# Control with Patterns: A D-learning Method

arXiv: https://arxiv.org/abs/2206.03809 · HTML: https://mlsanity.com/paper/2206.03809/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2022.

## Built on by (most cited first, 2 of 2)

- [A Fast Initialization Method for Neural Network Controllers: A Case Study of Image-based Visual Servoing Control for the multicopter Interception](https://mlsanity.com/paper/2509.19110/) (2025)
- [MSACL: Multi-Step Actor-Critic Learning with Lyapunov Certificates for Exponentially Stabilizing Control](https://mlsanity.com/paper/2512.24955/) (2025)

## Abstract (arXiv)

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.