The design and implementation of an architectural dimming control for multicolor LED-based lighting fixtures is complicated by the need to maintain a consistent color balance under a wide variety of operating conditions. Factors to consider include nonlinear relationships between luminous flux intensity and drive current, junction temperature dependencies, LED manufacturing tolerances and binning parameters, device aging characteristics, variations in color sensor spectral responsitivities, and the approximations introduced by linear color space models. In this paper we formulate this problem as a nonlinear multidimensional function, where maintaining a consistent color balance is equivalent to determining the hyperplane representing constant chromaticity. To be useful for an architectural dimming control design, this determination must be made in real time as the lighting fixture intensity is adjusted. Further, the LED drive current must be continuously adjusted in response to color sensor inputs to maintain constant chromaticity for a given intensity setting. Neural networks are known to be universal approximators capable of representing any continuously differentiable bounded function. We therefore use a radial basis function neural network to represent the multidimensional function and provide the feedback signals needed to maintain constant chromaticity. The network can be trained on the factory floor using individual device measurements such as spectral radiant intensity and color sensor characteristics. This provides a flexible solution that is mostly independent of LED manufacturing tolerances and binning parameters.