In recent years, the increasing interest in Stochastic model predictive control (SMPC) schemes has highlighted the limitation arising from their inherent computational demand, which has restricted their applicability to slow-dynamics and high-performing systems. To reduce the computational burden, in this paper we extend the probabilistic scaling approach to obtain low-complexity inner approximation of chance-constrained sets. This approach provides probabilistic guarantees at a lower computational cost than other schemes for which the sample complexity depends on the design space dimension. To design candidate simple approximating sets, which approximate the shape of the probabilistic set, we introduce two possibilities: i) fixed-complexity polytopes, and ii) $\ell_p$-norm based sets. Once the candidate approximating set is obtained, it is scaled around its center so to enforce the expected probabilistic guarantees. The resulting scaled set is then exploited to enforce constraints in the classical SMPC framework. The computational gain obtained with the proposed approach with respect to the scenario one is demonstrated via simulations, where the objective is the control of a fixed-wing UAV performing a monitoring mission over a sloped vineyard.

中文翻译：

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计算高效的随机 MPC：概率缩放方法

近年来，对随机模型预测控制 (SMPC) 方案的兴趣日益浓厚，凸显了其固有计算需求所带来的局限性，这限制了它们对慢动力学和高性能系统的适用性。为了减少计算负担，在本文中，我们扩展了概率缩放方法以获得机会约束集的低复杂度内部近似。与样本复杂性取决于设计空间维度的其他方案相比，这种方法以更低的计算成本提供概率保证。为了设计近似概率集形状的候选简单近似集，我们引入了两种可能性：i）固定复杂度的多面体，以及 ii）基于 $\ell_p$-norm 的集。一旦得到候选逼近集，它围绕其中心进行缩放，以强制执行预期的概率保证。然后利用生成的缩放集来强制执行经典 SMPC 框架中的约束。使用所提出的方法获得的关于场景一的计算增益是通过模拟来证明的，其中目标是控制固定翼无人机在倾斜的葡萄园上执行监测任务。