AI 中文总结
针对鲁棒MPC的最大扰动半径，提出双侧储备损耗包络的任意时刻原始-对偶验证算法，可提前终止并实现最高4.97倍加速，无验证违规。
AI 中文摘要
可调集鲁棒模型预测控制（MPC）具有与状态相关的最大扰动半径，可被解释为已验证的鲁棒性储备。现有方法主要关注在集合内扰动下对该储备进行优化和传播。本文研究在有限的集合外扰动后，无需立即重新求解完整优化问题时，剩余的储备量有多少。为此，我们提出了一种由独立原始和对偶校正层级构成的双侧储备损耗包络，分别提供单调的下界和上界。该包络在活动集变化时仍保持有效，具有可在线计算的宽度，且在子空间扩展时单调收缩。利用其有限步精确性，我们提出了一种基于基优先的自适应算法，该算法以任意时刻方式运行：每完成一次简化求解即可返回一个有效的验证结果，一旦达到规定的容忍度即可提前终止。在测试案例中，数值研究表明，在2%的验证宽度容忍度下，该方法无验证结果违反情况，且相比热启动的完整重新优化，中位数加速比最高可达4.97倍。
英文摘要
Adjustable-set robust model predictive control (MPC) characterizes a state-dependent maximum disturbance radius, which can be interpreted as a certified robustness reserve. Existing methods primarily focus on optimizing and propagating this reserve under in-set disturbances. This letter investigates how much reserve remains after a finite out-of-set disturbance without immediately re-solving the full optimization problem. To this end, we propose a two-sided reserve-depletion envelope formed by independent primal and dual correction hierarchies, which supply monotone lower and upper bounds, respectively. The envelope remains valid across active-set changes, has an online-computable width, and contracts monotonically under subspace expansion. Leveraging its finite-step exactness, we present a basis-first adaptive algorithm that operates in an anytime manner: every completed reduced solve returns a valid certificate, enabling early termination once a prescribed tolerance is reached. Across the tested cases, numerical studies report no certificate violations and median speedups of up to 4.97x over warm-started full re-optimization at a 2% certificate-width tolerance.
