Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Adaptive Control

System Identification I

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.

/pdf/cautious-model-predictive-control-using-gaussian-process-22h61bh9m4.pdf

Cautious Model Predictive Control Using Gaussian Process Regression

We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant systems. The scheme uses an implicit model description based on behavioral systems theory and past measured trajectories. In particular, it does not require any prior identification step, but only an initially measured input–output trajectory as well as an upper bound on the order of the unknown system. First, we prove exponential stability of a nominal data-driven MPC scheme with terminal equality constraints in the case of no measurement noise. For bounded additive output measurement noise, we propose a robust modification of the scheme, including a slack variable with regularization in the cost. We prove that the application of this robust MPC scheme in a multistep fashion leads to practical exponential stability of the closed loop w.r.t. the noise level. The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme.

Data-Driven Model Predictive Control With Stability and Robustness Guarantees

Recent successes in the field of machine learning, as well as the availability of increased sensing and computational capabilities in modern control systems, have led to a growing interest in learn...

https://www.annualreviews.org/doi/pdf/10.1146/annurev-control-090419-075625

Learning-Based Model Predictive Control: Toward Safe Learning in Control

In this letter, we present a learning-based control approach for autonomous racing with an application to the AMZ Driverless race car gotthard 
. One major issue in autonomous racing is that accurate vehicle models that cover the entire performance envelope of a race car are highly nonlinear, complex, and complicated to identify, rendering them impractical for control. To address this issue, we employ a relatively simple nominal vehicle model, which is improved based on measurement data and tools from machine learning.The resulting formulation is an online learning data-driven model predictive controller, which uses Gaussian processes regression to take residual model uncertainty into account and achieve safe driving behavior. To improve the vehicle model online, we select from a constant in-flow of data points according to a criterion reflecting the information gain, and maintain a small dictionary of 300 data points. The framework is tested on the full-size AMZ Driverless race car, where it is able to improve the vehicle model and reduce lap times by $ {\mathbf{10}{\%}}$ while maintaining safety of the vehicle.

/pdf/learning-based-model-predictive-control-for-autonomous-hel0mymyfc.pdf

Learning-Based Model Predictive Control for Autonomous Racing

High-precision trajectory tracking is fundamental in robotic manipulation. While industrial robots address this through stiffness and high-performance hardware, compliant and cost-effective robots require advanced control to achieve accurate position tracking. In this letter, we present a model-based control approach, which makes use of data gathered during operation to improve the model of the robotic arm and thereby the tracking performance. The proposed scheme is based on an inverse dynamics feedback linearization and a data-driven error model, which are integrated into a model predictive control formulation. In particular, we show how offset-free tracking can be achieved by augmenting a nominal model with both a Gaussian process, which makes use of offline data, and an additive disturbance model suitable for efficient online estimation of the residual disturbance via an extended Kalman filter. The performance of the proposed offset-free GPMPC scheme is demonstrated on a compliant 6 degrees of freedom robotic arm, showing significant performance improvements compared to other robot control algorithms.

Data-Driven Model Predictive Control for Trajectory Tracking With a Robotic Arm

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.

/pdf/cautious-nmpc-with-gaussian-process-dynamics-for-autonomous-333p2f5uxe.pdf

Lukas Hewing

Papers

Learning-Based Model Predictive Control: Toward Safe Learning in Control

Cautious Model Predictive Control Using Gaussian Process Regression

Learning-Based Model Predictive Control for Autonomous Racing

Data-Driven Model Predictive Control for Trajectory Tracking With a Robotic Arm

Cautious NMPC with Gaussian Process Dynamics for Autonomous Miniature Race Cars