Complex engineered systems require coordinated design choices across heterogeneous components under multiple conflicting objectives and uncertain specifications. Monotone co-design provides a compositional framework for such problems by modeling each subsystem as a design problem: a feasible relation between provided functionalities and required resources in partially ordered sets. 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 interconnection operations remain compositional under this richer notion of uncertainty. We further introduce queries and observations that extract probabilistic design trade-offs, including feasibility probabilities, confidence bounds, and distributions of minimal required resources. A task-driven unmanned aerial vehicle case study illustrates how the framework captures risk-sensitive and information-dependent design choices that interval-based models cannot express.

翻译：复杂工程系统需要在多重冲突目标与不确定规范下，对异质组件进行协调的设计选择。单调协同设计通过将每个子系统建模为一个设计问题——即部分有序集中提供的功能与所需资源之间的可行关系——为此类问题提供了一个组合式框架。现有的不确定协同设计模型依赖于区间界，其支持最坏情况推理，但无法表示概率风险或多阶段自适应决策。我们提出了协同设计的分布扩展，将不确定的设计结果建模为设计问题上的分布，并通过马尔可夫核重参数化支持自适应决策过程。利用拟可测与拟通用空间，我们证明了在此更丰富的不确定性概念下，标准协同设计互连操作仍保持组合性。我们进一步引入了查询与观测机制，以提取概率性设计权衡，包括可行性概率、置信界以及最小所需资源的分布。一项任务驱动的无人机案例研究展示了该框架如何捕捉基于区间模型无法表达的风险敏感型与信息依赖型设计选择。