A novel varying-parameter periodic rhythm neural network for solving time-varying matrix equation in finite energy noise environment and its application to robot arm

Solving matrix equation with noise interference is a challenging problem in mathematical and engineering applications. Unlike the traditional recurrent neural network, a novel varying-parameter periodic rhythm neural network (VP-PRNN) is proposed and used to solve the time-varying matrix equation in finite energy noise environment online. Particularly, VP-PRNN can enable the state solution to converge to the theoretical solution rapidly and robustly, which is also proved by theoretical analysis. Four kinds of noise are used to test the system, which proves the effectiveness of VP-PRNN. Compared with the zeroing neural network and circadian rhythms learning network with fixed parameters, VP-PRNN with variable parameters shows superior convergence performance in the disturbance of finite energy noise.