AI 中文总结
针对路径积分控制中噪声协方差与控制成本矩阵耦合难满足的问题，提出BOTC框架，通过优化有效近似空间来最小化真实代价函数上界，推导测度变换公式并结合新的重要性采样方案，在有限时域随机线性二次调节器问题上验证其能跟踪约束最优解。
AI 中文摘要
路径积分（PI）控制是一种强大的基于采样的随机最优控制方法，但它要求噪声协方差和控制成本矩阵之间存在严格耦合，这在实际中很少能满足，尤其是在航空航天和网络物理系统中。我们提出了边界优化任务选择（BOTC）框架，该框架在满足PI耦合约束的有效近似（即任务）的整个空间上进行优化。我们证明每个任务都为真实的代价函数提供了一个上界，并且BOTC能最小化这个界。我们推导了一种测度变换公式，可从一组蒙特卡罗样本评估所有候选任务，无需为每个候选任务重新采样。所得优化由一个半正定矩阵参数化。此外，我们提出了一种基于正态 - 逆 - 威沙特分布的新型重要性采样方案来改进全局优化。我们在有限时域随机线性二次调节器问题上验证了BOTC，证明它能跟踪约束最优解。
英文摘要
Path Integral (PI) control is a powerful sampling-based method for stochastic optimal control, but it requires a restrictive coupling between the noise covariance and the control cost matrix that is rarely satisfied in practice, particularly in aerospace and cyber-physical systems. We propose Bound-Optimized Task Choice (BOTC), a framework that optimizes over the entire space of valid approximations, termed tasks, satisfying the PI coupling constraint. We prove that every task provides an upper bound on the true cost-to-go and that BOTC minimizes this bound. We derive a change-of-measure formulation that enables evaluation of all candidate tasks from a single set of Monte Carlo samples, eliminating the need to resample for each candidate task. The resulting optimization is parameterized by a positive semi-definite matrix. Furthermore, we propose a novel Normal-Inverse-Wishart distribution-based importance sampling scheme to improve global optimization. We validate BOTC on a finite-horizon stochastic linear-quadratic regulator problem, demonstrating that it tracks the constrained optimum.
Comments7 pages, 2 figures, to be published in CDC 2026
