Lukas Hewing

Lukas Hewing, Juraj Kabzan, Melanie N. Zeilinger

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. Approximation techniques for propagating the state distribution are reviewed and 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, highlighting improvements with regard to both performance and safety over a nominal controller.

Lukas Hewing, Kim P. Wabersich, Melanie N. Zeilinger

We present a stochastic model predictive control (MPC) method for linear discrete-time systems subject to possibly unbounded and correlated additive stochastic disturbance sequences. Chance constraints are treated in analogy to robust MPC using the concept of probabilistic reachable sets for constraint tightening. We introduce an initialization of each MPC iteration which is always recursively feasibility and thereby allows that chance constraint satisfaction for the closed-loop system can readily be shown. Under an i.i.d. zero mean assumption on the additive disturbance, we furthermore provide an average asymptotic performance bound. Two examples illustrate the approach, highlighting feedback properties of the novel initialization scheme, as well as the inclusion of time-varying, correlated disturbances in a building control setting.

Lukas P. Fröhlich, Christian Küttel, Elena Arcari et al.

Learning-based model predictive control has been widely applied in autonomous racing to improve the closed-loop behaviour of vehicles in a data-driven manner. When environmental conditions change, e.g., due to rain, often only the predictive model is adapted, but the controller parameters are kept constant. However, this can lead to suboptimal behaviour. In this paper, we address the problem of data-efficient controller tuning, adapting both the model and objective simultaneously. The key novelty of the proposed approach is that we leverage a learned dynamics model to encode the environmental condition as a so-called context. This insight allows us to employ contextual Bayesian optimization to efficiently transfer knowledge across different environmental conditions. Consequently, we require fewer data to find the optimal controller configuration for each context. The proposed framework is extensively evaluated with more than 3'000 laps driven on an experimental platform with 1:28 scale RC race cars. The results show that our approach successfully optimizes the lap time across different contexts requiring fewer data compared to other approaches based on standard Bayesian optimization.

Lukas Hewing, Elena Arcari, Lukas P. Fröhlich et al.

Established techniques for simulation and prediction with Gaussian process (GP) dynamics often implicitly make use of an independence assumption on successive function evaluations of the dynamics model. This can result in significant error and underestimation of the prediction uncertainty, potentially leading to failures in safety-critical applications. This paper discusses methods that explicitly take the correlation of successive function evaluations into account. We first describe two sampling-based techniques; one approach provides samples of the true trajectory distribution, suitable for `ground truth' simulations, while the other draws function samples from basis function approximations of the GP. Second, we propose a linearization-based technique that directly provides approximations of the trajectory distribution, taking correlations explicitly into account. We demonstrate the procedures in simple numerical examples, contrasting the results with established methods.

Lukas Hewing, Melanie N. Zeilinger

In this paper we propose a stochastic model predictive control (MPC) algorithm for linear discrete-time systems affected by possibly unbounded additive disturbances and subject to probabilistic constraints. Constraints are treated in analogy to robust MPC using a constraint tightening based on the concept of probabilistic reachable sets, which is shown to provide closed-loop fulfillment of chance constraints under a unimodality assumption on the disturbance distribution. A control scheme reverting to a backup solution from a previous time step in case of infeasibility is proposed, for which an asymptotic average performance bound is derived. Two examples illustrate the approach, highlighting closed-loop chance constraint satisfaction and the benefits of the proposed controller in the presence of unmodeled disturbances.

Lukas Hewing, Alexander Liniger, Melanie N. Zeilinger

This paper presents an adaptive high performance control method for autonomous miniature race cars. Racing dynamics are notoriously hard to model from first principles, which is addressed by means of a cautious nonlinear model predictive control (NMPC) approach that learns to improve its dynamics model from data and safely increases racing performance. The approach makes use of a Gaussian Process (GP) and takes residual model uncertainty into account through a chance constrained formulation. We present a sparse GP approximation with dynamically adjusting inducing inputs, enabling a real-time implementable controller. The formulation is demonstrated in simulations, which show significant improvement with respect to both lap time and constraint satisfaction compared to an NMPC without model learning.