Optimal control for quadrotors UAV based on deep neural network approximations of stable manifold of HJB equation
This paper proposes a deep learning algorithm for solving the infinite-horizon optimal feedback control problem of a quadrotor unmanned aerial vehicle (UAV). The optimal control is represented by the stable manifold of the Hamilton–Jacobi–Bellman (HJB) equation in a 12-dimensional state space. Moreo...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2025-04-01
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| Series: | Automatika |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/00051144.2025.2461827 |
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| author | Yuhuan Yue |
| author_facet | Yuhuan Yue |
| author_sort | Yuhuan Yue |
| collection | DOAJ |
| description | This paper proposes a deep learning algorithm for solving the infinite-horizon optimal feedback control problem of a quadrotor unmanned aerial vehicle (UAV). The optimal control is represented by the stable manifold of the Hamilton–Jacobi–Bellman (HJB) equation in a 12-dimensional state space. Moreover, a deep learning algorithm is proposed to compute approximations of semiglobal stable manifold. The method is built on the geometric feature of the problem. The algorithm generates random data by solving the two-point boundary value problem of the characteristic Hamiltonian system of the HJB equation without discretizing the state space. The resulting data set lies on the stable manifold, and a deep neural network (NN) is trained to fit the data. The training process is conducted offline on a standard laptop without the use of a GPU. Generating feedback control for the quadrotor from the trained NN takes less than one millisecond, compared to several milliseconds required by existing methods for the same operation. The effectiveness of this approach is demonstrated by Monte Carlo tests and simulations in various scenarios. |
| format | Article |
| id | doaj-art-0787a376b79843a497aad41cfa616bfa |
| institution | Kabale University |
| issn | 0005-1144 1848-3380 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Automatika |
| spelling | doaj-art-0787a376b79843a497aad41cfa616bfa2025-08-20T03:48:13ZengTaylor & Francis GroupAutomatika0005-11441848-33802025-04-0166220121610.1080/00051144.2025.2461827Optimal control for quadrotors UAV based on deep neural network approximations of stable manifold of HJB equationYuhuan Yue0Jiaxing Vocational and Technical College, Zhejiang, People's Republic of ChinaThis paper proposes a deep learning algorithm for solving the infinite-horizon optimal feedback control problem of a quadrotor unmanned aerial vehicle (UAV). The optimal control is represented by the stable manifold of the Hamilton–Jacobi–Bellman (HJB) equation in a 12-dimensional state space. Moreover, a deep learning algorithm is proposed to compute approximations of semiglobal stable manifold. The method is built on the geometric feature of the problem. The algorithm generates random data by solving the two-point boundary value problem of the characteristic Hamiltonian system of the HJB equation without discretizing the state space. The resulting data set lies on the stable manifold, and a deep neural network (NN) is trained to fit the data. The training process is conducted offline on a standard laptop without the use of a GPU. Generating feedback control for the quadrotor from the trained NN takes less than one millisecond, compared to several milliseconds required by existing methods for the same operation. The effectiveness of this approach is demonstrated by Monte Carlo tests and simulations in various scenarios.https://www.tandfonline.com/doi/10.1080/00051144.2025.2461827Hamitlon–Jacobi–Bellman equationoptimal controlstable manifoldquadrotor UAVdeep learning algorithmreal-time control |
| spellingShingle | Yuhuan Yue Optimal control for quadrotors UAV based on deep neural network approximations of stable manifold of HJB equation Automatika Hamitlon–Jacobi–Bellman equation optimal control stable manifold quadrotor UAV deep learning algorithm real-time control |
| title | Optimal control for quadrotors UAV based on deep neural network approximations of stable manifold of HJB equation |
| title_full | Optimal control for quadrotors UAV based on deep neural network approximations of stable manifold of HJB equation |
| title_fullStr | Optimal control for quadrotors UAV based on deep neural network approximations of stable manifold of HJB equation |
| title_full_unstemmed | Optimal control for quadrotors UAV based on deep neural network approximations of stable manifold of HJB equation |
| title_short | Optimal control for quadrotors UAV based on deep neural network approximations of stable manifold of HJB equation |
| title_sort | optimal control for quadrotors uav based on deep neural network approximations of stable manifold of hjb equation |
| topic | Hamitlon–Jacobi–Bellman equation optimal control stable manifold quadrotor UAV deep learning algorithm real-time control |
| url | https://www.tandfonline.com/doi/10.1080/00051144.2025.2461827 |
| work_keys_str_mv | AT yuhuanyue optimalcontrolforquadrotorsuavbasedondeepneuralnetworkapproximationsofstablemanifoldofhjbequation |