Computer Science

Computer Science ›› 2024, Vol. 51 ›› Issue (8): 324-332.doi: 10.11896/jsjkx.230500052

• Artificial Intelligence • Previous Articles     Next Articles

Fixed-time Recurrent Neural Networks for Time-variant Matrix Computing and Its Application in Repeatable Motion Planning

LI Xing, ZHONG Guomin   

  1. College of Information Engineering,Zhejiang University of Technology,Hangzhou 310023,China
  • Received:2023-05-09 Revised:2023-10-12 Online:2024-08-15 Published:2024-08-13
  • About author:LI Xing, born in 1994,Ph.D.Her main research interests include neural networks and robotics.
    ZHONG Guomin,born in 1983,Ph.D,lecturer.His main research interests include iterative learning algorithms and neural networks.
  • Supported by:
    National Natural Science Foundation of China(62073291).

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Abstract: Fixed-time recurrent neural network(RNN) models with logarithmic settling time are proposed for solving time-variant neural computing problems.Two novel RNN models are designed and analyzed in detail,deriving the explicit expressions of settling time functions and providing the upper bounds of the settling times under any initial condition.Compared with the existing RNN models with fixed-time convergence,the two novel models with logarithmic settling time have a smaller upper bound on the settling time and faster convergence speeds.Taking into account initial conditions located within a region with a definite finite radius,the settling time functions of the RNN models with logarithmic settling time are given,and the upper bounds on the settling time functions in the semi-global sense are derived.Modified RNN models adopt the inverse of the bound to ensure that the semi-global predefined time converges to the exact solution,and its prescribed time is an adjustable parameter.Simulation results of the proposed RNN model for solving time-variant Lyapunov and Sylvester equations are given.The proposed RNNs are applied to the repetitive motion planning of a redundant manipulator with initial errors,and numerical results are presented to verify the effectiveness of the proposed RNN models.

Key words: Time-variant neural computing, Logarithmic settling time, Fixed/predefined-time convergence, Industrial manipulators, Repetitive motion planning

CLC Number: 

