Data-Driven Finite-Horizon H∞ Tracking Control With Event-Triggered Mechanism for the Continuous-Time Nonlinear Systems

In this article, the neural network (NN)-based adaptive dynamic programming (ADP) event-triggered control method is presented to obtain the near-optimal control policy for the model-free finite-horizon <inline-formula> <tex-math notation="LaTeX">H_\infty </tex-math></i...

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Veröffentlicht in:	IEEE transaction on neural networks and learning systems Jg. 34; H. 8; S. 4687 - 4701
Hauptverfasser:	Zhang, Huaguang, Ming, Zhongyang, Yan, Yuqing, Wang, Wei
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Piscataway IEEE 01.08.2023 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Adaptation models Adaptive control Adaptive dynamic programming (ADP) Artificial neural networks Closed loops Control methods Cost function data driven Dynamic programming event triggered Feedback control finite horizon H-infinity control Mathematical models Neural networks neural networks (NNs) Nonlinear systems Optimal control Power system dynamics Terminal constraints Time dependence Tracking control Tracking errors
ISSN:	2162-237X, 2162-2388, 2162-2388
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Abstract	In this article, the neural network (NN)-based adaptive dynamic programming (ADP) event-triggered control method is presented to obtain the near-optimal control policy for the model-free finite-horizon <inline-formula> <tex-math notation="LaTeX">H_\infty </tex-math></inline-formula> optimal tracking control problem with constrained control input. First, using available input-output data, a data-driven model is established by a recurrent NN (RNN) to reconstruct the unknown system. Then, an augmented system with event-triggered mechanism is obtained by a tracking error system and a command generator. We present a novel event-triggering condition without Zeno behavior. On this basis, the relationship between event-triggered Hamilton-Jacobi-Isaacs (HJI) equation and time-triggered HJI equation is given in <xref ref-type="theorem" rid="theorem3">Theorem 3 . Since the solution of the HJI equation is time-dependent for the augmented system, the time-dependent activation functions of NNs are considered. Moreover, an extra error is incorporated to satisfy the terminal constraints of cost function. This adaptive control pattern finds, in real time, approximations of the optimal value while also ensuring the uniform ultimate boundedness of the closed-loop system. Finally, the effectiveness of the proposed near-optimal control pattern is verified by two simulation examples.
AbstractList	In this article, the neural network (NN)-based adaptive dynamic programming (ADP) event-triggered control method is presented to obtain the near-optimal control policy for the model-free finite-horizon [Formula Omitted] optimal tracking control problem with constrained control input. First, using available input–output data, a data-driven model is established by a recurrent NN (RNN) to reconstruct the unknown system. Then, an augmented system with event-triggered mechanism is obtained by a tracking error system and a command generator. We present a novel event-triggering condition without Zeno behavior. On this basis, the relationship between event-triggered Hamilton–Jacobi–Isaacs (HJI) equation and time-triggered HJI equation is given in Theorem 3 . Since the solution of the HJI equation is time-dependent for the augmented system, the time-dependent activation functions of NNs are considered. Moreover, an extra error is incorporated to satisfy the terminal constraints of cost function. This adaptive control pattern finds, in real time, approximations of the optimal value while also ensuring the uniform ultimate boundedness of the closed-loop system. Finally, the effectiveness of the proposed near-optimal control pattern is verified by two simulation examples. In this article, the neural network (NN)-based adaptive dynamic programming (ADP) event-triggered control method is presented to obtain the near-optimal control policy for the model-free finite-horizon <inline-formula> <tex-math notation="LaTeX">H_\infty </tex-math></inline-formula> optimal tracking control problem with constrained control input. First, using available input-output data, a data-driven model is established by a recurrent NN (RNN) to reconstruct the unknown system. Then, an augmented system with event-triggered mechanism is obtained by a tracking error system and a command generator. We present a novel event-triggering condition without Zeno behavior. On this basis, the relationship between event-triggered Hamilton-Jacobi-Isaacs (HJI) equation and time-triggered HJI equation is given in <xref ref-type="theorem" rid="theorem3">Theorem 3 . Since the solution of the HJI equation is time-dependent for the augmented system, the time-dependent activation functions of NNs are considered. Moreover, an extra error is incorporated to satisfy the terminal constraints of cost function. This adaptive control pattern finds, in real time, approximations of the optimal value while also ensuring the uniform ultimate boundedness of the closed-loop system. Finally, the effectiveness of the proposed near-optimal control pattern is verified by two simulation examples. In this article, the neural network (NN)-based adaptive dynamic programming (ADP) event-triggered control method is presented to obtain the near-optimal control policy for the model-free finite-horizon H∞ optimal tracking control problem with constrained control input. First, using available input-output data, a data-driven model is established by a recurrent NN (RNN) to reconstruct the unknown system. Then, an augmented system with event-triggered mechanism is obtained by a tracking error system and a command generator. We present a novel event-triggering condition without Zeno behavior. On this basis, the relationship between event-triggered Hamilton-Jacobi-Isaacs (HJI) equation and time-triggered HJI equation is given in Theorem 3. Since the solution of the HJI equation is time-dependent for the augmented system, the time-dependent activation functions of NNs are considered. Moreover, an extra error is incorporated to satisfy the terminal constraints of cost function. This adaptive control pattern finds, in real time, approximations of the optimal value while also ensuring the uniform ultimate boundedness of the closed-loop system. Finally, the effectiveness of the proposed near-optimal control pattern is verified by two simulation examples.In this article, the neural network (NN)-based adaptive dynamic programming (ADP) event-triggered control method is presented to obtain the near-optimal control policy for the model-free finite-horizon H∞ optimal tracking control problem with constrained control input. First, using available input-output data, a data-driven model is established by a recurrent NN (RNN) to reconstruct the unknown system. Then, an augmented system with event-triggered mechanism is obtained by a tracking error system and a command generator. We present a novel event-triggering condition without Zeno behavior. On this basis, the relationship between event-triggered Hamilton-Jacobi-Isaacs (HJI) equation and time-triggered HJI equation is given in Theorem 3. Since the solution of the HJI equation is time-dependent for the augmented system, the time-dependent activation functions of NNs are considered. Moreover, an extra error is incorporated to satisfy the terminal constraints of cost function. This adaptive control pattern finds, in real time, approximations of the optimal value while also ensuring the uniform ultimate boundedness of the closed-loop system. Finally, the effectiveness of the proposed near-optimal control pattern is verified by two simulation examples.
Author	Yan, Yuqing Wang, Wei Ming, Zhongyang Zhang, Huaguang
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SubjectTerms	Adaptation models Adaptive control Adaptive dynamic programming (ADP) Artificial neural networks Closed loops Control methods Cost function data driven Dynamic programming event triggered Feedback control finite horizon H-infinity control Mathematical models Neural networks neural networks (NNs) Nonlinear systems Optimal control Power system dynamics Terminal constraints Time dependence Tracking control Tracking errors
Title	Data-Driven Finite-Horizon H∞ Tracking Control With Event-Triggered Mechanism for the Continuous-Time Nonlinear Systems
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