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2010•Unpublished venueRequires access

Replacement of Lyapunov's direct method in Model Reference Adaptive Control with Robust Fixed Point Transformations

József K. Tar, J.F. Bitó, Imre J. Rudas

Open publisher page 61 citations

Abstract

The “Model Reference Adaptive Control (MRAC)” is a popular and efficient controller that normally is designed by the use of Lyapunov's 2nd(“direct”) method guaranteeing global asymptotic stability. However, the use of Lyapunov function can entail a relatively complicated tuning that may have disadvantages whenever very fast applications are needed. In this paper an alternative background, the application of “Robust Fixed Point Transformations (RFPT)” working with local basin of attraction of convergence is recommended to simplify this task. As a potential application example the adaptive control of an “Electrostatic Micro-actuator (EμA)” is considered that contains considerable non-linearities. The conclusions of the paper are substantiated by simulation results.

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What this paper is about

The “Model Reference Adaptive Control (MRAC)” is a popular and efficient controller that normally is designed by the use of Lyapunov's 2nd(“direct”) method guaranteeing global asymptotic stability. However, the use of Lyapunov function can entail a relatively complicated tuning that may have disadvantages whenever very fast applications are needed. In this paper an alternative background, the application of “Robust Fixed Point Transformations (RFPT)” working with local basin of attraction of convergence is recommended to simplify this task. As a potential application example the adaptive control of an “Electrostatic Micro-actuator (EμA)” is considered that contains considerable non-linearities. The conclusions of the paper are substantiated by simulation results.

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OpenAlex reports 61 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The “Model Reference Adaptive Control (MRAC)” is a popular and efficient controller that normally is designed by the use of Lyapunov's 2nd(“direct”) method guaranteeing global asymptotic stability. However, the use of Lyapunov function can entail a relatively complicated tuning that may have disadvantages whenever very fast applications are needed. In this paper an alternative background, the application of “Robust Fixed Point Transformations (RFPT)” working with local basin of attraction of convergence is recommended to simplify this task. As a potential application example the adaptive control of an “Electrostatic Micro-actuator (EμA)” is considered that contains considerable non-linearities. The conclusions of the paper are substantiated by simulation results.

Key concepts: Lyapunov function, Adaptive control, Control theory (sociology), Convergence (economics), Controller (irrigation), Lyapunov redesign, Computer science, Fixed point

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