Constrained Optimal Control for Nonlinear Multi-Input Safety-Critical Systems with Time-Varying Safety Constraints
In this paper, we investigate the constrained optimal control problem of nonlinear multi-input safety-critical systems with uncertain disturbances and time-varying safety constraints. By utilizing a barrier function transformation, together with a new disturbance-related term and a smooth safety bou...
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| Format: | Article |
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/15/2744 |
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| author | Jinguang Wang Chunbin Qin Xiaopeng Qiao Dehua Zhang Zhongwei Zhang Ziyang Shang Heyang Zhu |
| author_facet | Jinguang Wang Chunbin Qin Xiaopeng Qiao Dehua Zhang Zhongwei Zhang Ziyang Shang Heyang Zhu |
| author_sort | Jinguang Wang |
| collection | DOAJ |
| description | In this paper, we investigate the constrained optimal control problem of nonlinear multi-input safety-critical systems with uncertain disturbances and time-varying safety constraints. By utilizing a barrier function transformation, together with a new disturbance-related term and a smooth safety boundary function, a nominal system-dependent multi-input barrier transformation architecture is developed to deal with the time-varying safety constraints and uncertain disturbances. Based on the obtained transformation system, the coupled Hamilton–Jacobi–Bellman (HJB) function is established to obtain the constrained Nash equilibrium solution. In addition, due to the fact that it is difficult to solve the HJB function directly, the single critic neural network (NN) is constructed to approximate the optimal performance index function of different control inputs, respectively. It is proved theoretically that, under the influence of uncertain disturbances and time-varying safety constraints, the system states and neural network parameters can be uniformly ultimately bounded (UUB) by the proposed neural network approximation method. Finally, the effectiveness of the proposed method is verified by two nonlinear simulation examples. |
| first_indexed | 2024-03-09T10:06:46Z |
| format | Article |
| id | doaj.art-aca6d0877a484cad919dab1b0065cb3b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T10:06:46Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-aca6d0877a484cad919dab1b0065cb3b2023-12-01T23:02:27ZengMDPI AGMathematics2227-73902022-08-011015274410.3390/math10152744Constrained Optimal Control for Nonlinear Multi-Input Safety-Critical Systems with Time-Varying Safety ConstraintsJinguang Wang0Chunbin Qin1Xiaopeng Qiao2Dehua Zhang3Zhongwei Zhang4Ziyang Shang5Heyang Zhu6School of Artificial Intelligence, Henan University, Zhengzhou 450000, ChinaSchool of Artificial Intelligence, Henan University, Zhengzhou 450000, ChinaSchool of Artificial Intelligence, Henan University, Zhengzhou 450000, ChinaSchool of Artificial Intelligence, Henan University, Zhengzhou 450000, ChinaSchool of Artificial Intelligence, Henan University, Zhengzhou 450000, ChinaSchool of Artificial Intelligence, Henan University, Zhengzhou 450000, ChinaSchool of Artificial Intelligence, Henan University, Zhengzhou 450000, ChinaIn this paper, we investigate the constrained optimal control problem of nonlinear multi-input safety-critical systems with uncertain disturbances and time-varying safety constraints. By utilizing a barrier function transformation, together with a new disturbance-related term and a smooth safety boundary function, a nominal system-dependent multi-input barrier transformation architecture is developed to deal with the time-varying safety constraints and uncertain disturbances. Based on the obtained transformation system, the coupled Hamilton–Jacobi–Bellman (HJB) function is established to obtain the constrained Nash equilibrium solution. In addition, due to the fact that it is difficult to solve the HJB function directly, the single critic neural network (NN) is constructed to approximate the optimal performance index function of different control inputs, respectively. It is proved theoretically that, under the influence of uncertain disturbances and time-varying safety constraints, the system states and neural network parameters can be uniformly ultimately bounded (UUB) by the proposed neural network approximation method. Finally, the effectiveness of the proposed method is verified by two nonlinear simulation examples.https://www.mdpi.com/2227-7390/10/15/2744barrier functiontime-varying safety constraintsadaptive dynamic programmingmulti-input system |
| spellingShingle | Jinguang Wang Chunbin Qin Xiaopeng Qiao Dehua Zhang Zhongwei Zhang Ziyang Shang Heyang Zhu Constrained Optimal Control for Nonlinear Multi-Input Safety-Critical Systems with Time-Varying Safety Constraints Mathematics barrier function time-varying safety constraints adaptive dynamic programming multi-input system |
| title | Constrained Optimal Control for Nonlinear Multi-Input Safety-Critical Systems with Time-Varying Safety Constraints |
| title_full | Constrained Optimal Control for Nonlinear Multi-Input Safety-Critical Systems with Time-Varying Safety Constraints |
| title_fullStr | Constrained Optimal Control for Nonlinear Multi-Input Safety-Critical Systems with Time-Varying Safety Constraints |
| title_full_unstemmed | Constrained Optimal Control for Nonlinear Multi-Input Safety-Critical Systems with Time-Varying Safety Constraints |
| title_short | Constrained Optimal Control for Nonlinear Multi-Input Safety-Critical Systems with Time-Varying Safety Constraints |
| title_sort | constrained optimal control for nonlinear multi input safety critical systems with time varying safety constraints |
| topic | barrier function time-varying safety constraints adaptive dynamic programming multi-input system |
| url | https://www.mdpi.com/2227-7390/10/15/2744 |
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