Analysis of Input-Affine Dynamical Systems Using Parameterized Robust Counterparts

• 成果类型: Article
• 署名作者: Miller, Jared; Sznaier, Mario
• 署名单位: University of Stuttgart; Northeastern University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3545766
• 发表日期: 2025
• 关键词: convex computation; CONTROLLER-DESIGN; set; approximation; optimization

摘要

Common tasks in system analysis and control include optimal control, peak estimation, reachable set estimation, and maximum control invariant set estimation. A standard method to solve these problems is to lift them into infinite-dimensional convex linear programs. However, finite-dimensional truncations of these problems suffer a curse of dimensionality with respect to the size of the state and input. In the case where the dynamical system is input-affine and the input is restricted to a convex set, decomposition methods may be employed to eliminate the input and yield more tractable finite-dimensional truncations. Prior work on these eliminations include enforcing vertex constraints (switching), or employing facial decompositions in the case where the polytopic set is a scaled box. This work generalizes the box-facial technique toward the decompositions of arbitrary convex input-constraining sets using methods from robust optimization. The robustified programs are proven to have the same optimal value and an equivalent set of optimizers as the original program under mild compactness and regularity constraints. Specific attention is paid toward robust-counterpart decomposition of semidefinite representable sets when employing the moment-sum-of-squares hierarchy for polynomial optimization. Efficacy is demonstrated under data-driven peak and distance estimation problems.