  We present a Bayesian optimization (BO) framework for tuning model predictive
controllers (MPC) of central heating, ventilation, and air conditioning (HVAC)
plants. This approach treats the functional relationship between the
closed-loop performance of MPC and its tuning parameters as a black-box. The
approach is motivated by the observation that evaluating the closed-loop
performance of MPC by trial-and-error is time-consuming (e.g., every
closed-loop simulation can involve solving thousands of optimization problems).
The proposed BO framework seeks to quickly identify the optimal tuning
parameters by strategically exploring and exploiting the space of the tuning
parameters. The effectiveness of the BO framework is demonstrated by using an
MPC controller for a central HVAC plant using realistic data. Here, the BO
framework tunes back-off terms for thermal storage tanks to minimize year-long
closed-loop costs. Simulation results show that BO can find the optimal
back-off terms by conducting 13 year-long simulations, which significantly
reduces the computational burden of a naive grid search. We also find that the
back-off terms obtained with BO reduce the closed-loop costs.
