Safe learning of regions of attraction for uncertain, nonlinear systems with Gaussian processes
Felix Berkenkamp,Riccardo Moriconi,Angela P. Schoellig,Andreas Krause +3 more
- pp 4661-4666
TLDR
This paper considers an approach that learns the ROA from experiments on a real system, without ever leaving the true ROA and, thus, without risking safety-critical failures.Abstract:
Control theory can provide useful insights into the properties of controlled, dynamic systems. One important property of nonlinear systems is the region of attraction (ROA), a safe subset of the state space in which a given controller renders an equilibrium point asymptotically stable. The ROA is typically estimated based on a model of the system. However, since models are only an approximation of the real world, the resulting estimated safe region can contain states outside the ROA of the real system. This is not acceptable in safety-critical applications. In this paper, we consider an approach that learns the ROA from experiments on a real system, without ever leaving the true ROA and, thus, without risking safety-critical failures. Based on regularity assumptions on the model errors in terms of a Gaussian process prior, we use an underlying Lyapunov function in order to determine a region in which an equilibrium point is asymptotically stable with high probability. Moreover, we provide an algorithm to actively and safely explore the state space in order to expand the ROA estimate. We demonstrate the effectiveness of this method in simulation.read more
Citations
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References
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Gaussian Processes for Machine Learning
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Essentials of Robust Control
Kemin Zhou,John Doyle +1 more
TL;DR: In this article, the authors introduce linear algebraic Riccati Equations and linear systems with Ha spaces and balance model reduction, and Ha Loop Shaping, and Controller Reduction.
Proceedings Article
Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental Design
TL;DR: This work analyzes GP-UCB, an intuitive upper-confidence based algorithm, and bound its cumulative regret in terms of maximal information gain, establishing a novel connection between GP optimization and experimental design and obtaining explicit sublinear regret bounds for many commonly used covariance functions.
Journal ArticleDOI
Convex Computation of the Region of Attraction of Polynomial Control Systems
Didier Henrion,Milan Korda +1 more
TL;DR: The ROA can be computed by solving a convex linear programming (LP) problem over the space of measures and this problem can be solved approximately via a classical converging hierarchy of convex finite-dimensional linear matrix inequalities (LMIs).
Proceedings ArticleDOI
Reachability-based safe learning with Gaussian processes
Anayo K. Akametalu,Shahab Kaynama,Jaime F. Fisac,Melanie N. Zeilinger,Jeremy H. Gillula,Claire J. Tomlin +5 more
TL;DR: This work proposes a novel method that uses a principled approach to learn the system's unknown dynamics based on a Gaussian process model and iteratively approximates the maximal safe set and further incorporates safety into the reinforcement learning performance metric, allowing a better integration of safety and learning.