Inverse-free zeroing neural network for time-variant nonlinear optimization with manipulator applications

In this paper, the problem of time-variant optimization subject to nonlinear equation constraint is studied. To solve the challenging problem, methods based on the neural networks, such as zeroing neural network and gradient neural network, are commonly adopted due to their performance on handling n...

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Vydané v:	Neural networks Ročník 178; s. 106462
Hlavní autori:	Chen, Jielong, Pan, Yan, Zhang, Yunong, Li, Shuai, Tan, Ning
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	United States Elsevier Ltd 01.10.2024
Predmet:	Algorithms Computer Simulation Humans Inverse-free algorithm Low computational complexity Neural Networks, Computer Nonlinear Dynamics Robot control Robotics Time Factors Time-variant nonlinear optimization Zeroing neural network Time-variant nonlinear optimization Zeroing neural network Robot control Low computational complexity Inverse-free algorithm
ISSN:	0893-6080, 1879-2782, 1879-2782
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Abstract	In this paper, the problem of time-variant optimization subject to nonlinear equation constraint is studied. To solve the challenging problem, methods based on the neural networks, such as zeroing neural network and gradient neural network, are commonly adopted due to their performance on handling nonlinear problems. However, the traditional zeroing neural network algorithm requires computing the matrix inverse during the solving process, which is a complicated and time-consuming operation. Although the gradient neural network algorithm does not require computing the matrix inverse, its accuracy is not high enough. Therefore, a novel inverse-free zeroing neural network algorithm without matrix inverse is proposed in this paper. The proposed algorithm not only avoids the matrix inverse, but also avoids matrix multiplication, greatly reducing the computational complexity. In addition, detailed theoretical analyses of the convergence performance of the proposed algorithm is provided to guarantee its excellent capability in solving time-variant optimization problems. Numerical simulations and comparative experiments with traditional zeroing neural network and gradient neural network algorithms substantiate the accuracy and superiority of the novel inverse-free zeroing neural network algorithm. To further validate the performance of the novel inverse-free zeroing neural network algorithm in practical applications, path tracking tasks of three manipulators (i.e., Universal Robot 5, Franka Emika Panda, and Kinova JACO2 manipulators) are conducted, and the results verify the applicability of the proposed algorithm. •Time-variant nonlinear optimization subject to nonlinear equation constraint is concerned.•A novel inverse-free zeroing neural network for solving time-variant nonlinear optimization is proposed in this paper.•Detailed theoretical analyses substantiate the convergence performance of the algorithm.•The proposed inverse-free algorithm is verified by applications on multi-type manipulators.
AbstractList	In this paper, the problem of time-variant optimization subject to nonlinear equation constraint is studied. To solve the challenging problem, methods based on the neural networks, such as zeroing neural network and gradient neural network, are commonly adopted due to their performance on handling nonlinear problems. However, the traditional zeroing neural network algorithm requires computing the matrix inverse during the solving process, which is a complicated and time-consuming operation. Although the gradient neural network algorithm does not require computing the matrix inverse, its accuracy is not high enough. Therefore, a novel inverse-free zeroing neural network algorithm without matrix inverse is proposed in this paper. The proposed algorithm not only avoids the matrix inverse, but also avoids matrix multiplication, greatly reducing the computational complexity. In addition, detailed theoretical analyses of the convergence performance of the proposed algorithm is provided to guarantee its excellent capability in solving time-variant optimization problems. Numerical simulations and comparative experiments with traditional zeroing neural network and gradient neural network algorithms substantiate the accuracy and superiority of the novel inverse-free zeroing neural network algorithm. To further validate the performance of the novel inverse-free zeroing neural network algorithm in practical applications, path tracking tasks of three manipulators (i.e., Universal Robot 5, Franka Emika Panda, and Kinova JACO2 manipulators) are conducted, and the results verify the applicability of the proposed algorithm. In this paper, the problem of time-variant optimization subject to nonlinear equation constraint is studied. To solve the challenging problem, methods based on the neural networks, such as zeroing neural network and gradient neural network, are commonly adopted due to their performance on handling nonlinear problems. However, the traditional zeroing neural network algorithm requires computing the matrix inverse during the solving process, which is a complicated and time-consuming operation. Although the gradient neural network algorithm does not require computing the matrix inverse, its accuracy is not high enough. Therefore, a novel inverse-free zeroing neural network algorithm without matrix inverse is proposed in this paper. The proposed algorithm not only avoids the matrix inverse, but also avoids matrix multiplication, greatly reducing the computational complexity. In addition, detailed theoretical analyses of the convergence performance of the proposed algorithm is provided to guarantee its excellent capability in solving time-variant optimization problems. Numerical simulations and comparative experiments with traditional zeroing neural network and gradient neural network algorithms substantiate the accuracy and superiority of the novel inverse-free zeroing neural network algorithm. To further validate the performance of the novel inverse-free zeroing neural network algorithm in practical applications, path tracking tasks of three manipulators (i.e., Universal Robot 5, Franka Emika Panda, and Kinova JACO2 manipulators) are conducted, and the results verify the applicability of the proposed algorithm. •Time-variant nonlinear optimization subject to nonlinear equation constraint is concerned.