  Composite adaptive radial basis function neural network (RBFNN) control with
a lattice distribution of hidden nodes has three inherent demerits: 1) the
approximation domain of adaptive RBFNNs is difficult to be determined a priori;
2) only a partial persistence of excitation (PE) condition can be guaranteed;
and 3) in general, the required number of hidden nodes of RBFNNs is enormous.
This paper proposes an adaptive feedforward RBFNN controller with an optimized
distribution of hidden nodes to suitably address the above demerits. The
distribution of the hidden nodes calculated by a K-means algorithm is optimally
distributed along the desired state trajectory. The adaptive RBFNN satisfies
the PE condition for the periodic reference trajectory. The weights of all
hidden nodes will converge to the optimal values. This proposed method
considerably reduces the number of hidden nodes, while achieving a better
approximation ability. The proposed control scheme shares a similar rationality
to that of the classical PID control in two special cases, which can thus be
seen as an enhanced PID scheme with a better approximation ability. For the
controller implemented by digital devices,the proposed method, for a
manipulator with unknown dynamics, potentially achieves better control
performance than model-based schemes with accurate dynamics.Simulation results
demonstrate the effectiveness of the proposed scheme. This result provides a
deeper insight into the coordination of the adaptive neural network control and
the deterministic learning theory.
