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The local cluster neural network is a feedforward RBF network that has been implemented in analogue neural net chip. The LCNN chip can be trained by chip-in-the-loop training and this training method has been demonstrated to work efficiently. In order to increase the functionality of LCNN chip, we proposed on-chip training for the LCNN chip. In this paper, we describe two training algorithms -Gradient Descent and Probabilistic Random Weight Change, which are used in LCNN on-chip training simulations. We also present the experiment results from the simulations in multidimensional function approximation. The training convergence is investigated and analyzed. The circuite signal flow chart for these two algorithms are designed.