Constraints-Informed Neural-Laguerre Approximation of Nonlinear MPC with Application in Power Electronics

Duo Xu, Rody Aerts, Petros Karamanakos, Mircea Lazar
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Abstract

This paper considers learning online (implicit) nonlinear model predictive control (MPC) laws using neural networks and Laguerre functions. Firstly, we parameterize the control sequence of nonlinear MPC using Laguerre functions, which typically yields a smoother control law compared to the original nonlinear MPC law. Secondly, we employ neural networks to learn the coefficients of the Laguerre nonlinear MPC solution, which comes with several benefits, namely the dimension of the learning space is dictated by the number of Laguerre functions and the complete predicted input sequence can be used to learn the coefficients. To mitigate constraints violation for neural approximations of nonlinear MPC, we develop a constraints-informed loss function that penalizes the violation of polytopic state constraints during learning. Box input constraints are handled by using a clamp function in the output layer of the neural network. We demonstrate the effectiveness of the developed framework on a nonlinear buck-boost converter model with sampling rates in the sub-millisecond range, where online nonlinear MPC would not be able to run in real time. The developed constraints-informed neural-Laguerre approximation yields similar performance with long-horizon online nonlinear MPC, but with execution times of a few microseconds, as validated on a field-programmable gate array (FPGA) platform.
非线性 MPC 的约束条件神经-拉盖尔逼近法在电力电子技术中的应用
本文考虑利用神经网络和拉盖尔函数学习在线(隐式)非线性模型预测控制(MPC)法则。首先,我们使用拉盖尔函数对非线性 MPC 的控制序列进行参数化,与原始的非线性 MPC 规律相比,这种方法通常能得到更平滑的控制规律。其次,我们利用神经网络来学习拉盖尔非线性 MPC 解决方案的系数,这样做有几个好处,即学习空间的维度由拉盖尔函数的数量决定,而且可以使用完整的预测输入序列来学习系数。为了减轻非线性 MPC 神经逼近的约束违反情况,我们开发了一种约束信息损失函数,对学习过程中违反多点状态约束的情况进行惩罚。在神经网络的输出层中使用钳位函数来处理盒式输入约束。我们在一个非线性降压-升压转换器模型上演示了所开发框架的有效性,该模型的采样率在亚毫秒范围内,在线非线性 MPC 无法实时运行。经现场可编程门阵列 (FPGA) 平台验证,所开发的约束信息神经-拉盖尔逼近方法与长视距在线非线性 MPC 性能相似,但执行时间仅为几微秒。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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