Analysis of local optima in predictive control for energy efficient buildings

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 use while satisfying occupant comfort and actuator constraints by using predictive knowledge of weather and occupancy. The objective of this paper is to investigate the phenomenon of local optima. In particular, the product between air temperatures and mass 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. In the first part of the paper, models and MPC control 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. Our ultimate goal is to use this analysis to derive branch and bound rules which allow a nonlinear programming solver to converge to globally optimal control sequences.