17 research outputs found
Meta Learning MPC using Finite-Dimensional Gaussian Process Approximations
Data availability has dramatically increased in recent years, driving
model-based control methods to exploit learning techniques for improving the
system description, and thus control performance. Two key factors that hinder
the practical applicability of learning methods in control are their high
computational complexity and limited generalization capabilities to unseen
conditions. Meta-learning is a powerful tool that enables efficient learning
across a finite set of related tasks, easing adaptation to new unseen tasks.
This paper makes use of a meta-learning approach for adaptive model predictive
control, by learning a system model that leverages data from previous related
tasks, while enabling fast fine-tuning to the current task during closed-loop
operation. The dynamics is modeled via Gaussian process regression and,
building on the Karhunen-Lo{\`e}ve expansion, can be approximately reformulated
as a finite linear combination of kernel eigenfunctions. Using data collected
over a set of tasks, the eigenfunction hyperparameters are optimized in a
meta-training phase by maximizing a variational bound for the log-marginal
likelihood. During meta-testing, the eigenfunctions are fixed, so that only the
linear parameters are adapted to the new unseen task in an online adaptive
fashion via Bayesian linear regression, providing a simple and efficient
inference scheme. Simulation results are provided for autonomous racing with
miniature race cars adapting to unseen road conditions
Bayesian Learning-Based Adaptive Control for Safety Critical Systems
Deep learning has enjoyed much recent success, and applying state-of-the-art
model learning methods to controls is an exciting prospect. However, there is a
strong reluctance to use these methods on safety-critical systems, which have
constraints on safety, stability, and real-time performance. We propose a
framework which satisfies these constraints while allowing the use of deep
neural networks for learning model uncertainties. Central to our method is the
use of Bayesian model learning, which provides an avenue for maintaining
appropriate degrees of caution in the face of the unknown. In the proposed
approach, we develop an adaptive control framework leveraging the theory of
stochastic CLFs (Control Lyapunov Functions) and stochastic CBFs (Control
Barrier Functions) along with tractable Bayesian model learning via Gaussian
Processes or Bayesian neural networks. Under reasonable assumptions, we
guarantee stability and safety while adapting to unknown dynamics with
probability 1. We demonstrate this architecture for high-speed terrestrial
mobility targeting potential applications in safety-critical high-speed Mars
rover missions.Comment: Corrected an error in section II, where previously the problem was
introduced in a non-stochastic setting and wrongly assumed the solution to an
ODE with Gaussian distributed parametric uncertainty was equivalent to an SDE
with a learned diffusion term. See Lew, T et al. "On the Problem of
Reformulating Systems with Uncertain Dynamics as a Stochastic Differential
Equation