Control with Patterns: A D-learning Method

TL;DR

This paper introduces Control with Patterns (CWP), a novel control method that guarantees stability for nonlinear systems using data-driven D-learning, demonstrated through multicopter flight stabilization with visual feedback.

Contribution

It presents a new stability concept called exponential attraction, transforms control problems into pattern classification tasks, and introduces D-learning for system-agnostic control.

Findings

CWP achieves stability in nonlinear systems.

D-learning enables control without system knowledge.

Successful multicopter stabilization with visual feedback.

Abstract

Learning-based control policies are widely used in various tasks in the field of robotics and control. However, formal (Lyapunov) stability guarantees for learning-based controllers with nonlinear dynamical systems are difficult to obtain. We propose a novel control approach, namely Control with Patterns (CWP), to address the stability issue over data sets corresponding to nonlinear dynamical systems. For such data sets, we introduce a new definition, namely exponential attraction on data sets, to describe the nonlinear dynamical systems under consideration. The problem of exponential attraction on data sets is transformed into a problem of pattern classification one based on the data sets and parameterized Lyapunov functions. Furthermore, D-learning is proposed as a method to perform CWP without knowledge of the system dynamics. Finally, the effectiveness of CWP based on D-learning is demonstrated through simulations and real flight experiments. In these experiments, the position of the multicopter is stabilized using real-time images as feedback, which can be considered as an Image-Based Visual Servoing (IBVS) problem.