High-Throughput FPGA Implementation of Matrix Inversion for Control Systems

• Published in: IEEE transactions on industrial electronics (1982) Vol. 68; no. 7; pp. 6205 - 6216
• Main Authors: Zhang, Xiao-Wei, Zuo, Lei, Li, Ming, Guo, Jian-Xin
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Algorithms; Antenna arrays; Beamforming; Computation; Control stability; Field programmable gate arrays; Field-programmable gate array (FPGA); Hardware; Hermitian matrix; LDL factorization; Matrices (mathematics); Matrix decomposition; matrix inversion; Multiplication; Numerical stability; Phased arrays; Radar; Radar arrays; Robustness (mathematics)
• DOI: 10.1109/TIE.2020.2994865
• ISSN: 0278-0046

In control engineering, numerical stability and real time are the two most important requirements for the matrix inversion. This article presents an efficient and robust method for the field-programmable gate array (FPGA) calculation of the matrix inversion. We initially consider the scenario that the matrix to be processed is a nonsingular Hermitian matrix. The proposed computation procedures are composed of the matrix decomposition, triangular matrix inversion, and matrices multiplication. The first procedure is completed by LDL factorization based on the outer form of Cholesky's method, whereas the recursive algorithm for block submatrices is adopted to achieve the triangular matrix inversion. The new method has the high level in the parallel pipelining mechanism and steals the characteristics of both the upper triangular matrix and its inversion to reduce the computation load and improve the numerical stability. Furthermore, the non-Hermitian matrix inversion can be easily solved if another procedure is added in the new method. Finally, we compare our method with the exiting FPGA-based techniques on one Xilinx Virtex-7 XC7VX690T FPGA. Meanwhile, it has solved one array antenna control problem of the adaptive digital beam forming for one phased array radar successfully.