An optimization framework for control of non-square smart lighting systems with saturation constraints

Smart lighting systems are illumination systems that use feedback measurements from a network of color sensors to drive a set of spectrally tunable light sources to achieve a desired light field in an illuminated space. This paper proposes a general feedback control design framework for non-square smart lighting systems with saturation bounds, i.e., systems with a larger number of source channels (with limited maximum light output) than sensor channels. Since the number of inputs is larger than the number of measurements, a one-to-one setpoint based feedback control design is not possible because of the inherent redundancies. The feedback control design for such lighting systems is therefore posed as a constrained optimization problem with a cost function penalizing quality of light output and power consumed; and solved through a closed loop feedback approach. Two solutions to this problem are proposed: one based on Newton-Raphson method with projection and the second based on the interior point algorithm. We demonstrate the stability of the feedback loop for the projected Newton-Raphson method. The two proposed smart lighting algorithms are experimentally validated by implementation in a full-scale in-use smart conference room and a comparison of their performance is presented.