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Noise-suppressing zeroing neural network for online solving time-varying nonlinear optimization problem: a control-based approach

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Abstract

Time-varying nonlinear optimization problems with different noises often arise in the fields of scientific and engineering research. Noises are unavoidable in the practical workspace, but the most existing models for time-varying nonlinear optimization problems carry out with one assume that the computing process is free of noises. In this paper, from a control-theoretical framework, noise-suppressing zeroing neural dynamic (NSZND) model is developed, analyzed and investigated by feat of continuous-time zeroing neural network model, which behaves efficiently for hurdling online time-varying nonlinear optimization problems with the presence of different noises. Further, for speeding the rate of convergence, general noise-suppressing zeroing neural network (GNSZNN) model with different activation functions is discussed. Then, theoretical analyses show that the proposed noise-suppressing zeroing neural network model derived from NSZND model has the global convergence property in the presence of different kinds of noises. Besides, how GNSZNN model performs with different activation functions is also proved in detail. In addition, numerical results are provided to substantiate the feasibility and superiority of GNSZNN model for online time-varying nonlinear optimization problems with inherent tolerance to noises.

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References

  1. Yang Y, Zhang Y (2013) Superior robustness of power-sum activation functions in Zhang neural networks for time-varying quadratic programs perturbed with large implementation errors. Neural Comput Appl 22:175–185

    Article  Google Scholar 

  2. Zhang Y, Yang Y, Cai B, Guo D (2012) Zhang neural network and its application to Newton iteration for matrix square root estimation. Neural Comput Appl 21:453–460

    Article  Google Scholar 

  3. Andrei N (2018) An adaptive scaled BFGS method for unconstrained optimization. Numer Algorithms 77(2):413–432

    Article  MathSciNet  MATH  Google Scholar 

  4. Abubakar AB, Kumam P (2019) A descent Dai-Liao conjugate gradient method for nonlinear equations. Numer Algorithms 81(1):197–210

    Article  MathSciNet  MATH  Google Scholar 

  5. Sun ZB, Tian YT, Wang J (2018) A novel projected Fletcher–Reeves conjugate gradient approach for finite-time optimal robust controller of linear constraints optimization problem: application to bipedal walking robots. Optim Control Appl Methods 39(1):130–159

    Article  MathSciNet  MATH  Google Scholar 

  6. Sun ZB, Sun YY, Li Y, Liu KP (2019) A new trust region-sequential quadratic programming approach for nonlinear systems based on nonlinear model predictive control. Eng Optim 51(6):1071–1096

    Article  MathSciNet  Google Scholar 

  7. Jin L, Li S, La H, Zhang X, Hu B (2019) Dynamic task allocation in multi-robot coordination for moving target tracking: a distributed approach. Automatica 100:75–81

    Article  MathSciNet  MATH  Google Scholar 

  8. Jin L, Li S, Luo X, Li Y, Qin B (2018) Neural dynamics for cooperative control of redundant robot manipulators. IEEE Trans Ind Inform 14:3812–3821

    Article  Google Scholar 

  9. Livieris IE, Tampakas V, Pintelas P (2018) A descent hybrid conjugate gradient method based on the memoryless BFGS update. Numer Algorithms 79(4):1169–1185

    Article  MathSciNet  MATH  Google Scholar 

  10. Andrei N (2018) A Dai-Liao conjugate gradient algorithm with clustering of eigenvalues. Numer Algorithms 77(4):1273–1282

    Article  MathSciNet  MATH  Google Scholar 

  11. Dai YH, Liao LZ (2001) New conjugacy conditions and related nonlinear conjugate gradient methods. Appl. Math Optim 43(1):87–101

    Article  MathSciNet  MATH  Google Scholar 

  12. Andrei N (2013) On three-term conjugate gradient algorithms for unconstrained optimization. Appl Math Comput 219:6316–6327

    MathSciNet  MATH  Google Scholar 

  13. Liu JK, Li SJ (2014) New three-term conjugate gradient method with guaranteed global convergence. Int J Comput Math 91(8):1744–1754

    Article  MathSciNet  MATH  Google Scholar 

  14. Sun ZB, Li HY, Wang J, Tian YT (2018) Two modified spectral conjugate gradient methods and their global convergence for unconstrained optimization. Int J Comput Math 95(10):2082–2099

