, A Model Based Approach, CRC press, Taylor & Francis, Boca Raton, FL, 2010.
  • M. Johansson and A. Rantzer, Computation of piecewise quadratic Lyapunov functions for hybrid systems, IEEE Trans. Automat. Contr. 43 (1998), pp. 555–559.
  • M. Johansson and A. Rantzer, Piecewise quadratic stability of fuzzy systems, IEEE Trans. Fuzzy Syst. 7 (2000), pp. 713–722.
  • Y. Wang, Z. Sun, and F. Sun, Stability Analysis and Control of Discrete-time Fuzzy Systems: A Fuzzy Lyapunov Function Approach, Proceedings of the 5th Asian Control Conference, IEEE, 2004.
  • C. Sun, Y. Su, and C. Chuang, Relaxed Stabilization Criterion for TS Fuzzy Discrete System, Kainan University, Taiwan, 2009.
  • E. Kim and H. Lee, New approaches to relaxed quadratic stability condition of fuzzy control systems, IEEE Trans. Fuzzy Syst. 8 (2000), pp. 523–534.
  • E. Kim, D. Kim, and S. Analysis, Synthesis for an affine fuzzy system via LMI and ILMI: discrete case, IEEE Trans. Syst. Man Cybern. B Cybern. 31 (2001), pp. 132–140.
  • T.M. Guerra, A. Kruszewski, and M. Bernal, Control law proposition for the stabilization of discrete Takagi–Sugeno models, IEEE Trans. Fuzzy Syst. 17 (2009), pp. 724–731.
  • T. Guerra and L. Vermeiren, LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno’s form, Automatica 40 (5) (2004), pp. 823–829.
  • B. Ding, H. Sun, and P. Yang, Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takgi-Sugeno’s form, Automatica 402 (3) (2006), pp. 503–508.
  • A. Kruszewski, R. Wang, and T.M. Guerra, Nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time TS fuzzy models: a new approach, IEEE Trans. Automat. Contr. 53 (2008), pp. 606–611.
  • S. Zhou, J. Lam, and A. Xue, H-∞ filtering of discrete-time fuzzy systems via basis-dependent Lyapunov function approach, Fuzzy Sets Syst. 158 (2007), pp. 180–193.
  • G. Gregorcic and G. Lightbody, Nonlinear system identification: from multiple-model networks to Gaussian processes, Eng. Appl. Artif. Intell. 21 (2008), pp. 1035–1055.
  • H.-K. Lam and F.H.-F. Leung, Stability Analysis of Fuzzy-Model-Based Control Systems, Springer-Verlag, New York, 2011.
  • C. Mayr, C. Hametner, M. Kozek, and S. Jakubek, Relaxed Fuzzy Lyapunov Approach for Dynamic Local Model Networks, Proceedings of the 2011 IEEE International Conference on Fuzzy Systems, Christian Doppler Laboratory for Model Based Calibration Methodologies, Vienna University of Technology, 2011.
  • G.C. Goodwin and R.L. Payne, Dynamic system identification: experiment design and data analysis, Math. Sci. Eng. 136 (1977), p. 291.
  • C. Hametner and S. Jakubek, New Concepts for the Identification of Dynamic Takagi-Sugeno Fuzzy Models, IEEE Conference on Cybernetics and Intelligent Systems, IEEE, 2006, pp. 185–190.
  • O. Nelles and R. Isermann, Basis Function Networks for Interpolation of Local Linear Models, Proceedings of the 35th Conference on Decision and Control 1, IEEE, 1996, pp. 470–475.
  • O. Nelles, Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models, Springer Verlag, Berlin, Heidelberg, 2001.
  • C. Hametner and S. Jakubek, Neuro-Fuzzy Modelling Using a Logistic Discriminant Tree, Proceedings of the 2007 American Control Conference, IEEE, 2007, pp. 864–869.
  • L. Breiman, Hinging hyperplanes for regression, classification, and function approximation, IEEE Trans. Inform. Theory 39 (1993), pp. 999–1013.
