Analysis of local optima in predictive control for energy efficient buildings

Abstract

We study the problem of heating, ventilation and air conditioning (HVAC) control in a typical commercial building. We propose a model predictive control (MPC) approach which minimizes energy cost while satisfying occupant comfort and control actuator constraints, using a simplified system model and incorporating predictions of future weather and occupancy inputs. In simplified physics-based models of HVAC systems, the product between air temperatures and flow rates arising from energy balance equations leads to a non-convex MPC problem. Fast computational techniques for solving non-convex optimization can only provide certificates of local optimality. Local optima can potentially cause MPC to have worse performance than existing control implementations, so deserve careful consideration. The objective of this article is to investigate the phenomenon of local optima in the MPC optimization problem for a simple HVAC system model. In the first part of the article, simplified physics-based models and MPC design for two common HVAC configurations are introduced. In the second part, simulation results exhibiting local optima for both configurations are presented. We perform a detailed analysis on the different types of local optima and their physical interpretation. We then use this analysis to derive physics-based rules to exclude classes of locally optimal control sequences under specific conditions.