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arXiv 2309.04444eess.SYcs.SYmath.OC
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保证稳定性的实时MPC广义停止准则

A Generalized Stopping Criterion for Real-Time MPC with Guaranteed Stability

Kristína Fedorová, Yuning Jiang, Juraj Oravec, Colin N. Jones, Michal Kvasnica

AI总结:

本文提出一种保证渐近稳定性的线性二次MPC实时评估广义停止准则,通过固定迭代次数降低计算量,在PGDM和ADMM方法中实现次优率低于2%且计算量减少超80%。

摘要:

大多数稳定最优控制动作的实时实现都面临需要提供高计算量的问题。本文提出了一种用于实时评估线性二次模型预测控制(MPC)的前沿方法,该方法采用一种新颖的广义停止准则,在存在输入约束的情况下实现渐近稳定性。所提方法评估与初始条件无关的固定迭代次数,消除了对计算昂贵方法的需求。我们通过实现两种广泛使用的一阶优化方法:投影梯度下降法(PGDM)和乘子交替方向法(ADMM),展示了所引入技术的有效性。数值模拟证实迭代次数显著减少,导致次优率低于2%,同时计算量减少超过80%。这些结果使所提准则成为MPC控制器高效实时实现方法的优选。

英文摘要:

Most of the real-time implementations of the stabilizing optimal control actions suffer from the necessity to provide high computational effort. This paper presents a cutting-edge approach for real-time evaluation of linear-quadratic model predictive control (MPC) that employs a novel generalized stopping criterion, achieving asymptotic stability in the presence of input constraints. The proposed method evaluates a fixed number of iterations independent of the initial condition, eliminating the necessity for computationally expensive methods. We demonstrate the effectiveness of the introduced technique by its implementation of two widely-used first-order optimization methods: the projected gradient descent method (PGDM) and the alternating directions method of multipliers (ADMM). The numerical simulation confirmed a significantly reduced number of iterations, resulting in suboptimality rates of less than 2\,\%, while the effort reductions exceeded 80\,\%. These results nominate the proposed criterion for an efficient real-time implementation method of MPC controllers.

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