A Riccati Matrix Equation Solver Design Based Neurodynamics Method and Its Application
Pingdan Xiao, Junjie Fang, Zhengmiao Wei, Yu Dong, Sichun Du, Shiping Wen, Qinghui Hong
Abstract
Riccati matrix equation (RME), a critical nonlinear matrix equation in autonomous driving and deep learning. However, memory-compute separation in traditional solving systems leads to latency and inefficiency when solving nonlinear equations, particularly under real-time requirements. Existing hardware lacks dedicated accelerators for RME, no specialized solvers quick addressing its nonlinear complexity. To address this issue, we propose a novel RME solver based on a memristive array, which leverages the parallel and fast computing advantages of analog circuits to quickly solve any order RME. Inspired by Neurodynamics for non-linear matrix equations, we first introduce an innovative Neurodynamics-based RME solving algorithm specifically designed from an analog circuit perspective. Based on this algorithm, we constructed a pioneering closed-loop analog circuit solver, overcoming bottlenecks in using circuits for such nonlinear matrix equations. Our evaluation demonstrates that the proposed solver achieves over 90% accuracy for a 128th-order parameter Riccati matrix equation. Compared to traditional digital processors, the solver offers significant energy efficiency advantages and is three orders of magnitude faster than CPU. Additionally, the solver successfully accelerates our proposed dung beetle optimizer-linear quadratic control algorithm for vehicle suspension control, achieving high precision while significantly reducing time and energy consumption compared to CPU and GPU.