基于高斯混合不确定性传播的随机非线性模型预测控制
Stochastic Nonlinear Model Predictive Control with Gaussian Mixture Uncertainty Propagation
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中文总结 AI 辅助
该研究针对带加性噪声的非线性系统，提出基于高斯混合不确定性传播的SNMPC框架，可高效求解控制问题并提供形式化保证，在多模态扰动场景中性能优于现有方法。
中文摘要 AI 辅助
针对带有加性噪声的非线性系统，我们提出了一种新颖的随机非线性模型预测控制（Stochastic Nonlinear Model Predictive Control, SNMPC）框架。基于非线性不确定性传播的最新进展，我们证明系统的状态分布可通过高斯混合分布随时间进行易处理的近似，且具有Wasserstein距离下的形式误差界。该表示可得到期望成本和机会约束的闭式表达式，对于仿射约束这些表达式是精确的，对于二次成本则精确到一个常数。因此，所得控制问题可通过非线性规划高效求解，同时提供形式化的开环正确性保证和渐近最优性。在一组基准上的实验表明，所提方法在具有多模态扰动的非线性场景中，相比现有方法表现更优，而标准方法会导致尺度不佳的解以及不安全或过于保守的控制动作。
英文摘要
We propose a novel Stochastic Nonlinear Model Predictive Control (SNMPC) framework for nonlinear systems with additive noise. Building on recent advances in nonlinear uncertainty propagation, we show that the state distribution of the system can be tractably approximated over time by Gaussian mixture distributions, with formal error bounds in Wasserstein distance. This representation yields closed-form expressions for expected costs and chance constraints, which become exact for affine constraints and exact up to a constant for quadratic costs. Consequently, the resulting control problem can be solved efficiently via nonlinear programming, while providing formal open-loop guarantees of correctness and asymptotic optimality. Experiments on a set of benchmarks demonstrate that the proposed approach compares favorably with existing methods in nonlinear settings with multi-modal disturbances, where standard approaches lead to poorly scaled solutions and unsafe or overly conservative control actions.
发表机构
- Delft Center for Systems and Control, Delft University of Technology（代尔夫特系统与控制中心，代尔夫特理工大学）
- AI4I, Turin, Italy（AI4I，意大利都灵）
机构由 AI 辅助整理，请以论文原文为准。
