用路径积分方法解决高维随机控制难题，支持实时计算。
Advancing Frontiers of Path Integral Theory for Stochastic Optimal Control
- 将随机控制问题转化为轨迹期望，通过采样求解
- 在六类问题上验证有效，实现实时部署
- 适合机器人、金融等复杂不确定场景研究者
随机最优控制（SOC）问题广泛存在于受不确定性影响的系统中，如自主机器人或金融模型。传统动态规划方法在高维非线性系统中因维数灾难难以应用。本文探索路径积分控制框架，作为一种可扩展的采样式替代方案。通过将SOC问题重构成随机轨迹上的期望，实现基于蒙特卡洛采样的高效策略生成，并借助GPU并行化支持实时实现。该框架应用于六类SOC问题：机会约束控制、随机微分博弈、欺骗性控制、任务分层控制、隐蔽攻击风险缓解及离散时间LQR。还提供了离散时间情形下的样本复杂度分析。这些成果为复杂不确定环境中的仿真驱动自主系统奠定了基础。
原文摘要 · Abstract (English)
Stochastic Optimal Control (SOC) problems arise in systems influenced by uncertainty, such as autonomous robots or financial models. Traditional methods like dynamic programming are often intractable for high-dimensional, nonlinear systems due to the curse of dimensionality. This dissertation explores the path integral control framework as a scalable, sampling-based alternative. By reformulating SOC problems as expectations over stochastic trajectories, it enables efficient policy synthesis via Monte Carlo sampling and supports real-time implementation through GPU parallelization. We apply this framework to six classes of SOC problems: Chance-Constrained SOC, Stochastic Differential Games, Deceptive Control, Task Hierarchical Control, Risk Mitigation of Stealthy Attacks, and Discrete-Time LQR. A sample complexity analysis for the discrete-time case is also provided. These contributions establish a foundation for simulator-driven autonomy in complex, uncertain environments.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。