Iterative learning tracking control for second‐order nonlinear hyperbolic impulsive partial differential systems
This paper studies the iterative learning control (ILC) for a class of second‐order nonlinear hyperbolic impulsive partial differential systems. Firstly, to follow the discontinuous desired output, a P‐type learning law is adopted, and sufficient conditions for the convergence of the tracking error...
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Published in | IET control theory & applications Vol. 17; no. 9; pp. 1227 - 1241 |
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Abstract | This paper studies the iterative learning control (ILC) for a class of second‐order nonlinear hyperbolic impulsive partial differential systems. Firstly, to follow the discontinuous desired output, a P‐type learning law is adopted, and sufficient conditions for the convergence of the tracking error is established under identified initial state value. The rigorous analysis is also given using the impulsive Gronwall inequality. Secondly, the tracking error of output trajectory is considered in systems with state initial values shifting based on an initial learning algorithm. These results of this paper show that the tracking error on the finite time interval can uniform converge to 0 as the iteration index goes to infinity if impulse number of the systems is only a finite numbers. Finally, two numerical simulation examples are given to verify the effectiveness of the theoretical results.
In this paper, iterative learning control is used to realize the accurate tracking of second‐order hyperbolic partial differential systems with impulsive effect. Considering the fixed initial state and the change of the initial state with the number of iterations. |
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AbstractList | This paper studies the iterative learning control (ILC) for a class of second‐order nonlinear hyperbolic impulsive partial differential systems. Firstly, to follow the discontinuous desired output, a P‐type learning law is adopted, and sufficient conditions for the convergence of the tracking error is established under identified initial state value. The rigorous analysis is also given using the impulsive Gronwall inequality. Secondly, the tracking error of output trajectory is considered in systems with state initial values shifting based on an initial learning algorithm. These results of this paper show that the tracking error on the finite time interval can uniform converge to 0 as the iteration index goes to infinity if impulse number of the systems is only a finite numbers. Finally, two numerical simulation examples are given to verify the effectiveness of the theoretical results.
In this paper, iterative learning control is used to realize the accurate tracking of second‐order hyperbolic partial differential systems with impulsive effect. Considering the fixed initial state and the change of the initial state with the number of iterations. This paper studies the iterative learning control (ILC) for a class of second‐order nonlinear hyperbolic impulsive partial differential systems. Firstly, to follow the discontinuous desired output, a P‐type learning law is adopted, and sufficient conditions for the convergence of the tracking error is established under identified initial state value. The rigorous analysis is also given using the impulsive Gronwall inequality. Secondly, the tracking error of output trajectory is considered in systems with state initial values shifting based on an initial learning algorithm. These results of this paper show that the tracking error on the finite time interval can uniform converge to 0 as the iteration index goes to infinity if impulse number of the systems is only a finite numbers. Finally, two numerical simulation examples are given to verify the effectiveness of the theoretical results. Abstract This paper studies the iterative learning control (ILC) for a class of second‐order nonlinear hyperbolic impulsive partial differential systems. Firstly, to follow the discontinuous desired output, a P‐type learning law is adopted, and sufficient conditions for the convergence of the tracking error is established under identified initial state value. The rigorous analysis is also given using the impulsive Gronwall inequality. Secondly, the tracking error of output trajectory is considered in systems with state initial values shifting based on an initial learning algorithm. These results of this paper show that the tracking error on the finite time interval can uniform converge to 0 as the iteration index goes to infinity if impulse number of the systems is only a finite numbers. Finally, two numerical simulation examples are given to verify the effectiveness of the theoretical results. Abstract This paper studies the iterative learning control (ILC) for a class of second‐order nonlinear hyperbolic impulsive partial differential systems. Firstly, to follow the discontinuous desired output, a P‐type learning law is adopted, and sufficient conditions for the convergence of the tracking error is established under identified initial state value. The rigorous analysis is also given using the impulsive Gronwall inequality. Secondly, the tracking error of output trajectory is considered in systems with state initial values shifting based on an initial learning algorithm. These results of this paper show that the tracking error on the finite time interval can uniform converge to 0 as the iteration index goes to infinity if impulse number of the systems is only a finite numbers. Finally, two numerical simulation examples are given to verify the effectiveness of the theoretical results. |
Author | Wu, Jing Zhang, Jianxiang Dai, Xisheng Zhou, Guopeng |
Author_xml | – sequence: 1 givenname: Xisheng orcidid: 0000-0002-1600-8176 surname: Dai fullname: Dai, Xisheng email: mathdxs@163.com organization: Hubei University of Science and Technology – sequence: 2 givenname: Jing surname: Wu fullname: Wu, Jing organization: Guangxi University of Science and Technology – sequence: 3 givenname: Jianxiang surname: Zhang fullname: Zhang, Jianxiang organization: Guangxi University of Science and Technology – sequence: 4 givenname: Guopeng surname: Zhou fullname: Zhou, Guopeng organization: Hubei University of Science and Technology |
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Autom. contributor: fullname: Norrlof M. – volume: 103 start-page: 38 year: 2019 ident: e_1_2_11_23_1 article-title: Robust control of a silicone soft robot using neural networks publication-title: ISA Trans. contributor: fullname: Zheng G. – volume: 6 start-page: 77 issue: 1 year: 1999 ident: e_1_2_11_9_1 article-title: Nonlinear impulsive evolution equations publication-title: Dyn. Contin., Discrete and Impulsive Syst. Ser. A: Math. Anal. contributor: fullname: Liu J. – ident: e_1_2_11_32_1 doi: 10.1016/j.cnsns.2014.12.002 – ident: e_1_2_11_16_1 doi: 10.1007/s10883-009-9068-x |
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Snippet | This paper studies the iterative learning control (ILC) for a class of second‐order nonlinear hyperbolic impulsive partial differential systems. Firstly, to... Abstract This paper studies the iterative learning control (ILC) for a class of second‐order nonlinear hyperbolic impulsive partial differential systems.... Abstract This paper studies the iterative learning control (ILC) for a class of second‐order nonlinear hyperbolic impulsive partial differential systems.... |
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StartPage | 1227 |
SubjectTerms | Algorithms Batch processing Control systems Energy consumption Error analysis iterative learning control Machine learning Nonlinear control Nonlinear systems Ordinary differential equations Partial differential equations System effectiveness tracking Tracking control Tracking errors Trajectory analysis |
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Title | Iterative learning tracking control for second‐order nonlinear hyperbolic impulsive partial differential systems |
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