Koopman-BoxQP：在kHz速率下求解大规模非线性模型预测控制问题
Koopman-BoxQP: Solving Large-Scale NMPC at kHz Rates
AI总结：
Koopman-BoxQP通过结合Koopman线性化和BoxQP优化方法，在kHz速率下高效求解大规模NMPC问题。
摘要：
在标准处理器上以千赫兹（kHz）的速率求解大规模非线性模型预测控制（NMPC）问题仍是一个严峻的挑战。本文提出了一种Koopman-BoxQP框架，该框架包括：i）学习一个线性Koopman高维模型；ii）消除高维观测变量以构建状态和控制输入的多步预测模型；iii）将多步预测模型惩罚到目标函数中，从而得到一个结构化的带箱约束的二次规划（BoxQP）问题，其决策变量包括系统状态和控制输入；iv）开发了针对BoxQP的结构利用和热启动支持的可行Mehrotra内点算法变体。数值结果表明，Koopman-BoxQP能够在kHz速率下求解具有1040个变量和2080个不等式的大型NMPC问题。
英文摘要：
Solving large-scale nonlinear model predictive control (NMPC) problems at kilohertz (kHz) rates on standard processors remains a formidable challenge. This paper proposes a Koopman-BoxQP framework that i) learns a linear Koopman high-dimensional model, ii) eliminates the high-dimensional observables to construct a multi-step prediction model of the states and control inputs, iii) penalizes the multi-step prediction model into the objective, which results in a structured box-constrained quadratic program (BoxQP) whose decision variables include both the system states and control inputs, iv) develops a structure-exploited and warm-starting-supported variant of the feasible Mehrotra's interior-point algorithm for BoxQP. Numerical results demonstrate that Koopman-BoxQP can solve a large-scale NMPC problem with $1040$ variables and $2080$ inequalities at a kHz rate.
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