从数据学习鲁棒预测控制的反馈策略，保证闭环稳定与可行性。
Data-driven learning of feedback maps for explicit robust predictive control: an approximation theoretic view
- 通过凸半无限规划生成状态-动作数据，构建可学习的反馈映射
- 在预设误差范围内逼近最优反馈策略，确保递归可行性
- 适用于需兼顾稳定性与鲁棒性的工业控制场景
本文提出一种数据驱动算法，用于学习一类鲁棒模型预测控制（MPC）问题的反馈映射。该算法在合成阶段直接考虑学习带来的近似误差，保证递归可行性。控制问题包含线性噪声动态系统、二次阶段与终端代价，以及对状态、控制和扰动序列的凸约束；控制量最小化目标，扰动量最大化目标。方法分为两步：(a) 数据生成：将原极小极大问题重构为凸半无限规划，并利用最新工具在状态空间网格点上精确求解，生成（状态，动作）数据；(b) 学习近似反馈映射：采用若干逼近方案，在允许状态空间内以预设均匀误差界实现紧致逼近，从而学习未知反馈策略。在标准假设下，闭环系统稳定性也得到保障。通过两个基准数值例子验证了结果的有效性。
原文摘要 · Abstract (English)
We establish an algorithm to learn feedback maps from data for a class of robust model predictive control (MPC) problems. The algorithm accounts for the approximation errors due to the learning directly at the synthesis stage, ensuring recursive feasibility by construction. The optimal control problem consists of a linear noisy dynamical system, a quadratic stage and quadratic terminal costs as the objective, and convex constraints on the state, control, and disturbance sequences; the control minimizes and the disturbance maximizes the objective. We proceed via two steps -- (a) Data generation: First, we reformulate the given minmax problem into a convex semi-infinite program and employ recently developed tools to solve it in an exact fashion on grid points of the state space to generate (state, action) data. (b) Learning approximate feedback maps: We employ a couple of approximation schemes that furnish tight approximations within preassigned uniform error bounds on the admissible state space to learn the unknown feedback policy. The stability of the closed-loop system under the approximate feedback policies is also guaranteed under a standard set of hypotheses. Two benchmark numerical examples are provided to illustrate the results.
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