Abstract: Conventional computing methods,by using recurrent neural networks,ensure the asymptotic convergence of the computing error such that the error converges to zero and the exact solution can be obtained as time approaches infinity.In this paper,a novel model of terminal recurrent neural networks was presented to address online computation problems arising from time-varying matrices.Such kind of network model is of the characteristics of the limited values of the right-hand side function and the finite settling time.Firstly,the shortcoming of asymptotically convergent network models in solving time-varying computational problems is analyzed,and the necessity of introducing the terminal network models is given.Then,the dynamics of the terminal network is characterized with the derivation for the expression of the settling time.For solving the problems of inverse and genera-lized inverses of time-varying matrices,an error function is defined,a terminal recurrent neural network is constructed based on the error function,so that the accurate solution can be achieved.For the path planning of industrial manipulators,the end effector tracks the closed trajectory by applying the terminal neural network,the joint angle returns to the initial position,and the repetitive motion is conducted in the presence of arbitrary initial position.MATLAB/SIMULINK is used for simulation of solving time-varying matrix computing problems and trajectory planning tasks of manipulators.By comparing the results obtained by the asymptotic network and the terminal network,it can be seen that the computing process using the terminal network converges in finite time and the computing accuracy is improved significantly.The presented solutions for different time-varying computing problems exhibit the applicability of the proposed terminal networks.

Key words: Generalized inverses, Industrial manipulators, Inverse matrix, Path planning, Terminal neural networks