Dynamic programming based approaches to optimal rooftop unit coordination

While buildings served by multiple rooftop units are widely prevalent in retail and food industries, optimal coordination among rooftop units has received little attention. Currently, most buildings utilize plain feedback or heuristic strategies to determine rooftop unit operations. This article presents a switched dynamic programming based approach for optimal scheduling of rooftop unit operations. Using a mid-sized restaurant served by multiple rooftop units as an example, a switched affine dynamic system model is first presented. The rooftop unit coordination control problem is then formulated as a switched optimal control problem with nontrivial switching cost. A dynamic programming based method is proposed for the solution of the switched optimal control problem, which has reasonable computational complexity and can be implemented either as a one-shot solution or as part of a model predictive control algorithm. To mitigate the growing computational complexity of the proposed algorithm, the approach is extended by proposing a distributed extension of the model predictive control formulation. Finally, a simulation based evaluation of the various formulations is conducted, and the salient features of the formulation are highlighted.