A Riccati Matrix Equation Solver Design Based Neurodynamics Method and Its Application

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. Note to Practitioners—The motivation for this study arises from the need for Riccati matrix equation in real world applications. Currently the main factors leading to the high time complexity of Riccati matrix equation (e.g., in the optimal algorithm solving, trajectory tracking and autonomous driving) originate from the large number of iterative computations, and the nonlinear structure of its essence. As such, the work in this paper propose a Neurodynamics-based algorithm for solving nonlinear matrix equation, and designs an efficient, non-iterative solver for Riccati matrix equations based on the proposed algorithm, essentially addressing the two problems mentioned above. Although the proposed circuit does not seem to be as perfect as numerical computation in terms of solution accuracy, the comparison with literature shows that the accuracy is generally sufficient to meet the usage requirements. It can also provide an initial solution for high precision solving, thereby saving a significant amount of time in searching for the initial solution, its effectiveness is preliminarily validated through applications demonstrated in the manuscript. In the future, we aim to advance the proposed RME solver for broad practical deployment in applications such as optimal control, edge computing, path tracking and so on.