Convex Neural Network-Based Cost Modifications for Learning Model Predictive Control

Katrine Seel;Arash Bahari Kordabad;Sébastien Gros;Jan Tommy Gravdahl
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引用次数: 7

Abstract

Developing model predictive control (MPC) schemes can be challenging for systems where an accurate model is not available, or too costly to develop. With the increasing availability of data and tools to treat them, learning-based MPC has of late attracted wide attention. It has recently been shown that adapting not only the MPC model, but also its cost function is conducive to achieving optimal closed-loop performance when an accurate model cannot be provided. In the learning context, this modification can be performed via parametrizing the MPC cost and adjusting the parameters via, e.g., reinforcement learning (RL). In this framework, simple cost parametrizations can be effective, but the underlying theory suggests that rich parametrizations in principle can be useful. In this paper, we propose such a cost parametrization using a class of neural networks (NNs) that preserves convexity. This choice avoids creating difficulties when solving the MPC problem via sensitivity-based solvers. In addition, this choice of cost parametrization ensures nominal stability of the resulting MPC scheme. Moreover, we detail how this choice can be applied to economic MPC problems where the cost function is generic and therefore does not necessarily fulfill any specific property.
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基于凸神经网络的学习模型预测控制成本修正
对于无法获得准确模型或开发成本过高的系统来说,开发模型预测控制(MPC)方案可能具有挑战性。随着数据和治疗工具的可用性不断增加,基于学习的MPC最近引起了广泛关注。最近的研究表明,当无法提供准确的模型时,不仅调整MPC模型,而且调整其成本函数,都有助于实现最佳闭环性能。在学习上下文中,这种修改可以通过参数化MPC成本和通过例如强化学习(RL)调整参数来执行。在这个框架中,简单的成本参数化可能是有效的,但基本理论表明,原则上丰富的参数化可能有用。在本文中,我们使用一类保持凸性的神经网络(NN)提出了这样一种成本参数化。这种选择避免了在通过基于灵敏度的求解器求解MPC问题时产生困难。此外,这种成本参数化的选择确保了所得MPC方案的标称稳定性。此外,我们详细介绍了这种选择如何应用于经济MPC问题,其中成本函数是通用的,因此不一定满足任何特定性质。
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Erratum to “Learning to Boost the Performance of Stable Nonlinear Systems” Generalizing Robust Control Barrier Functions From a Controller Design Perspective 2024 Index IEEE Open Journal of Control Systems Vol. 3 Front Cover Table of Contents
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