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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2206.03809 |
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| _version_ | 1866915753592094720 |
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| author | Quan, Quan Cai, Kai-Yuan Wang, Chenyu |
| author_facet | Quan, Quan Cai, Kai-Yuan Wang, Chenyu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_03809 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Control with Patterns: A D-learning Method Quan, Quan Cai, Kai-Yuan Wang, Chenyu Robotics 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. |
| title | Control with Patterns: A D-learning Method |
| topic | Robotics |
| url | https://arxiv.org/abs/2206.03809 |