Abstract
Matrix inversion is commonly encountered in the field of mathematics. Therefore, many methods, including zeroing neural network (ZNN), are proposed to solve matrix inversion. Despite conventional fixed-parameter ZNN (FPZNN), which can successfully address the matrix inversion problem, it may focus on either convergence speed or robustness. So, to surmount this problem, a double accelerated convergence ZNN (DAZNN) with noise-suppression and arbitrary time convergence is proposed to settle the dynamic matrix inversion problem (DMIP). The double accelerated convergence of the DAZNN model is accomplished by specially designing exponential decay variable parameters and an exponential-type sign-bi-power activation function (AF). Additionally, two theory analyses verify the DAZNN model’s arbitrary time convergence and its robustness against additive bounded noise. A matrix inversion example is utilized to illustrate that the DAZNN model has better properties when it is devoted to handling DMIP, relative to conventional FPZNNs employing other six AFs. Lastly, a dynamic positioning example that employs the evolution formula of DAZNN model verifies its availability.
Highlights
As a fundamental mathematical issue, matrix inversion plays a crucial role in applied mathematics and engineering fields such as control application [1], quaternion [2], MIMO systems [3,4], and robot kinematics [5,6,7]
As opposed to the zeroing neural network (ZNN) generated by the original error function for the static matrix inversion, this work develops the double accelerated convergence ZNN (DAZNN) generated by a novel error function to solve dynamic matrix inversion; Two new exponential decay variable parameters and a novel exponential-type Sign-bi-power AF (SBPAF)
Are incorporated into the DAZNN model in order to achieve double accelerated convergence and more stronger noise suppression; Two rigorous theoretical analyses are employed in order to demonstrate the arbitrary time convergence of the DAZNN model as well as its robustness under additive bounded noise; The illustrative example confirms that the DAZNN model is superior to the fixedparameter model activated by other six activation functions
Summary
As a fundamental mathematical issue, matrix inversion plays a crucial role in applied mathematics and engineering fields such as control application [1], quaternion [2], MIMO systems [3,4], and robot kinematics [5,6,7]. The double accelerated convergence ZNN (DAZNN) is proposed as a new model for dealing with dynamic matrix inversion problem (DMIP) as it is characterized by noise-suppression and arbitrary time convergence. As opposed to the ZNN generated by the original error function for the static matrix inversion, this work develops the DAZNN generated by a novel error function to solve dynamic matrix inversion; Two new exponential decay variable parameters and a novel exponential-type SBPAF are incorporated into the DAZNN model in order to achieve double accelerated convergence and more stronger noise suppression; Two rigorous theoretical analyses are employed in order to demonstrate the arbitrary time convergence of the DAZNN model as well as its robustness under additive bounded noise; The illustrative example confirms that the DAZNN model is superior to the fixedparameter model activated by other six activation functions. The evolution formula of DAZNN model is applied to the AOA dynamic positioning with sine noise to illustrate the model’s availability further
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