Replacement of lyapunov function by locally convergent robust fixed point transformations in Model-Based control a brief summary

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9 Citations (Scopus)

Abstract

Lyapunov's 2 nd Method is a popular approach in the model-based control of nonlinear systems since normally it can guarantee global asymptotic stability. However, the cost of the application of Lyapunov function frequently can be inefficient and complicated parameter tuning process containing unnecessary number of almost arbitrary control parameters, and vulnerability of the tuning process against not modeled, unknown external disturbances. Improved versions of the original, model-based tuning are especially sensitive to the external perturbations. All these disadvantages can simply be avoided by the application of robust fixed point transformations at the cost of giving up the guarantee of global asymptotic stability. Instead of that simple, stable iterative control of local basin of attraction can be constructed on the basis of an approximate system model that can well compensate the effects of unknown external disturbances, too. Since the basin of convergence of the method in principle can be left, setting the three adaptive parameters of this controller needs preliminary simulation investigations. These statements are illustrated and substantiated via simulation results obtained for the adaptive control of various physical systems.

Original languageEnglish
Pages (from-to)224-236
Number of pages13
JournalJournal of Advanced Computational Intelligence and Intelligent Informatics
Volume14
Issue number2
Publication statusPublished - Mar 2010

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Lyapunov functions
Tuning
Asymptotic stability
Nonlinear systems
Controllers
Costs

Keywords

  • Adaptive inverse dynamics controller
  • Iterative control
  • Lyapunov function
  • Robust fixed point transformations
  • Slotine-Li adaptive controller

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Vision and Pattern Recognition
  • Human-Computer Interaction

Cite this

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title = "Replacement of lyapunov function by locally convergent robust fixed point transformations in Model-Based control a brief summary",
abstract = "Lyapunov's 2 nd Method is a popular approach in the model-based control of nonlinear systems since normally it can guarantee global asymptotic stability. However, the cost of the application of Lyapunov function frequently can be inefficient and complicated parameter tuning process containing unnecessary number of almost arbitrary control parameters, and vulnerability of the tuning process against not modeled, unknown external disturbances. Improved versions of the original, model-based tuning are especially sensitive to the external perturbations. All these disadvantages can simply be avoided by the application of robust fixed point transformations at the cost of giving up the guarantee of global asymptotic stability. Instead of that simple, stable iterative control of local basin of attraction can be constructed on the basis of an approximate system model that can well compensate the effects of unknown external disturbances, too. Since the basin of convergence of the method in principle can be left, setting the three adaptive parameters of this controller needs preliminary simulation investigations. These statements are illustrated and substantiated via simulation results obtained for the adaptive control of various physical systems.",
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