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

In this paper, we propose a neural motion planner for learning to drive autonomously in complex urban scenarios that include traffic-light handling, yielding, and interactions with multiple road-users. Towards this goal, we design a holistic model that takes as input raw LIDAR data and a HD map and produces interpretable intermediate representations in the form of 3D detections and their future trajectories, as well as a cost volume defining the goodness of each position that the self-driving car can take within the planning horizon. We then sample a set of diverse physically possible trajectories and choose the one with the minimum learned cost. Importantly, our cost volume is able to naturally capture multi-modality. We demonstrate the effectiveness of our approach in real-world driving data captured in several cities in North America. Our experiments show that the learned cost volume can generate safer planning than all the baselines.

/pdf/end-to-end-interpretable-neural-motion-planner-1fccr9x1pe.pdf

End-To-End Interpretable Neural Motion Planner

Abstract Nuclear fusion using magnetic confinement, in particular in the tokamak configuration, is a promising path towards sustainable energy. A core challenge is to shape and maintain a high-temperature plasma within the tokamak vessel. This requires high-dimensional, high-frequency, closed-loop control using magnetic actuator coils, further complicated by the diverse requirements across a wide range of plasma configurations. In this work, we introduce a previously undescribed architecture for tokamak magnetic controller design that autonomously learns to command the full set of control coils. This architecture meets control objectives specified at a high level, at the same time satisfying physical and operational constraints. This approach has unprecedented flexibility and generality in problem specification and yields a notable reduction in design effort to produce new plasma configurations. We successfully produce and control a diverse set of plasma configurations on the Tokamak à Configuration Variable 1,2 , including elongated, conventional shapes, as well as advanced configurations, such as negative triangularity and ‘snowflake’ configurations. Our approach achieves accurate tracking of the location, current and shape for these configurations. We also demonstrate sustained ‘droplets’ on TCV, in which two separate plasmas are maintained simultaneously within the vessel. This represents a notable advance for tokamak feedback control, showing the potential of reinforcement learning to accelerate research in the fusion domain, and is one of the most challenging real-world systems to which reinforcement learning has been applied. 

/pdf/magnetic-control-of-tokamak-plasmas-through-deep-2xsf5s2a.pdf

Magnetic control of tokamak plasmas through deep reinforcement learning

Learning-based methods have been successful in solving complex control tasks without significant prior knowledge about the system. However, these methods typically do not provide any safety guarantees, which prevents their use in safety-critical, real-world applications. In this paper, we present a learning-based model predictive control scheme that can provide provable high-probability safety guarantees. To this end, we exploit regularity assumptions on the dynamics in terms of a Gaussian process prior to construct provably accurate confidence intervals on predicted trajectories. Unlike previous approaches, we do not assume that model uncertainties are independent. Based on these predictions, we guarantee that trajectories satisfy safety constraints. Moreover, we use a terminal set constraint to recursively guarantee the existence of safe control actions at every iteration. In our experiments, we show that the resulting algorithm can be used to safely and efficiently explore and learn about dynamic systems.

Learning-Based Model Predictive Control for Safe Exploration

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

While it has been repeatedly shown that learning-based controllers can provide superior performance, they often lack of safety guarantees. This paper aims at addressing this problem by introducing a model predictive safety certification (MPSC) scheme for linear systems with additive disturbances. The scheme verifies safety of a proposed learning-based input and modifies it as little as necessary in order to keep the system within a given set of constraints. Safety is thereby related to the existence of a model predictive controller (MPC) providing a feasible trajectory towards a safe target set. A robust MPC formulation accounts for the fact that the model is generally uncertain in the context of learning, which allows for proving constraint satisfaction at all times under the proposed MPSC strategy. The MPSC scheme can be used in order to expand any potentially conservative set of safe states and we provide an iterative technique for enlarging the safe set. Finally, a practical data-based design procedure for MPSC is proposed using scenario optimization.

Linear Model Predictive Safety Certification for Learning-Based Control

While it has been repeatedly shown that learning-based controllers can provide superior performance, they often lack of safety guarantees. This paper aims at addressing this problem by introducing a model predictive safety certification (MPSC) scheme for polytopic linear systems with additive disturbances. The scheme verifies safety of a proposed learning-based input and modifies it as little as necessary in order to keep the system within a given set of constraints. Safety is thereby related to the existence of a model predictive controller (MPC) providing a feasible trajectory towards a safe target set. A robust MPC formulation accounts for the fact that the model is generally uncertain in the context of learning, which allows proving constraint satisfaction at all times under the proposed MPSC strategy. The MPSC scheme can be used in order to expand any potentially conservative set of safe states for learning and we prove an iterative technique for enlarging the safe set. Finally, a practical data-based design procedure for MPSC is proposed using scenario optimization.

Kim P. Wabersich

Papers

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

Linear Model Predictive Safety Certification for Learning-Based Control

Linear model predictive safety certification for learning-based control

Recursively feasible stochastic model predictive control using indirect feedback

A predictive safety filter for learning-based control of constrained nonlinear dynamical systems