Supplementary Control for Quantized Discrete-Time Nonlinear Systems Under Goal Representation Heuristic Dynamic Programming

This article is concerned with supplementary control of discrete-time nonlinear systems with multiple controllers in the framework of goal representation heuristic dynamic programming (GrHDP), where a logarithmic quantizer is used to govern the network communication. For the addressed problem, a neu...

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Veröffentlicht in:	IEEE transaction on neural networks and learning systems Jg. 35; H. 3; S. 3202 - 3214
Hauptverfasser:	Wang, Xueli, Ding, Derui, Ge, Xiaohua, Han, Qing-Long
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	United States IEEE 01.03.2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algorithms Artificial neural networks Control systems Control tasks Discrete time systems Dynamic programming Dynamic stability Frequency modulation Goal programming Goal representation heuristic dynamic programming (GrHDP) Hamilton–Jacobi–Isaacs (HJI) equation Heuristic Neural networks Nonlinear control Nonlinear systems Observers Power system stability Problem solving quantization Quantization (signal) Representations supplementary control System performance Zero sum games
ISSN:	2162-237X, 2162-2388, 2162-2388
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Abstract	This article is concerned with supplementary control of discrete-time nonlinear systems with multiple controllers in the framework of goal representation heuristic dynamic programming (GrHDP), where a logarithmic quantizer is used to govern the network communication. For the addressed problem, a neural network (NN)-based observer is first proposed to estimate the unknown system state in the simultaneous presence of quantized influence. In light of the estimated states and the ideal control inputs via a zero-sum game, a GrHDP algorithm with a reinforced term is developed to implement the supplementary control task, where some novel weight updating rules are constructed by virtue of an additional tunable parameter to improve the system performance. Furthermore, a set of conditions about the stability of estimated error dynamics of both observer states and updated NNs' weights are derived by resorting to the Lyapunov stability theory. Finally, the effectiveness of the developed method is verified by a power system and a numerical experiment.
AbstractList	This article is concerned with supplementary control of discrete-time nonlinear systems with multiple controllers in the framework of goal representation heuristic dynamic programming (GrHDP), where a logarithmic quantizer is used to govern the network communication. For the addressed problem, a neural network (NN)-based observer is first proposed to estimate the unknown system state in the simultaneous presence of quantized influence. In light of the estimated states and the ideal control inputs via a zero-sum game, a GrHDP algorithm with a reinforced term is developed to implement the supplementary control task, where some novel weight updating rules are constructed by virtue of an additional tunable parameter to improve the system performance. Furthermore, a set of conditions about the stability of estimated error dynamics of both observer states and updated NNs’ weights are derived by resorting to the Lyapunov stability theory. Finally, the effectiveness of the developed method is verified by a power system and a numerical experiment. This article is concerned with supplementary control of discrete-time nonlinear systems with multiple controllers in the framework of goal representation heuristic dynamic programming (GrHDP), where a logarithmic quantizer is used to govern the network communication. For the addressed problem, a neural network (NN)-based observer is first proposed to estimate the unknown system state in the simultaneous presence of quantized influence. In light of the estimated states and the ideal control inputs via a zero-sum game, a GrHDP algorithm with a reinforced term is developed to implement the supplementary control task, where some novel weight updating rules are constructed by virtue of an additional tunable parameter to improve the system performance. Furthermore, a set of conditions about the stability of estimated error dynamics of both observer states and updated NNs' weights are derived by resorting to the Lyapunov stability theory. Finally, the effectiveness of the developed method is verified by a power system and a numerical experiment.This article is concerned with supplementary control of discrete-time nonlinear systems with multiple controllers in the framework of goal representation heuristic dynamic programming (GrHDP), where a logarithmic quantizer is used to govern the network communication. For the addressed problem, a neural network (NN)-based observer is first proposed to estimate the unknown system state in the simultaneous presence of quantized influence. In light of the estimated states and the ideal control inputs via a zero-sum game, a GrHDP algorithm with a reinforced term is developed to implement the supplementary control task, where some novel weight updating rules are constructed by virtue of an additional tunable parameter to improve the system performance. Furthermore, a set of conditions about the stability of estimated error dynamics of both observer states and updated NNs' weights are derived by resorting to the Lyapunov stability theory. Finally, the effectiveness of the developed method is verified by a power system and a numerical experiment.
Author	Ding, Derui Han, Qing-Long Wang, Xueli Ge, Xiaohua
Author_xml	– sequence: 1 givenname: Xueli surname: Wang fullname: Wang, Xueli email: xuelywang@163.com organization: Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai, China – sequence: 2 givenname: Derui orcidid: 0000-0001-7402-6682 surname: Ding fullname: Ding, Derui email: deruiding2010@usst.edu.cn organization: Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai, China – sequence: 3 givenname: Xiaohua orcidid: 0000-0003-0180-0897 surname: Ge fullname: Ge, Xiaohua email: xge@swin.edu.au organization: School of Science, Computing and Engineering Technologies, Swinburne University of Technology, Melbourne, VIC, Australia – sequence: 4 givenname: Qing-Long orcidid: 0000-0002-7207-0716 surname: Han fullname: Han, Qing-Long email: qhan@swin.edu.au organization: School of Science, Computing and Engineering Technologies, Swinburne University of Technology, Melbourne, VIC, Australia
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SubjectTerms	Algorithms Artificial neural networks Control systems Control tasks Discrete time systems Dynamic programming Dynamic stability Frequency modulation Goal programming Goal representation heuristic dynamic programming (GrHDP) Hamilton–Jacobi–Isaacs (HJI) equation Heuristic Neural networks Nonlinear control Nonlinear systems Observers Power system stability Problem solving quantization Quantization (signal) Representations supplementary control System performance Zero sum games
Title	Supplementary Control for Quantized Discrete-Time Nonlinear Systems Under Goal Representation Heuristic Dynamic Programming
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