Square Root Attracting Laws With Application To Terminal Recurrent Neural Networks And Motor Control

Neural network calculation is a common method to solve problems such as time-varying matrix calculation and time-varying nonlinear equations.Problems such as manipulator trajectory planning can obtain ideal calculation results after neural network solution after conversion to optimization problem because of the terminal neural network has the characteristics of fast error convergence and finite time converge to zero while the asymptotic neural network not.And the attracting law is an equation that describes the convergence characteristics of systematic errors,and has the advantage of the error converges to the origin in finite time.So the motor system can resist the disturbance effectively while the square root attracting law is applied to the motor control.In this dissertation,the square root attracting law is applied to the termianl neural network and motor control.The neural calculation method and motor control algorithm are studied,and the simulation and motor experiments are carried out to demonstrate the effectiveness and wide application of the square root attracting law.The main work of this dissertation is as follows:(1)For the square root attracting law based on barrier function,parabolic function,elliptic function and root power function,the corresponding terminal recurrent neural network models are constructed.Their convergence characteristics are analyzed according to their respective activation function graphs respectively.And then the Stability analysis and derive the time when the error converges to zero.According to the solution of Lyapunov equation,different forms of terminal neural network models are constructed,and do the same work to the problem of ime-varying nonlinear equations.The simulation is compared with the asymptotic neural network method,and the error convergence time of the terminal neural network is calculated according to the formula.(2)For the repetitive motion planning problem of fixed manipulators,a repetitive motion planning scheme based on the terminal attracting factor is designed on the velocity layer,which the trajectory planning scheme is converted into a quadratic optimization problem and then the neural computation is performed.At the same time,for the Jacobian matrix of the manipulator,three solutions for calculating the Jacobian matrix are carried out,which is based on the mechanical structure to calculate the Jacobian matrix,the adaptive method to obtain the Jacobian matrix and the Jacobian matrix based on the extended state observer.The simulation verifies the feasibility and effectiveness of the proposed solution.(3)For the repetitive motion planning problem of the mobile manipulator,a repetitive motion planning scheme based on the termianl attracting factor is designed on the velocity layer.The Jacobian matrix of the moving part is obtained by the motion constraint equation,and the overall Jacobian matrix is obtained after the unified coordinate system of the fixed part of the Jacobian matrix.The effectiveness of the proposed scheme is verified by simulation.(4)A discrete repetitive control method of the square root attracting law is proposed to solve the periodic trajectory tracking problem in discrete time systems.This method can reduce the system chattering effectively.And futher,the disturbed expansion state observation technique is used to suppress the unknown disturbance of the system effectively,and the repeated control technology is used to eliminate the system periodic disturbance completely.To characterize the dynamic performance of the error,the expressions of the range of the steady state error,the absolute attraction layer,the boundary of the monotonically decreasing region,and the maximum steps of system error entering the range of the steady state error are derived.The permanent magnet synchronous motor system was built and the motor experiment was carried out to verify the effectiveness of the proposed method.