基于鲁棒线性化余项界的机会约束非线性协方差控制
Chance-Constrained Nonlinear Covariance Control via Robust Linearization Remainder Bounds
- Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出序列凸规划框架，结合鲁棒线性化余项界与随机线性矩阵不等式，实现非线性系统的机会约束协方差控制，仿真验证其约束满足性。
AI中文摘要：
在处理非线性系统时，传统协方差转向通常通过一阶线性化传播不确定性，丢弃高阶泰勒余项。这种截断会导致计算出的统计矩与真实物理状态分布偏离，常引发机会约束违反。本文提出一种离散时间序列凸规划（SCP）框架，将确定性单步非线性数值映射转化为线性随机包含关系。泰勒余项被限定在均匀包络上的非结构化不确定性块内。通过Petersen引理推导的鲁棒随机线性矩阵不等式（S-LMI）传播二阶矩管，提供了期望非中心二阶矩的上界。通过马尔可夫迹不等式解析界定域退出风险，并在差分凸规划内通过高斯单峰二阶矩界实施空间机会约束。对状态依赖非线性动态系统的仿真表明该方法可满足约束要求。
英文摘要：
When dealing with nonlinear systems, classical covariance steering typically propagates uncertainty via first-order linearizations, discarding higher-order Taylor remainders. This truncation causes computed statistical moments to diverge from the true physical state distribution, often leading to chance constraint violations. This paper introduces a discrete-time Sequential Convex Programming (SCP) framework that casts the deterministic one-step nonlinear numerical map as a Linear Stochastic Inclusion. The The Taylor remainder is modeled as a state-independent unstructured uncertainty block, bounded over a uniform envelope. The second-moment tubes are propagated via what we refer to as a robust Stochastic Linear Matrix Inequality (S-LMI) derived from the Petersen's lemma, providing an upper bound on the expected uncentered second moment. Domain-exit risk is bounded analytically via a Markov trace inequality, and spatial chance constraints are enforced via Gauss unimodal second-moment bounds within a Difference-of-Convex program. Simulations on a state-dependent nonlinear dynamic system demonstrate constraint satisfaction.
