通过双重凸性安全压缩优化问题，实现高速高安全的自动驾驶控制。
SHIELD: Scalable Optimal Control with Certification using Duality and Convexity
- 利用对偶性和强凸性，自动识别可删除的约束与变量。
- 在复杂交通场景中计算速度提升数量级，且保证安全可行。
- 适合需要轻量化与可证明安全性的实时控制系统设计者。
我们提出SHIELD，一种分层算法，通过$\\$\ell_1$-正则化凸规划中的强凸性与拉格朗日对偶性，降低决策变量维度和约束集规模。该方法可安全地移除约束和变量，同时保证被移除的约束始终满足、被移除的变量均为零。为加速算法，我们引入基于Transformer的深度神经网络以指导对偶证书推断。在复杂多模态交通场景下的随机模型预测控制（SMPC）中验证了SHIELD，与全维SMPC策略对比，数值仿真显示计算速度提升数量级，同时保持可行性与闭环安全性，凸显了可证明安全、轻量级MPC在复杂驾驶场景中的实用性。
原文摘要 · Abstract (English)
We present SHIELD, a hierarchical algorithm that reduces both the decision-variable dimension and the constraint set in $\ell_1$-regularized convex programs. From strong convexity and Lagrangian duality, we derive certificates that \emph{safely} discard constraints and decision variables while guaranteeing that all removed constraints remain satisfied and all removed variables are null. To further accelerate the proposed algorithm, we propose a transformer-based deep neural network to guide the dual certificate inference. We validate SHIELD on stochastic model predictive control (SMPC) in complex, multi-modal traffic scenarios, comparing against a full-dimensional SMPC policy. Numerical simulations demonstrate order-of-magnitude computational speedups while preserving feasibility and closed-loop safety, highlighting the practicality of certifiably safe, lightweight MPC in complex driving scenes.
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