In this work, we formulate the extended flexibility analysis, which takes into account two different types of uncertain parameters: measured (θ_m) and unmeasured (θ_u), as a rigorous multi-level optimization problem. We recursively reformulate the inner optimization problems by the KKT conditions and with a mixed-integer representation of the complementarity conditions to solve the resulting multilevel optimization problem. Special cases are identified, where models are comprised of convex constraints or constraints with monotonic variation of the uncertain parameters. In these cases, a vertex enumeration can be performed to solve the flexibility test. We propose two MINLP reformulations for the more general case yielding to similar results but different model sizes. The formulations are tested and compared with several examples.

在这项工作中，我们制定扩展灵活性分析，其中考虑到两种不同类型的不确定参数：测量（θ_米）和未测定（θ _û），作为严格的多级优化问题。我们通过KKT条件并使用互补条件的混合整数表示来递归地重新构造内部优化问题，以解决由此产生的多级优化问题。确定特殊情况，其中模型由凸约束或不确定参数单调变化的约束组成。在这些情况下，可以执行顶点枚举来解决灵活性测试。对于较一般的情况，我们提出了两种MINLP公式，得出的结果相似但模型大小不同。测试制剂并与几个实施例比较。