Performance-Oriented Learning of Hybrid Models for Model Predictive Control

Model predictive control (MPC) is the most widely used advanced control strategy for constrained multivariable systems in a wide range of applications [1] . An important practical consideration in MPC design is the model quality, which can greatly affect the closed-loop control performance especially when the inherent robustness provided by receding-horizon control is insufficient to mitigate model uncertainties.

Inspired by the notion of identification for control (I4C) [2], this talk presents a strategy for performance-oriented learning of data-driven models for MPC. The traditional practice in MPC design has relied on developing models independent of their control-oriented performance, i.e., how the predictive quality of models would influence the closed-loop control performance. An alternative view in handling system uncertainties in model-based control is to focus on the performance-oriented quality of models, rather than their general predictive quality. The fundamental idea of I4C is that the model that provides the best closed-loop performance may not be the one yielding the smallest prediction errors. Hence, for control applications, data-driven models must be identified or adapted by optimizing for their control-oriented predictive quality, which can be quantified in terms of closed-loop performance measures of interest. To this end, we present a hybrid modeling approach in which a residual neural network model [3] representing high-fidelity system knowledge (i.e., a surrogate of a first-principles model) is combined with transfer learning to enable performance-oriented adaptation of a subset of model parameters. Transfer learning has emerged as a popular technique in machine learning applications where knowledge acquired in one task is used to enhance the learning efficiency in a different but similar task [4]. The proposed hybrid modeling approach integrates domain knowledge (i.e., via a first-principles model) into a deep neural network model to improve data efficiency and model interpretability while improving the learning efficiency of model adaptation given a fixed budget of process runs.

To solve the performance-oriented model learning problem, we use constrained Bayesian optimization (CBO) that can directly handle black-box, expensive and noisy function evaluations, while accounting for the feasibility region of a black-box optimization problem [5]. BO has been employed in various applications, including automated controller tuning [6]. A key advantage of initializing the CBO procedure using a hybrid model includes efficient discovery of a performance-oriented model whose predictions retain their physical relevance and, as such, greatly aid with constraint satisfaction.

The proposed approach is demonstrated on a benchmark bioreactor case study [7]. Simulation results indicate that, given a fixed budget of process runs, performance-oriented adaptation of the hybrid model can yield control-oriented models that result in a significant improvement in closed-loop performance compared to model re-identification using closed-loop data. The proposed performance-oriented hybrid modeling approach can be especially useful for model-based control of batch processes, where each process run is associated with a high monetary value and/or high labor costs.

[1] Rawlings, J. B., Mayne, D. Q., & Diehl, M. (2017). Model predictive control: theory, computation, and design (Vol. 2). Madison, WI: Nob Hill Publishing.

[2] Gevers, M. (2005). Identification for control: From the early achievements to the revival of experiment design. European journal of control, 11(4-5), 335-352.

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[4] Pan, S. J., & Yang, Q. (2009). A survey on transfer learning. IEEE Transactions on knowledge and data engineering, 22(10), 1345-1359.

[5] Gardner, J. R., Kusner, M. J., Xu, Z. E., Weinberger, K. Q., & Cunningham, J. P. (2014). Bayesian Optimization with Inequality Constraints. In ICML (Vol. 2014, pp. 937-945).

[6] Sorourifar, F., Makrygirgos, G., Mesbah, A., & Paulson, J. A. (2020). A Data-Driven Automatic Tuning Method for MPC under Uncertainty using Constrained Bayesian Optimization. arXiv preprint arXiv:2011.11841.

[7] Agrawal, P., Koshy, G., & Ramseier, M. (1989). An algorithm for operating a fed‐batch fermentor at optimum specific‐growth rate. Biotechnology and bioengineering, 33(1), 115-125.