A Data-Driven Automatic Tuning Method for MPC under Uncertainty using Constrained Bayesian Optimization

The closed-loop performance of model predictive controllers (MPCs) is sensitive to the choice of prediction models, controller formulation, and tuning parameters. However, prediction models are typically optimized for prediction accuracy instead of performance, and MPC tuning is typically done manually to satisfy (probabilistic) constraints. In this work, we demonstrate a general approach for automating the tuning of MPC under uncertainty. In particular, we formulate the automated tuning problem as a constrained black-box optimization problem that can be tackled with derivative-free optimization. We rely on a constrained variant of Bayesian optimization (BO) to solve the MPC tuning problem that can directly handle noisy and expensive-to-evaluate functions. The benefits of the proposed automated tuning approach are demonstrated on a benchmark continuously stirred tank reactor example.

[1]  Andreas Krause,et al.  Safe controller optimization for quadrotors with Gaussian processes , 2015, 2016 IEEE International Conference on Robotics and Automation (ICRA).

[2]  Victor M. Zavala,et al.  MPC Controller Tuning using Bayesian Optimization Techniques , 2020, ArXiv.

[3]  Nando de Freitas,et al.  Theoretical Analysis of Bayesian Optimisation with Unknown Gaussian Process Hyper-Parameters , 2014, ArXiv.

[4]  Jasper Snoek,et al.  Practical Bayesian Optimization of Machine Learning Algorithms , 2012, NIPS.

[5]  M. Soroush,et al.  Model Predictive Control Tuning Methods: A Review , 2010 .

[6]  Alexander Shapiro,et al.  The Sample Average Approximation Method for Stochastic Discrete Optimization , 2002, SIAM J. Optim..

[7]  Joel A. Paulson,et al.  Nonlinear Model Predictive Control with Explicit Backoffs for Stochastic Systems under Arbitrary Uncertainty , 2018 .

[8]  Marco Forgione,et al.  Efficient Calibration of Embedded MPC , 2019, ArXiv.

[9]  Jasper Snoek,et al.  Bayesian Optimization with Unknown Constraints , 2014, UAI.

[10]  Farhad Nili,et al.  Theoretical Analysis , 2017, Encyclopedia of GIS.

[11]  Matthew W. Hoffman,et al.  A General Framework for Constrained Bayesian Optimization using Information-based Search , 2015, J. Mach. Learn. Res..

[12]  Remis Balaniuk,et al.  Structural identification , 1997, Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robot and Systems. Innovative Robotics for Real-World Applications. IROS '97.

[13]  Matt J. Kusner,et al.  Bayesian Optimization with Inequality Constraints , 2014, ICML.

[14]  M. Hoshiya,et al.  Structural Identification by Extended Kalman Filter , 1984 .

[15]  Nando de Freitas,et al.  Taking the Human Out of the Loop: A Review of Bayesian Optimization , 2016, Proceedings of the IEEE.

[16]  Nikolaos V. Sahinidis,et al.  Simulation optimization: a review of algorithms and applications , 2014, 4OR.

[17]  Sergey Levine,et al.  Goal-driven dynamics learning via Bayesian optimization , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[18]  Paul W. Goldberg,et al.  Regression with Input-dependent Noise: A Gaussian Process Treatment , 1997, NIPS.

[19]  Joel A. Paulson,et al.  Fast approximate learning-based multistage nonlinear model predictive control using Gaussian processes and deep neural networks , 2020, Comput. Chem. Eng..

[20]  Michel Gevers,et al.  Identification for Control: From the Early Achievements to the Revival of Experiment Design , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[21]  Dieter Schwarzmann,et al.  Data-Efficient Autotuning With Bayesian Optimization: An Industrial Control Study , 2018, IEEE Transactions on Control Systems Technology.

[22]  John Lygeros,et al.  Performance-Driven Cascade Controller Tuning With Bayesian Optimization , 2020, IEEE Transactions on Industrial Electronics.

[23]  Alberto Bemporad,et al.  Performance-Oriented Model Learning for Data-Driven MPC Design , 2019, IEEE Control Systems Letters.

[24]  Joel A. Paulson,et al.  Data-Driven Scenario Optimization for Automated Controller Tuning With Probabilistic Performance Guarantees , 2020, IEEE Control Systems Letters.

[25]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.