    Article  MathSciNet  Google Scholar 

  15. Huang XJ, Cui BT (2018) A neural dynamic system for solving convex nonlinear optimization problems with hybrid constraints. Neural Comput Appl 31:6027–6038. https://doi.org/10.1007/s00521-018-3422-4

    Article  Google Scholar 

  16. Jin L, Zhang YN, Qiu BB (2018) Neural network-based discrete-time Z-type model of high accuracy in noisy environments for solving dynamic system of linear equations. Neural Comput Appl 29:1217–1232

    Article  Google Scholar 

  17. Li S, Cui H, Li Y, Liu B, Lou Y (2013) Decentralized control of collaborative redundant manipulators with partial command coverage via locally connected recurrent neural networks. Neural Comput Appl 23:1051–1060

    Article  Google Scholar 

  18. Xie Z, Jin L, Du X, Xiao X, Li H, Li S (2019) On generalized RMP scheme for redundant robot manipulators aided with dynamic neural networks and nonconvex bound constraints. IEEE Trans Ind Inform 15:5172–5181. https://doi.org/10.1109/TII.2019.2899909

    Article  Google Scholar 

  19. Liao L, Qi H, Qi L (2004) Neurodynamical optimization. J Global Optim 28(2):175–195

    Article  MathSciNet  MATH  Google Scholar 

  20. Jin L, Li S (2017) Nonconvex function activated zeroing neural network models for dynamic quadratic programming subject to equality and inequality constraints. Neurocomputing 267:107–113

    Article  Google Scholar 

  21. Jin L, Zhang YN (2016) Continuous and discrete Zhang dynamics for real-time varying nonlinear optimization. Numer Algorithms 73(1):115–140

    Article  MathSciNet  MATH  Google Scholar 

  22. Qi YM, Jin L, Wang YN, Xiao L, Zhang JL (2019) Complex-valued discrete-time neural dynamics for perturbed time-dependent complex quadratic programming with applications. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2019.2944992

    Article  Google Scholar 

  23. Wei L, Jin L, Yang CG, Chen K, Li WB (2019) New noise-tolerant neural algorithms for future dynamic nonlinear optimization with estimation on Hessian matrix inversion. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2019.2916892

    Article  Google Scholar 

  24. Jin L, Zhang YN, Li S, Zhang YY (2016) Modified ZNN for time-varying quadratic programming with inherent tolerance to noises and its application to kinematic redundancy resolution of robot manipulators. IEEE Trans Ind Electron 63(11):6978–6988

    Article  Google Scholar 

  25. Zhang Z, Zheng L, Li L, Deng X, Xiao L, Huang G (2018) A new finite-time varying-parameter convergent-differential neural-network for solving nonlinear and nonconvex optimization problems. Neurocomputing. https://doi.org/10.1016/j.neucom.2018.07.005

    Article  Google Scholar 

  26. Huang B, Hui G, Gong D, Wang ZS, Meng XP (2014) A projection neural network with mixed delays for solving linear variational inequality. Neurocomputing 125(11):28–32

    Article  Google Scholar 

  27. Zhang S, Xia Y, Zheng W (2015) A complex-valued neural dynamical optimization approach and its stability analysis. Neural Netw 61:59–67

    Article  MATH  Google Scholar 

  28. Zhang Y, Guo D (2015) Zhang functions and various models. Springer, Berlin

    Book  MATH  Google Scholar 

  29. Zhang Z, Zhang YN (2013) Design and experimentation of acceleration-level drift-free scheme aided by two recurrent neural networks. IET Control Theory Appl. 7:25–42

    Article  MathSciNet  Google Scholar 

  30. Oppenheim AV, Willsky AS (1997) Signals and systems. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  31. Zhang Y, Li Z (2009) Zhang neural network for online solution of time-varying convex quadratic program subject to time-varying linear-equality constraints. Phys Lett A 373(18–19):1639–1643