  • TP241
[1]MANHERZ R,JORDAN B,HAKIMI S.Analog methods forcomputation of the generalized inverse[J].IEEE Transactions on Automatic Control,1968,13(5):582-585.
[2]ZHANG Y N,YI C.Zhang neural networks and neural-dynamic method[M].New York:Nova Science Publishers,2011.
[3]HOPFIELD J J.Neurons with graded response have collectivecomputational properties like those of two-state neurons[J].Proceedings of the National Academy of Sciences,1984,81(10):3088-3092.
[4]CICHOCKI A,UNBEHAUEN R.Neural networks for solving systems of linear equation and related problems[J].IEEE Transactions on Circuits and Systems,1992,39(2):124-138.
[5]WANG J.Recurrent neural networks for solving linear matrixequations[J].Computers and Mathematics with Applications,1993,26(9):23-34.
[6]KENNEDY M,CHUA L.Neural networks for nonlinear pro-gramming[J].IEEE Transactions on Circuits and Systems,1988,35(5):554-562.
[7]MAA C Y,SHANBLATT M A.Linear and quadratic programming neural network analysis[J].IEEE Transactions on Neural Networks,1992,3(4):580-594.
[8]CHENG F,CHEN T,SUN Y.Resolving manipulator redundancy under inequality constraints[J].IEEE Transactions on Robotics and Automation,1994,10(1):65-71.
[9]KLEIN C A,KEE K B.The nature of drift in pseudoinversecontrol of kinematically redundant manipulators[J].IEEE Transactions on Robotics and Automation,1989,5(2):231-234.
[10]ZHANG Y N,TAN Z G,YANG Z,et al.Seif motion of planar redundant manipulator based on quadratic programming [J].Chinese Journal of Robot,2008,3(6):566-571.
[11]ZHANG Y N,JIANG D,WANG J.A recurrent neural network for solving Sylvester equation with time-varying coefficients[J].IEEE Transactions on Neural Networks,2002,13(5):1053-1063.
[12]ZHANG Y N,WANG J,XIA Y.A dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limits[J].IEEE Tran-sactions on Neural Networks,2003,14(3):658-667.
[13]ZHANG Y N,GE S.Design and analysis of a general recurrent neural network model for time-varying matrix inversion[J].IEEE Transactions on Neural Networks,2005,16(6):1477-1490.
[14]LI S,CHEN S,LIU B.Accelerating a recurrent neural network to finite-time convergence for solving time-varying Sylvesterequation by using a sign-bi-power activation function[J].Neural Processing Letters,2013,37:189-205.
[15]LI W B.A recurrent neural network with explicitly definableconvergence time for solving time-variant linear matrix equations[J].IEEE Transactions on Industrial Informatics,2018,14(12):5289-5298.
[16]XIAO L,LIAO B,LI S,et al.Design and analysis of FTZNN applied to the real-time solution of a nonstationary Lyapunov equation and tracking control of a wheeled mobile manipulator[J].IEEE Transactions on Industrial Informatics,2018,14(5):98-105.
[17]XIAO L,ZHANG Y N,HU Z,et al.Performance benefits of robust nonlinear zeroing neural network for finding accurate solution of Lyapunov equation in presence of various noises[J].IEEE Transactions on Industrial Informatics,2019,15(9):5161-5171.
[18]LI W B.Design and analysis of a novel finite-time convergent and noise tolerant recurrent neural network for time-variant matrix inversion[J].IEEE Transactions on Systems,Man,and Cybernetics:Systems,2020,50(11):4362-4376.
[19]XIAO L,LI K l,DUAN M.Computing time-varying quadraticoptimization with finite-time convergence and noise tolerance:a unified framework for zeroing neural network[J].IEEE Tran-sactions on Neural Networks and Learning Systems,2019,30(11):3360-3369.
[20]SUN M X,WENG D E,ZHNG Y.Time-variant neurocomputing with finite-value terminal recurrent neural networks [J].Computer Science,2020,47(1):212-218.
[21]SUN M X,ZHANG Y,WU Y X,et al.On a finitely-activatedterminal RNN approach to time-variant problem solving[J].IEEE Transactions on Neural Networks and Learning Systems,2022,33(12):7289-7302.
[22]POLYAKOV A.Nonlinear feedback design for fixed-time stabilization of linear control systems[J].IEEE Transactions on Automatic Control,2012,57(8):2106-2110.
[23]SUN M X,LI X,ZHONG G M.Semi-global fixed/predefined-time RNN models with comprehensive comparisons for time-variant neural computing[J].Neural Computing and Applications,2023,35:1675-1693.
[24]SANCHEZ-TORRES J D,SANCHEZ E N,LOUKIANOV AG.Predefined-time stability of dynamical systems with sliding modes[C]//Proceedings of American Control Conference.Chicago,IL,2015:5842-5846.
[25]XIAO L,ZHANG Y N,HU Z,et al.Performance benefits of ro-bust nonlinear zeroing neural network for finding accurate solution of Lyapunovequation in presence of various noises[J].IEEE Transactions on Industrial Informatics,2019,15(9):5161-5171.
[26]XIAO L,CAO Y,DAI J H,et al.Finite-Time and predefined-time convergence design for zeroing neural network:theorem,method,and verification[J].IEEE Transactions on Industrial Informatics,2021,17(7):4724-4732.
[27]LI W B.Predefined-time convergent neural solution to cyclical motion planning of redundant robots under physical constraints[J].IEEE Transactions on Industrial Electronics.2020,67(12):10732-10743.
[28]JIMENEZ-RODRIGUEZ E,SANCHEZ-TORRES J D,LOUKIANOV A G.Semi-global predefined time stable vector systems [C]//Proceedings of IEEE Conference on Decision and Control.Miami Beach,FL,2018:4809-4814.
[1] SUN Ming-xuan,WENG Ding-en,ZHANG Yu. Time-variant Neurocomputing with Finite-value Terminal Recurrent Neural Networks [J]. Computer Science, 2020, 47(1): 212-218.
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