Stochastic data-driven model predictive control using Gaussian processes
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Nonlinear model predictive control (NMPC) is one of the few control methods that can handle multivariable nonlinear control systems with constraints. Gaussian processes (GPs) present a powerful tool to identify the required plant model and quantify the residual uncertainty of the plant-model mismatch given its probabilistic nature . It is crucial to account for this uncertainty, since it may lead to worse control performance and constraint violations. In this paper we propose a new method to design a GP-based NMPC algorithm for finite horizon control problems. The method generates Monte Carlo samples of the GP offline for constraint tightening using back-offs. The tightened constraints then guarantee the satisfaction of joint chance constraints online. Advantages of our proposed approach over existing methods include fast online evaluation time, consideration of closed-loop behaviour, and the possibility to alleviate conservativeness by accounting for both online learning and state dependency of the uncertainty. The algorithm is verified on a challenging semi-batch bioprocess case study, with its high performance thoroughly demonstrated.
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