    Article  MATH  Google Scholar 

  32. Zhang Y, Yi C (2011) Zhang neural networks and neural-dynamic method. Nova Science Publishers, Hauppauge

    Google Scholar 

  33. Mathews JH, Fink KD (2005) Numerical methods using MATLAB. Prentice-Hall Inc, Englewood Cliffs

    Google Scholar 

  34. Martínez JM, Prudente LF (2012) Handling infeasibility in a large-scale nonlinear optimization algorithm. Numer Algorithms 60(2):263–277

    Article  MathSciNet  MATH  Google Scholar 

  35. Jin L, Li S, Xiao L, Lu RB, Liao BL (2018) Cooperative motion generation in a distributed network of redundant robot manipulators with noises. IEEE Trans Syst Man Cybern Syst 48(10):1715–1724

    Article  Google Scholar 

  36. Jin L, Zhang YN (2015) Discrete-time Zhang neural network for online time-varying nonlinear optimization with application to manipulator motion generation. IEEE Trans Neural Netw Learn Syst 26(7):1525–1531

    Article  MathSciNet  Google Scholar 

  37. Zhang J, Fiers P, Witte KA et al (2017) Human-in-the-loop optimization of exoskeleton assistance during walking. Science 356:1280–1284

    Article  Google Scholar 

  38. Rifaï H, Mohammed S, Djouani K, Amirat Y (2017) Toward lower limbs functional rehabilitation through a knee-joint exoskeleton. IEEE Trans Control Syst Technol 25:712–719

    Article  Google Scholar 

  39. Wang WQ, Hou ZG, Cheng L, Tong LN, Peng L, Tan M (2016) Toward patients’ motion intention recognition: dynamics modeling and identification of iLeg—an LLRR under motion constraints. IEEE Trans Syst Man Cybern Syst 46:980–992

    Article  Google Scholar 

  40. Shen P, Zhang X, Fang Y (2018) Complete and time-optimal path-constrained trajectory planning with torque and velocity constraints: theory and applications. IEEE/ASME Trans Mech 23:735–746

    Article  Google Scholar 

  41. Zhang X, Chen X, Farzadpour F, Fang Y (2018) A visual distance approach for multi-camera deployment with coverage optimization. IEEE/ASME Trans Mech 23:1007–1018

    Article  Google Scholar 

  42. Sun ZB, Li F, Zhang BC, Sun YY, Jin L (2019) Different modified zeroing neural dynamics with inherent tolerance to noises for time-varying reciprocal problems: a control-theoretic approach. Neurocomputing 337:165–179

    Article  Google Scholar 

Download references

Funding

The work is supported in part by the National Natural Science Foundation of China under Grants 61873304, 11701209 and 51875047, and also in part by the China Postdoctoral Science Foundation Funded Project under Grant 2018M641784, 2019T120240 and also in part by the Key Science and Technology Projects of Jilin Province, China, Grant Nos. 20190302025GX, 20170204067GX, and 20180201105GX and also in part by the Industrial Innovation Special Funds Project of Jilin Province, China, Grant No. 2018C038-2 and also in part by the Jilin Engineering Laboratory for Intelligence Robot and Visual Measurement Technology, Grant No. 2019C010 and also in part by the Fundamental Research Funds for the Central Universities (No. lzujbky-2019-89).

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Authors and Affiliations

  1. Department of Control Engineering, Changchun University of Technology, Changchun, 130012, China

    Zhongbo Sun & Keping Liu

  2. Key Laboratory of Bionic Engineering of Ministry of Education, Jilin University, Changchun, 130025, China

    Zhongbo Sun

  3. College of Communication Engineering, Jilin University, Changchun, 130025, China

    Tian Shi

  4. School of Information Science and Engineering, Lanzhou University, Lanzhou, 730000, China

    Lin Wei & Long Jin

  5. School of Information Technology, Jilin Agricultural University, Changchun, 130117, China

    Yingyi Sun

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  1. Zhongbo Sun
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  2. Tian Shi
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  3. Lin Wei
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  4. Yingyi Sun
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  5. Keping Liu
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  6. Long Jin
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Correspondence to Keping Liu.

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Sun, Z., Shi, T., Wei, L. et al. Noise-suppressing zeroing neural network for online solving time-varying nonlinear optimization problem: a control-based approach. Neural Comput & Applic 32, 11505–11520 (2020). https://doi.org/10.1007/s00521-019-04639-2

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