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The competitive associative net, called CAN2-2, is presented for learning to approximate time-varying dynamics of a plant in order to control the plant. Although the learning method has been shown effective in the previous studies, it uses the gradient method involving local minima problems. To overcome the problems, we here consider an asymptotic situation, where the number of units of the net is very large, and show that the mean square error of the CAN2-2 in approximating time-varying function decreases and is minimized as the number of units increases when the firing numbers of the units are equated. Next, we embed the condition for equating the firing numbers into the learning algorithm of the CAN2-2, and then examine the conventional model switching predictive controller using the modified CAN2-2 in temperature control of the RCA solutions for cleaning silicon wafers which expose the exothermic nonlinear and time-varying chemical reactions. The result confirms that the present method has better learning properties than the conventional one.