Improving the Performance of Robust Control through Event-Triggered Learning

Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes, pp. 3424–3430

Abstract

Robust controllers ensure stability in feedback loops designed under uncertainty but at the cost of performance. Model uncertainty in time-invariant systems can be reduced by recently proposed learning-based methods, which improve the performance of robust controllers using data. However, in practice, many systems also exhibit uncertainty in the form of changes over time, e.g., due to weight shifts or wear and tear, leading to decreased performance or instability of the learning-based controller. We propose an event-triggered learning algorithm that decides when to learn in the face of uncertainty in the LQR problem with rare or slow changes. Our key idea is to switch between robust and learned controllers. For learning, we first approximate the optimal length of the learning phase via Monte-Carlo estimations using a probabilistic model. We then design a statistical test for uncertain systems based on the moment-generating function of the LQR cost. The test detects changes in the system under control and triggers relearning when control performance deteriorates due to system changes. We demonstrate improved performance over a robust controller baseline in a numerical example.

Authors 3

1. Alexander von Rohr Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University · Max Planck Institute for Intelligent Systems · Ingenieurgesellschaft Auto und Verkehr (Germany)

   Affiliation as printed

   RWTH Aachen University,Institute for Data Science in Mechanical Engineering,Aachen,Germany

   IAV GmbH Ingenieurgesellschaft Auto und Verkehr, Germany

   Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Aachen, Germany

   Max Planck Institute for Intelligent Systems, Stuttgart, Germany

2. Friedrich Solowjow Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University · Max Planck Institute for Intelligent Systems

   Affiliation as printed

   RWTH Aachen University,Institute for Data Science in Mechanical Engineering,Aachen,Germany

   Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Aachen, Germany

   Max Planck Institute for Intelligent Systems, Stuttgart, Germany

3. Sebastian Trimpe Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University · Max Planck Institute for Intelligent Systems

   Affiliation as printed

   RWTH Aachen University,Institute for Data Science in Mechanical Engineering,Aachen,Germany

   Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Aachen, Germany

   Max Planck Institute for Intelligent Systems, Stuttgart, Germany