论文标题
随机模型预测控制的近乎最佳性能
Near-Optimal Performance of Stochastic Model Predictive Control
论文作者
论文摘要
本文对具有二次性能指数以及加性和乘法不确定性的线性系统中随机模型预测控制（SMPC）进行了动态遗憾分析。在有限的支持假设下，问题可以作为有限维二次程序的程序施放，但是由于问题大小在地平线长度上呈指数增长，问题变得迅速棘手。 SMPC的目的是通过解决截断预测范围的一系列问题并以退缩的方式进行解决方案来计算近似解决方案。尽管这种方法在实践中被广泛使用，但其相对于最佳解决方案的性能尚不清楚。本文首次报道了SMPC的严格近乎最佳性能保证：在稳定性和可检测性条件下，SMPC的动态遗憾在预测范围的长度上成倍小，允许SMPC在大幅降低的计算费用下实现近乎最佳的性能。
This article presents a dynamic regret analysis for stochastic model predictive control (SMPC) in linear systems with quadratic performance index and additive and multiplicative uncertainties. Under a finite support assumption, the problem can be cast as a finite-dimensional quadratic program, but the problem becomes quickly intractable as the problem size grows exponentially in the horizon length. SMPC aims to compute approximate solutions by solving a sequence of problems with truncated prediction horizons and committing the solution in a receding-horizon fashion. While this approach is widely used in practice, its performance relative to the optimal solution is not well understood. This article reports for the first time a rigorous near-optimal performance guarantee of SMPC: Under stabilizability and detectability conditions, the dynamic regret of SMPC is exponentially small in the prediction horizon length, allowing SMPC to achieve near-optimal performance at a substantially reduced computational expense.
