Robust Trajectory Tracking Control for Continuous-Time Nonlinear Systems with State Constraints and Uncertain Disturbances
In this paper, a robust trajectory tracking control method with state constraints and uncertain disturbances on the ground of adaptive dynamic programming (ADP) is proposed for nonlinear systems. Firstly, the augmented system consists of the tracking error and the reference trajectory, and the track...
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| Format: | Article |
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MDPI AG
2022-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/6/816 |
| _version_ | 1797487663549251584 |
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| author | Chunbin Qin Xiaopeng Qiao Jinguang Wang Dehua Zhang |
| author_facet | Chunbin Qin Xiaopeng Qiao Jinguang Wang Dehua Zhang |
| author_sort | Chunbin Qin |
| collection | DOAJ |
| description | In this paper, a robust trajectory tracking control method with state constraints and uncertain disturbances on the ground of adaptive dynamic programming (ADP) is proposed for nonlinear systems. Firstly, the augmented system consists of the tracking error and the reference trajectory, and the tracking control problems with uncertain disturbances is described as the problem of robust control adjustment. In addition, considering the nominal system of the augmented system, the guaranteed cost tracking control problem is transformed into the optimal control problem by using the discount coefficient in the nominal system. A new safe Hamilton–Jacobi–Bellman (HJB) equation is proposed by combining the cost function with the control barrier function (CBF), so that the behavior of violating the safety regulations for the system states will be punished. In order to solve the new safe HJB equation, a critic neural network (NN) is used to approximate the solution of the safe HJB equation. According to the Lyapunov stability theory, in the case of state constraints and uncertain disturbances, the system states and the parameters of the critic neural network are guaranteed to be uniformly ultimately bounded (UUB). At the end of this paper, the feasibility of the proposed method is verified by a simulation example. |
| first_indexed | 2024-03-09T23:51:53Z |
| format | Article |
| id | doaj.art-b0a0a764c0954430bba22145008ae7d1 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T23:51:53Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj.art-b0a0a764c0954430bba22145008ae7d12023-11-23T16:33:37ZengMDPI AGEntropy1099-43002022-06-0124681610.3390/e24060816Robust Trajectory Tracking Control for Continuous-Time Nonlinear Systems with State Constraints and Uncertain DisturbancesChunbin Qin0Xiaopeng Qiao1Jinguang Wang2Dehua Zhang3School 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, a robust trajectory tracking control method with state constraints and uncertain disturbances on the ground of adaptive dynamic programming (ADP) is proposed for nonlinear systems. Firstly, the augmented system consists of the tracking error and the reference trajectory, and the tracking control problems with uncertain disturbances is described as the problem of robust control adjustment. In addition, considering the nominal system of the augmented system, the guaranteed cost tracking control problem is transformed into the optimal control problem by using the discount coefficient in the nominal system. A new safe Hamilton–Jacobi–Bellman (HJB) equation is proposed by combining the cost function with the control barrier function (CBF), so that the behavior of violating the safety regulations for the system states will be punished. In order to solve the new safe HJB equation, a critic neural network (NN) is used to approximate the solution of the safe HJB equation. According to the Lyapunov stability theory, in the case of state constraints and uncertain disturbances, the system states and the parameters of the critic neural network are guaranteed to be uniformly ultimately bounded (UUB). At the end of this paper, the feasibility of the proposed method is verified by a simulation example.https://www.mdpi.com/1099-4300/24/6/816adaptive dynamic programmingrobust tracking controlcontrol barrier functionstate constraints |
| spellingShingle | Chunbin Qin Xiaopeng Qiao Jinguang Wang Dehua Zhang Robust Trajectory Tracking Control for Continuous-Time Nonlinear Systems with State Constraints and Uncertain Disturbances Entropy adaptive dynamic programming robust tracking control control barrier function state constraints |
| title | Robust Trajectory Tracking Control for Continuous-Time Nonlinear Systems with State Constraints and Uncertain Disturbances |
| title_full | Robust Trajectory Tracking Control for Continuous-Time Nonlinear Systems with State Constraints and Uncertain Disturbances |
| title_fullStr | Robust Trajectory Tracking Control for Continuous-Time Nonlinear Systems with State Constraints and Uncertain Disturbances |
| title_full_unstemmed | Robust Trajectory Tracking Control for Continuous-Time Nonlinear Systems with State Constraints and Uncertain Disturbances |
| title_short | Robust Trajectory Tracking Control for Continuous-Time Nonlinear Systems with State Constraints and Uncertain Disturbances |
| title_sort | robust trajectory tracking control for continuous time nonlinear systems with state constraints and uncertain disturbances |
| topic | adaptive dynamic programming robust tracking control control barrier function state constraints |
| url | https://www.mdpi.com/1099-4300/24/6/816 |
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