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A radial basis function network approach for the computation of inverse continuous time variant functions
René V Mayorga1, Jonathan Carrera
1Faculty of Engineering, University of Regina, Regina, Saskatchewan, Canada. Rene.mayorga@uregina.ca
International Journal of Neural Systems
|July 21, 2007
Summary
This study introduces a fast method for computing inverse continuous time variant functions using Radial Basis Function Networks (RBFNs). The approach prevents singularities by incorporating a novel null space vector into a damped least squares solution.
Area of Science:
- Robotics
- Control Systems
- Numerical Analysis
Background:
- Continuous time variant functions are crucial in dynamic systems.
- Computing their inverses efficiently and avoiding singularities is a significant challenge.
- Existing methods may struggle with real-time computation and singularity handling.
Purpose of the Study:
- To present an efficient and fast computational approach for inverse continuous time variant functions.
- To introduce a novel method for preventing singularities during inverse computation.
- To enhance the robustness and applicability of inverse function calculations.
Main Methods:
- Implementation of Radial Basis Function Networks (RBFNs) for function approximation.
- Development of an overall damped least squares solution.
- Derivation of a novel null space vector for singularity prevention based on a sufficiency condition.
Main Results:
- Demonstrated fast computation of inverse continuous time variant functions.
- Successfully prevented singularities using the proposed null space vector.
- Established characterizing matrices and a performance index for singularity avoidance.
Conclusions:
- The proposed RBFN-based approach offers an efficient solution for computing inverse continuous time variant functions.
- The novel null space vector effectively addresses the challenge of singularities in inverse computations.
- This method enhances the reliability of dynamic system analysis and control.
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