发表机构
Texas A&M University; University of Pennsylvania; KTH Royal Institute of Technology（德克萨斯农工大学; 宾夕法尼亚大学; 皇家理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一个验证框架，用于数值分析受约束非线性离散时间系统中不精确模型预测控制器的性能、稳定性与可行性，通过构造优化问题搜索最坏情况初始状态与输入，以量化次优性差距并验证闭环性质。
AI 中文摘要
我们引入了一个验证框架，用于在受约束的非线性离散时间设置中对不精确模型预测控制器（MPC）进行数值分析。我们不修改控制器以保证其性质成立，而是将控制器视为给定的。具体而言，我们关注两类不精确控制器：（a）其输入从满足非凸MPC问题的Karush-Kuhn-Tucker（KKT）条件的原始-对偶点提取；（b）其输入通过线性化动力学并求解凸二次规划获得。我们验证框架的主要思想是构造一个优化问题，在给定集合内搜索最坏情况下的初始状态，并与不精确控制器一致的输入，以最大化精心选择的性能指标。利用该框架，我们展示了如何验证（i）单个MPC问题的最坏情况次优性差距，（ii）给定数量的动力系统迭代上的最坏情况闭环次优性差距，（iii）闭环稳定性，以及（iv）闭环系统的可行性。通过数值示例，我们展示了该框架精确量化两类次优性以及测试不精确控制器的稳定性和可行性的能力。
英文摘要
We introduce a verification framework to numerically analyze inexact model predictive controllers (MPCs) in the constrained non-linear discrete-time setting. Rather than modifying the controller so that guarantees hold by construction, we treat the controller as given. In particular, we focus on two types of inexact controllers: (a) one whose input is extracted from a primal-dual point satisfying the Karush-Kuhn-Tucker (KKT) conditions of the non-convex MPC problem, and (b) one whose input is obtained by linearizing the dynamics and solving a convex quadratic program. The main idea of our verification framework is to formulate an optimization problem that searches over the worst-case initial state within a given set and control inputs consistent with the inexact controller to maximize a carefully-chosen performance metric. Using this framework, we show how to certify (i) the worst-case suboptimality gap of a single MPC problem, (ii) the worst-case closed-loop suboptimality gap over a given number of dynamical system iterations, (iii) closed-loop stability, and (iv) feasibility of the closed-loop system. Through numerical examples, we showcase the ability of our framework to precisely quantify both types of suboptimality, and to test the stability and feasibility of the inexact controllers.