  • S. Jakubek, N. Keuth, and A. Local Neuro-Fuzzy, Network for high-dimensional models and optimization, Eng. Appl. Artif. Intell. 19 (2006), pp. 705–717.
  • O. Nelles, Local Linear Model Trees for On-Line Identification of Time-Variant Nonlinear Dynamic Systems, International Conference on Artificial Neural Networks, Springer, Berlin, Heidelberg, 1996.
  • L. Thanh Ngo, L. Pham The, P. Hoang Nguyen, and K. Hirota, On Approximate Representation of Type-2 Fuzzy Sets Using Triangulated Irregular Network, Volume 4529, Foundations of Fuzzy Logic and Soft Computing, Springer, Berlin, Heidelberg, 2007.
  • B. Hartmann, O. Banfer, O. Nelles, A. Sodja, L. Teslic, and I. Skrjanc, Supervised hierarchical clustering in fuzzy model identification, IEEE Trans. Fuzzy Syst. 19 (2011), pp. 1163–1176.
  • J. Causa, G. Karer, A. Núñez, D. Sáez, I. Skrjanc, and B. Zupancic, Hybrid fuzzy predictive control based on genetic algorithms for the temperature control of a batch reactor, Comput. Chem. Eng. 32 (2008), pp. 3254–3263.
  • P. Van Overschee, B. De Moor, and D. N4SI, Subspace algorithms for the identification of combined deterministic-stochastic systems, Automatica 30 (1994), pp. 75–93.
  • C. Mayr, C. Hametner, M. Kozek, and S. Jakubek, Piecewise Quadratic Stability Analysis for Local Model Networks, Proceedings of the 2011 IEEE Multi-conference on System and Control, Christian Doppler Laboratory for Model Based Calibration Methodologies, Vienna University of Technology, 2011.
  • Y. Nesterov and A. Nemirovskii, Interior-Point Polynomial Algorithms in Convex Programming, Theory and Application, Society for Industrial Mathematics, Philadelphia, siam ed., 1994.
  • J. Sturm, Using SeDuMi 1. 02, a MATLAB toolbox for optimization over symmetric cones, Optim. Methods Softw. 11–12 (1999), pp. 625–653.
  • K. Toh and M. Todd, SDPT 3- A MATLAB software package for semidefinite programming, Optim. Methods Softw. 11 (1999), pp. 545–581.
  • M. Bernal and P. Husek, Non-quadratic performance design for Takagi-Sugeno fuzzy systems, Int. J. Appl. Math. Comput. Sci. 15 (2005), pp. 383–391.
  • S. Cao, N. Rees, and G. Feng, Quadratic stability analysis and design of continuous-time fuzzy control systems, Int. J. Syst. Sci. 27 (1996), pp. 193–203.
  • S. Cao, Analysis and design for a class of complex control systems part II: fuzzy controller design, Automatica 33 (1997), pp. 1029–1039.
  • K. Tanaka, T. Hori, H. Wang, and A. Multiple Lyapunov, Function approach to stabilization of fuzzy control systems, IEEE Trans. Fuzzy Syst. 11 (2003), pp. 582–589.
  • S. Zhou, G. Feng, J. Lam, and S. Xu, Robust H-∞ control for discrete-time fuzzy systems via basis-dependent Lyapunov functions, Inform. Sci. 174 (2005), pp. 197–217.
  • S. Zhou, J. Lam, and W.X. Zheng, Control design for fuzzy systems based on relaxed nonquadratic stability and H Performance Conditions, IEEE Trans. Fuzzy Syst. 15 (2007), pp. 188–199.
  • H.-N. Wu, Delay-dependent stability analysis and stabilization for discrete-time fuzzy systems with state delay: a fuzzy Lyapunov-Krasovskii functional approach, IEEE Trans. Syst. Man Cybern. B Cybern. 36 (2006), pp. 954–962.
  • I. Leontaritis and S. Billings, Input-output parametric models for nonlinear systems part I: deterministic non-linear systems, Int. J. Control. 41 (1985), pp. 303–328.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.