•A novel inverse-free zeroing neural network for solving time-variant nonlinear optimization is proposed in this paper.•Detailed theoretical analyses substantiate the convergence performance of the algorithm.•The proposed inverse-free algorithm is verified by applications on multi-type manipulators. In this paper, the problem of time-variant optimization subject to nonlinear equation constraint is studied. To solve the challenging problem, methods based on the neural networks, such as zeroing neural network and gradient neural network, are commonly adopted due to their performance on handling nonlinear problems. However, the traditional zeroing neural network algorithm requires computing the matrix inverse during the solving process, which is a complicated and time-consuming operation. Although the gradient neural network algorithm does not require computing the matrix inverse, its accuracy is not high enough. Therefore, a novel inverse-free zeroing neural network algorithm without matrix inverse is proposed in this paper. The proposed algorithm not only avoids the matrix inverse, but also avoids matrix multiplication, greatly reducing the computational complexity. In addition, detailed theoretical analyses of the convergence performance of the proposed algorithm is provided to guarantee its excellent capability in solving time-variant optimization problems. Numerical simulations and comparative experiments with traditional zeroing neural network and gradient neural network algorithms substantiate the accuracy and superiority of the novel inverse-free zeroing neural network algorithm. To further validate the performance of the novel inverse-free zeroing neural network algorithm in practical applications, path tracking tasks of three manipulators (i.e., Universal Robot 5, Franka Emika Panda, and Kinova JACO2 manipulators) are conducted, and the results verify the applicability of the proposed algorithm.In this paper, the problem of time-variant optimization subject to nonlinear equation constraint is studied. To solve the challenging problem, methods based on the neural networks, such as zeroing neural network and gradient neural network, are commonly adopted due to their performance on handling nonlinear problems. However, the traditional zeroing neural network algorithm requires computing the matrix inverse during the solving process, which is a complicated and time-consuming operation. Although the gradient neural network algorithm does not require computing the matrix inverse, its accuracy is not high enough. Therefore, a novel inverse-free zeroing neural network algorithm without matrix inverse is proposed in this paper. The proposed algorithm not only avoids the matrix inverse, but also avoids matrix multiplication, greatly reducing the computational complexity. In addition, detailed theoretical analyses of the convergence performance of the proposed algorithm is provided to guarantee its excellent capability in solving time-variant optimization problems. Numerical simulations and comparative experiments with traditional zeroing neural network and gradient neural network algorithms substantiate the accuracy and superiority of the novel inverse-free zeroing neural network algorithm. To further validate the performance of the novel inverse-free zeroing neural network algorithm in practical applications, path tracking tasks of three manipulators (i.e., Universal Robot 5, Franka Emika Panda, and Kinova JACO2 manipulators) are conducted, and the results verify the applicability of the proposed algorithm.
ArticleNumber	106462
Author	Tan, Ning Chen, Jielong Li, Shuai Pan, Yan Zhang, Yunong
Author_xml	– sequence: 1 givenname: Jielong surname: Chen fullname: Chen, Jielong email: chenjlong5@mail2.sysu.edu.cn organization: School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China – sequence: 2 givenname: Yan surname: Pan fullname: Pan, Yan email: panyan5@mail.sysu.edu.cn organization: School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China – sequence: 3 givenname: Yunong surname: Zhang fullname: Zhang, Yunong email: zhynong@mail.sysu.edu.cn organization: School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China – sequence: 4 givenname: Shuai surname: Li fullname: Li, Shuai email: shuai.li@oulu.fi organization: Faculty of Information Technology and Electrical Engineering, University of Oulu, Oulu 905706, Finland – sequence: 5 givenname: Ning orcidid: 0000-0003-0710-6409 surname: Tan fullname: Tan, Ning email: tann5@mail.sysu.edu.cn organization: School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China
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Keywords	Time-variant nonlinear optimization Zeroing neural network Robot control Low computational complexity Inverse-free algorithm
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Snippet	In this paper, the problem of time-variant optimization subject to nonlinear equation constraint is studied. To solve the challenging problem, methods based on...
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SubjectTerms	Algorithms Computer Simulation Humans Inverse-free algorithm Low computational complexity Neural Networks, Computer Nonlinear Dynamics Robot control Robotics Time Factors Time-variant nonlinear optimization Zeroing neural network
Title	Inverse-free zeroing neural network for time-variant nonlinear optimization with manipulator applications
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