Bayesian optimization with reference models: A case study in MPC for HVAC central plants

Abstract

We present a framework for exploiting reference models in Bayesian optimization (BO). Our approach is motivated by a model predictive control (MPC) tuning application for central heating, ventilation, and air conditioning (HVAC) plants. Evaluating the closed-loop performance of MPC by trial-and-error is time-consuming (e.g., a closed-loop simulation can involve solving thousands of optimization problems). The BO algorithm can accelerate this process by treating the functional relationship between the closed-loop performance of MPC and its tuning parameters (e.g., constraint back off terms and objective weights) as a black-box model and by systematically navigating the parameter space to maximize MPC performance. Traditional BO algorithms have been recently developed to tune controllers but such frameworks tend not to use pre-existing (prior) system information. In this work, we propose to incorporate such information in the form of reference models and we show that such models can be constructed in creative ways. Specifically, we propose to construct a reference model by evaluating the closed-loop performance of a low-complexity MPC controller. We show that the use of a reference model changes the goal of BO from learning the objective function to learning the residual function (error between the reference and the objective function), which is a much easier task. Specifically, we show that the use of a reference model can help BO to more judiciously sample the parameter estimate and more rapidly discover regions where the solution exists. This feature significantly reduces the number of function evaluations and can help avoid getting stuck in local minima. The effectiveness of our BO framework is demonstrated using a central HVAC plant study with realistic data. The reference model is built by training a kriging model based on data collected for 21 low-fidelity, closed-loop MPC simulations. Using this reference model, we show that our BO method can find the optimal constraint back-off terms within 3 high-fidelity, closed-loop simulations (total computation time of 20 h). In contrast, a traditional BO approach without a reference model requires 14 high-fidelity, closed simulations (total time of 28 h). Our approach thus reduces the computational time by 28%.