(623d) Bayesian Optimization with Reference Models: A Case Study in MPC for HVAC Central Plants

Model-predictive control (MPC) has been widely used in the industry owing to its exceptional capabilities in handling constraints, multivariable models, and operational objectives [1]. However, the control performance of a typical MPC strongly depends on the tuning of its parameters such as control horizon, prediction horizon, weights in the objective function, and constraint back-off terms [2]. Traditional MPC tuning methods rely extensively on trial-and-error or expert heuristics [3]. This is impractical for large-scale systems, like commercial heating, ventilation, and air-conditioning (HVAC) plants. Simulation of such systems involves solving a computationally expensive optimization problems requiring significant wall-clock time. Self-tuning MPC treats the tuning problem as a black-box optimization, where algorithms such as sampling- or direct search-based methods have been previously used [4]. However, these methods are slow in progress and lack convergence guarantees. Recently, Bayesian optimization (BO), a data-driven black-box optimization approach, has shown great potential to improve MPC tuning for large-scale systems [5].

In this work we present a novel BO-based approach for tuning MPC controllers [6]. Unlike existing BO-based methods for MPC tuning [7], our approach incorporates preexisting information about the system into BO resulting in a hybrid algorithm. Our research focuses on a real MPC application for central HVAC plants where the control objective is to minimize the operation cost. The operating cost of HVAC plants is strongly affected by unpredictable disturbance that can lead to frequent constraint violations (e.g., overfill or dry-up of thermal energy storage tanks). Adding constraint back-off terms to MPC can effectively mitigate this issue. However, optimally tuning the back-off terms requires extensive simulations, that involve solving over 8700 optimization problems (about 2 hours of wall-clock time) for simulating a year-long HVAC operation [8]. We propose to include a reference model into traditional BO algorithm to accelerate the tuning process. The reference model is built based on the data from 21 low-fidelity (i.e., using reduced-horizon MPC) closed-loop simulations under different tuning parameters. Our simulations show that the presence of a reference model can quickly and effectively drive the search of tuning parameters towards the optimum. Specifically, our results show that by using the proposed reference model-based BO, the optimal back-off terms can be discovered after 3 iterations of high-fidelity simulations, in contrast to 14 high-fidelity simulations from the traditional BO method [9]; this amounts to an 8-hour reduction in the computation time after accounting for the time required to build the reference model. Moreover, the discovered optimal back-off parameters can decrease the operating cost compared with the benchmark values currently used in the literature [8].

References

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[2] R.W. Koller, L.A. Ricardez-Sandoval, and L.T. Biegler, “Stochastic back-off algorithm for simultaneous design, control, and scheduling of multiproduct systems under uncertainty,” AlChE Journal, 64(7): 2379-2389, 2018.

[3] J.L. Garriga, and M. Soroush, “Model predictive control tuning methods: A review,” Industrial & Engineering Chemistry Research, 49(8): 3505-3515, 2010.

[4] T.G. Kolda, R.M. Lewis, and V. Torczon, “Optimization by direct search: New perspectives on some classical and modern methods,” SIAM Review, 45(3): 385-482, 2003.

[5] J.A. Paulson, and A. Mesbah, “Data-driven scenario optimization for automated controller tuning with probabilistic performance guarantees,” IEEE Control Systems Letters, 5(4): 1477-1482, 2020.

[6] Q. Lu, L.D. González, R. Kumar, and V.M. Zavala, “Bayesian optimization with reference models: A case study in MPC for HVAC central plants,” Computers & Chemical Engineering, 154: 107491, 2021.

[7] J.A. Paulson, G. Makrygiorgos, and A. Mesbah, “Adversarially robust Bayesian optimization for efficient auto‐tuning of generic control structures under uncertainty,” AIChE Journal, e17591, 2021.

[8] R. Kumar, M.J. Wenzel, M.N. ElBsat, M.J. Risbeck, K.H. Drees, and V.M. Zavala, “Stochastic model predictive control for central HVAC plants,” Journal of Process Control, 90: 1-17, 2020.

[9] Q. Lu, R. Kumar, and V.M. Zavala, “MPC controller tuning using Bayesian optimization techniques,” arXiv preprint arXiv:2009.14175, 2020.