Neurocomputing
Introduction to artificial neural systems
Introduction to artificial neural systems
On the early history of the singular value decomposition
On the early history of the singular value decomposition
Stable redesign of predictive control
Automatica (Journal of IFAC)
Robust nonlinear control design: state-space and Lyapunov techniques
Robust nonlinear control design: state-space and Lyapunov techniques
Optimal adaptive fuzzy control for a class of unknown nonlinear systems
WSEAS Transactions on Systems and Control
Decentralized adaptive fuzzy control for a class of nonlinear systems
WSEAS Transactions on Systems and Control
Adaptive fuzzy tracking control of nonlinear systems
WSEAS Transactions on Systems and Control
INES'10 Proceedings of the 14th international conference on Intelligent engineering systems
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A comparative study concerning the robustness of a novel, Fixed Point Transformations/Singular Value Decomposition (FPT/SVD)-based adaptive controller and the Slotine-Li (S&L) approach is given by numerical simulations using a three degree of freedom paradigm of typical Classical Mechanical systems, the cart + double pendulum. The effects of the imprecision of the available dynamical model, presence of dynamic friction at the axles of the drives, and the existence of external disturbance forces unknown and not modeled by the controller are considered. While the Slotine-Li approach tries to identify the parameters of the formally precise, available analytical model of the controlled system with the implicit assumption that the generalized forces are precisely known, the novel one makes do with a very rough, affine form and a formally more precise approximate model of that system, and uses temporal observations of its desired vs. realized responses. Furthermore, it does not assume the lack of unknown perturbations caused either by internal friction and/or external disturbances. Its another advantage is that it needs the execution of the SVD as a relatively time-consuming operation on a grid of a rough system-model only one time, before the commencement of the control cycle within which it works only with simple computations. The simulation examples exemplify the superiority of the FPT/SVD-based control that otherwise has the deficiency that it can get out of the region of its convergence. Therefore its design and use needs preliminary simulation investigations. However, the simulations also exemplify that its convergence can be guaranteed for various practical purposes.