Adaptation of centers of approximation for nonlinear tracking control

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Sufficient conditions for the asymptotic stability and exponential convergence of tracking control for nonlinear systems have proliferated in recent research. Various theories for stability have been related to, and rely upon, the functional form of the governing nonlinear equations, the linearizability of the governing equations by canonical (Lie) transformations, the linear appearance of adaptive parameters, and the richness of the input excitation. Previously, sufficient conditions have been derived for a class of Hamiltonian adaptive tracking control problems using radial basis function approximants. We demonstrate that a crucial element determining the performance of this class of tracking control methodologies is the location of the centers of approximation in the radial basis approximant/network. A learning vector quantization algorithm is employed to simultaneously adapt both the centers of approximation and the feedback gains. The simultaneous adaptation of both approximant centers in configuration space and feedback gains can demonstrate remarkable improvements in convergence rate, as compared to adaptation of feedback gains alone.