Cautious Model Predictive Control Using Gaussian Process Regression

By Lukas Hewing, Juraj Kabzan, Melanie Nicole Zeilinger. IEEE Transactions on Control Systems Technology, 2017

660 citations recorded by the source corpus.

Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for modeling of nonlinear dynamical systems from data, as it allows the direct assessment of residual model uncertainty. We present a model predictive control (MPC) approach that integrates a nominal system with an additive nonlinear part of the dynamics modeled as a GP. We describe a principled way of formulating the chance-constrained MPC problem, which takes into account residual uncertainties provided by the GP model to enable cautious control. Using additional approximations for efficient computation, we finally demonstrate the approach in a simulation example, as well as in a hardware implementation for autonomous racing of remote-controlled race cars with fast sampling times of 20 ms, highlighting improvements with regard to both performance and safety over a nominal controller.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/b3035f6b00ff01bd582d70e30fe54737b2df5472

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Citations in the corpus

Learning-Based Model Predictive Control for Autonomous Racing (2019, methodology): “uncertainty in the states over the MPC prediction horizon, we propagate the mean and variance using successive linearizations, similar to extended Kalman filtering [8].”
Learning to Synthesize Programs as Interpretable and Generalizable Policies (2021, background): “[71] Lukas Hewing, Juraj Kabzan, and Melanie N.”
Learning-Based Model Predictive Control: Toward Safe Learning in Control (2020, background): “…of GP-based MPC to robotic systems have been presented, e.g., for trajectory tracking with robotic manipulators (95), path following of off-road mobile robots (87, 96), autonomous racing (86, 90, 97), process control (98), and telescope systems in the context of periodic additive disturbances (99).”
Data-Driven Model Predictive Control With Stability and Robustness Guarantees (2019, background): “Similarly, MPC based on Gaussian processes has received increasing attraction [10], but proving desirable closed-loop properties remains an open issue.”
A Review of Safe Reinforcement Learning: Methods, Theory and Applications (2022, background): “propose safe control gym [310] 7, an extension benchmark of OpenAI Gym [43], which integrates traditional control methods [46], learning based-control methods [111] and reinforcement learning methods [104, 246] into a framework, in which model-based and data-based control approaches are both support”
Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning (2021, methodology): “, fixing the GP’s covariances over the prediction horizon (63)) are usually required to achieve real-time implementation.”
A Review of Safe Reinforcement Learning: Methods, Theories, and Applications (2024, positive): “…et al. propose safe control gym [243] 10 , an extension benchmark of OpenAI Gym [241], which integrates traditional control methods [244], learning based-control meth-ods [245] and RL methods [246], [247] into a framework, in which model-based and data-based control approaches are both supported.”
Data-Driven MPC for Quadrotors (2021, methodology): “For the propagation of the covariance, we refer to the formulation in [11], [12].”