A convex approach to a class of non-convex building HVAC control problems: Illustration by two case studies

In this paper, a convexification approach is presented for a class of non-convex optimal/model predictive control problems more specifically applied to building HVAC control problems. The original non-convex problems are convexified using a convex envelope approach. The approach is tested on two case studies: a benchmark building HVAC system control problem from the literature and control of a hybrid ground-coupled heat pump (HybGCHP) system. For the first application, convexified model predictive control was used and results were compared with fuzzy and adaptive control results. For the HybGCHP system, convexified optimal control was applied and the results were compared with dynamic programming based optimal control. In the first case superior performance was observed over the corresponding fuzzy and adaptive control results from the literature. For the HybGCHP system the associated convexified optimal control gave almost global optimal results in terms of responses and cost criteria. The suggested method is especially useful for optimal building HVAC control/design problems which include non-convex bilinear or fractional terms. Since a polynomial expression can be recursively expressed as a system of bilinear equations, the proposed method, in principle, can be applied to all systems where polynomial non-convexities exist.