Modified Newton Integration Algorithm With Noise Tolerance for Discrete Algebraic Matrix Riccati Equation

Nowadays, the discrete algebraic matrix Riccati equation (DAMRE) is widely used in control system theory, engineering application, etc. In order to solve the problem with the high accuracy of DAMRE, a large number of researchers have achieved great success in theoretical analysis and actively explored methods. In addition, they have achieved great success in both theoretical analysis and practical investigation, and some actively explored methods or practical investigations have been very effective. However, since previous research has not considered noise tolerance, this may cause unacceptable results and unsatisfactory effectiveness in practical utilization scenarios. To this end, inspired by the traditional Newton-Raphson iterative (NRI) algorithm, a modified Newton integration (MNI) algorithm is proposed with excellent noise tolerance ability. Through theoretical analyses, the proposed MNI algorithm is confirmed to retain the fast convergence property of the NRI algorithm and also possess strong noise tolerance. The numerical experiment results demonstrate that the proposed MNI algorithm has advantages in accuracy and noise tolerance compared with other algorithms.