High-Throughput FPGA Implementation of Matrix Inversion for Control Systems
In control engineering, numerical stablility and real-time are the two most important requirements for the matrix inversion. This paper presents an efficient and robust method for the field-programmable gate array (FPGA) calculation of the matrix inversion. We initially con- sider the scenario that the matrix to be processed is a non- singular Hermitian matrix. The proposed computation pro- cedures are composed of the matrix decomposition, triang- ular matrix inversion and matrices multiplication. The first procedure is completed by LDL factorization based on the outer form of Cholesky‚??s method, while the recursive algorithm for block sub-matrices 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.
Field-programmable gate array (FPGA), LDL factorization, Hermitian matrix, Matrix inversion.