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On the Design of LQR Kernels for Efficient Controller Learning

2017

Conference Paper

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Finding optimal feedback controllers for nonlinear dynamic systems from data is hard. Recently, Bayesian optimization (BO) has been proposed as a powerful framework for direct controller tuning from experimental trials. For selecting the next query point and finding the global optimum, BO relies on a probabilistic description of the latent objective function, typically a Gaussian process (GP). As is shown herein, GPs with a common kernel choice can, however, lead to poor learning outcomes on standard quadratic control problems. For a first-order system, we construct two kernels that specifically leverage the structure of the well-known Linear Quadratic Regulator (LQR), yet retain the flexibility of Bayesian nonparametric learning. Simulations of uncertain linear and nonlinear systems demonstrate that the LQR kernels yield superior learning performance.

Author(s): Alonso Marco and Philipp Hennig and Stefan Schaal and Sebastian Trimpe
Book Title: Proceedings of the 56th IEEE Conference on Decision and Control
Year: 2017
Month: December
Department(s): Autonomous Motion, Intelligent Control Systems, Probabilistic Numerics
Research Project(s): Automatic Controller Tuning using Bayesian Optimization
Bibtex Type: Conference Paper (conference)
Paper Type: Conference
State: Accepted
Links: arXiv
PDF

BibTex 

@conference{MaHeScTr17,
  title = {On the Design of {LQR} Kernels for Efficient Controller Learning},
  author = {Marco, Alonso and Hennig, Philipp and Schaal, Stefan and Trimpe, Sebastian},
  booktitle = {Proceedings of the 56th IEEE Conference on Decision and Control},
  month = dec,
  year = {2017},
  month_numeric = {12}
}