The Research On Robustness Of ZNN For Solving Time-varying Matrix Problems And Its Applications

Matrix problems have been closely integrated with many research directions in computer science.Among these matrix problems,the time-varying matrix problems are very special in that their input data and solutions change continuously with time.When solving time-varying matrix problems,traditional numerical algorithms cannot meet the real-time requirements because of their high time complexity,while the gradient neural network's time lag error is persisted because of not considering the matrix change rate.Zeroing neural network(ZNN)is a superior solution to the time-varying matrix problem by using matrix-based error indicator and parameter derivative compensation.For solving the time-varying matrix problem,this paper focuses on analyzing and enhancing the robustness of ZNN after being contaminated by noise,i.e.,noise resistence,and making ZNN robustness and fast convergence coexist.Finally,this paper applies those research results in practical applications such as robot manipulator control.The main work of this paper are as follows:(1)Aiming at solving the time-varying Moore-Penrose pseudoinverse,this paper designs the traditional ZNN(TZNN).TZNN uses the simplified finite-time convergent activation function,making its convergence rate faster than that provided by common functions.This paper finds TZNN's stable error upper bound under time-varying noise,confirming that the robustness of TZNN is related to activation function,noise size,etc.The finite-time convergent activation function not only affects TZNN's convergence speed but also enhances its noise resistence.Then,the redundant planar robot manipulator inverse kinematic control is achieved by using TZNN.(2)In order to solve the more generalized time-varying Lyapunov equation,this paper develops the noise-resistant finite-time convergent ZNN(NRFZNN).In this paper,an integral term is introduced into the NRFZNN neurodynamic equation to correct the cumulative error so that it can resist fixed noise without loss and maintain a low level of steady-state error against linearly increasing noise.In contrast,TZNN is completely disturbed by constant noise.The noise-tolerant ZNN(NTZNN)also performs weaker than NRFZNN under linear noise.Moreover,NTZNN converges slower than NRFZNN.(3)This paper proposes the predefined-time convergent and noise-resistant ZNN(PNRZNN)for solving the time-varying quadratic programming,so that the problems solved by ZNN are no longer restricted to matrix equality equations.This paper proves that PNRZNN has the same level of noise resistence as NRFZNN.On the other hand,PNRZNN's predefined convergence time can be set precisely and is more reliable than that of NRFZNN.This paper then applies PNRZNN in two tasks,motion-constrained robot manipulator path tracking and image fusion noise reduction,demonstrating the outstanding performance of ZNN in practical usage.(4)This paper studies and proposes the Adams-type integration-enhanced discrete-time zeroing neural dynamic(AIDTZD)that can solve the time-varying complex Sylvester equation.Unlike TZNN,NRFZNN and PNRZNN,the AIDTZD model running in a computer enhances ZNN's robustness from the working environment perspective.AIDTZD models with and without parametric derivatives are developed separately in this paper to meet different requirements.Furthermore,AIDTZD has higher accuracy(about O(?5))but lower computational complexity than the conventional discrete-time ZNN.To suppress noise from input data,AIDTZD also uses integral reinforcement and the results show that AIDTZD robustness is indeed enhanced.