将不确定性建模为分布，支持动态决策的系统协同设计方法
Distributional Uncertainty and Adaptive Decision-Making in System Co-design
- 用分布替代区间表示设计不确定性，支持概率化分析
- 可计算可行性概率与最小资源需求分布，指导风险敏感决策
- 适合需动态调整的复杂系统设计，如无人机任务规划
复杂工程系统在目标冲突和规格不确定下，需对异构组件进行协同设计。单调协同设计提供了一种组合式框架，将每个子系统性能建模为设计问题（即资源与功能的映射关系）。现有不确定协同设计模型依赖区间边界，虽支持最坏情况分析，但无法表达概率风险或多阶段自适应决策。本文提出协同设计的分布扩展，将不确定设计结果建模为设计问题的分布，并通过马尔可夫核重参数化支持自适应决策过程。利用拟可测空间与拟普遍空间，证明标准协同设计组合在更丰富的不确定性下仍保持组合性。引入查询与观测机制，可提取概率性权衡信息，包括可行性概率、置信区间及最小资源需求分布。一项面向任务驱动的无人飞行器案例研究显示，该框架能捕捉区间模型无法表达的风险敏感与信息依赖型设计选择。
原文摘要 · Abstract (English)
Complex engineered systems require coordinated design choices across heterogeneous components under conflicting objectives and uncertain specifications. Monotone co-design provides a compositional framework for such problems. Performance of each subsystem is modeled with a design problem: a relation specifying what resources suffice to provide each functionality. Existing uncertain co-design models rely on interval bounds, which support worst-case reasoning but cannot represent probabilistic risk or multi-stage adaptive decisions. We develop a distributional extension of co-design that models uncertain design outcomes as distributions over design problems and supports adaptive decision processes through Markov-kernel re-parameterizations. Using quasi-measurable and quasi-universal spaces, we show that the standard co-design compositions remain compositional under this richer uncertainty, and introduce queries and observations extracting probabilistic trade-offs, including feasibility probabilities, confidence bounds, and distributions of minimal required resources. A task-driven unmanned aerial vehicle case study shows how the framework captures risk-sensitive and information-dependent design choices that interval models cannot express.
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