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In the design of adaptive controllers the “Robust Fixed Point Transformations (RFPT)“-based approach is a recently developed, very simple alternative of “Lyapunov's 2nd Method”. The main difference between them is that while the traditional approach concentrates on guaranteeing global stability at the cost of directly not considering the primary design intent (i.e. the dynamic details of the tracking...
For replacing Lyapunov's ingenious but complicated “2nd method” in designing adaptive controllers for nonlinear systems the use of “Robust Fixed Point Transformations (RFPT)” was extensively studied in the past few years mainly for “Classical Mechanical Systems (CMS)”. In spite of the strongly nonlinear coupling that is typical in the Euler-Lagrange equations of motion CMS are simple in the sense...
In this paper a “Robust Fixed Point Transformation (RFPT)” based adaptive control of an underactuated physical system is stabilized by adaptively tuning only one parameter of a single fuzzy membership function. This approach serves as an alternative to Lyapunov's “direct” method that suffers from mathematical difficulties when a Lyapunov function candidate has to be found for the control of a dynamically...
As is well known various neuron models show interesting behavior as producing stable, non-sinusoidal limit cycles or even chaotic regimes of motion. Realization of precise tracking of a chaotic trajectory generated by a “master system” by a controlled, quite different “slave” system also having aptitude for chaotic motion is an interesting challenge. Lyapunov's 2nd or “Direct” Method is generally...
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