This article presents a new efficient variant of the state-dependent Riccati equation (SDRE) scheme in a general scope, by analytically alleviating the computational burden in solving the pointwise algebraic Riccati equations (AREs). The novel contributions include a more efficient construction of feasible state-dependent coefficients (named alternative SDRE), which is critical at the early design stage, and more efficient solvability check for the classical SDRE scheme. For the selected robotic application—balance control of a two-wheeled robot, the contribution lies in the system-specific analysis that further enhances the computational performance toward an agile mobility. This novelty is with respect to a state-of-the-art ARE solver. An offline/a priori analytical formulation replaces the very first stage of the solving process, which more efficiently integrates the ARE solver into the SDRE design framework. Notably, all the results not only benefit the classical SDRE scheme but, more significantly, favor the proposed alternative SDRE owing to its much better computational efficiency—mainly in terms of time while promisingly for memory saving. In addition, simulations reveal more potential advantages using the variants—such as the control effort efficiency or required regulation time—within and beyond the scope of SDRE.

中文翻译：

---

SDRE方案的计算增强：一般理论和机器人控制系统

本文通过分析减轻求解逐点代数 Riccati 方程 (ARE) 的计算负担，在一般范围内提出了状态相关 Riccati 方程 (SDRE) 方案的一种新的有效变体。新的贡献包括更有效地构建可行的状态相关系数（称为替代 SDRE），这在早期设计阶段至关重要，以及对经典 SDRE 方案更有效的可解性检查。对于选定的机器人应用——两轮机器人的平衡控制，贡献在于系统特定的分析，进一步提高了计算性能，实现了敏捷移动。这种新颖性与最先进的 ARE 求解器有关。离线/先验分析公式取代了求解过程的第一阶段，将 ARE 求解器更有效地集成到 SDRE 设计框架中。值得注意的是，所有结果不仅有利于经典 SDRE 方案，而且更重要的是，由于其更好的计算效率——主要是在时间方面，同时有希望节省内存，因此有利于所提出的替代 SDRE。此外，模拟揭示了使用变体的更多潜在优势 - 例如控制工作效率或所需的调节时间 - 在 SDRE 范围内外。