用于决策依赖不确定性的鲁棒最优控制的广义半无限规划
Generalized Semi-Infinite Programming for Robust Optimal Control with Decision-Dependent Uncertainty
- Imperial College London（帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出通用框架，将决策依赖不确定性下的GSIP转化为带存在性约束的半无限规划，用现成求解器求解，可扩展至鲁棒非线性最优控制，在基准问题和卫星消旋问题上验证有效。
AI中文摘要：
当容许不确定性依赖于状态或控制时，鲁棒最优控制中会出现广义半无限规划（GSIP）。现有GSIP方法要么施加限制性结构假设，要么需要全局优化，而全局优化对于控制问题的扩展性较差。我们提出一种通用框架，该框架将具有温和正则性的任意GSIP重新表述为带存在性约束的半无限规划，将其析取可行性条件平滑化为固定索引超集上的可微存在性约束。所得规划仅使用现成的非线性规划求解器，通过成熟的自适应离散化（割平面）方法求解，且在标准假设下收敛。将状态轨迹视为不确定性的一部分，可将该框架扩展至具有状态依赖不确定性的鲁棒非线性最优控制。我们在一个非凸基准GSIP和一个惯性动态变化的卫星消旋问题上对其进行了验证。
英文摘要：
Generalized semi-infinite programs (GSIPs) arise in robust optimal control whenever the admissible uncertainty depends on the state or controls. Existing GSIP methods either impose restrictive structural assumptions or require global optimization that scales poorly to control problems. We present a general framework that reformulates any GSIP with mild regularity as an existence-constrained semi-infinite program, smoothing its disjunctive feasibility condition into differentiable existence constraints over a fixed index superset. The resulting program is solved by established adaptive discretization (cutting-plane) methods using only off-the-shelf nonlinear-programming solvers, and converges under standard assumptions. Treating the state trajectory as part of the uncertainty extends the framework to robust nonlinear optimal control with state-dependent uncertainty. We demonstrate it on a nonconvex benchmark GSIP and a satellite de-tumbling problem with dynamically varying inertia.
