Learning‐based adaptive‐scenario‐tree model predictive control with improved probabilistic safety using robust Bayesian neural networks
Learning‐based adaptive‐scenario‐tree model predictive control with improved probabilistic safety using robust Bayesian neural networks
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DOI：
10.1002/rnc.6560
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发表时间：
2022-12
影响因子：
3.9
通讯作者：
Yajie Bao;Kimberly J. Chan;A. Mesbah;Javad Mohammadpour Velni
中科院分区：
文献类型：
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作者：
Yajie Bao;Kimberly J. Chan;A. Mesbah;Javad Mohammadpour Velni
基于场景的模型预测控制（MPC）方法可以减轻开环鲁棒MPC固有的保守性。然而，场景通常是基于先验获得的最坏情况不确定性描述离线生成的，这反过来又限制了鲁棒控制性能的提高。为此，针对具有时变和/或难以建模动态的不确定非线性系统，提出了一种基于学习的自适应情景树模型预测控制方法.贝叶斯神经网络（BNN）用于学习模型不确定性的状态和输入相关描述，即系统的标称（基于物理或数据驱动）模型与其实际动态之间的不匹配。首先，我们提出了一种新的方法来训练强大的BNN（RBNN）使用概率Lipschitz界提供一个不太保守的不确定性量化。然后，我们提出了一种评估RBNN预测可信区间的方法，并确定在给定可信水平的情况下估计可信区间所需的样本数量。相对于标准BNN和高斯过程（GP）作为比较的基础，RBNN的性能进行了评估。采用RBNN描述被控对象模型失配，并验证精确可信区间，在线生成基于情景的MPC（sMPC）的自适应情景。所提出的具有自适应场景树的sMPC方法可以相对于具有固定的最坏情况场景树的sMPC和相对于使用冷大气等离子体系统上的GP回归的基于自适应场景的MPC（asMPC）提高鲁棒控制性能。此外，闭环仿真结果表明，通过RBNN的鲁棒模型不确定性学习可以提高asMPC的约束满足概率。
Scenario‐based model predictive control (MPC) methods can mitigate the conservativeness inherent to open‐loop robust MPC. Yet, the scenarios are often generated offline based on worst‐case uncertainty descriptions obtained a priori, which can in turn limit the improvements in the robust control performance. To this end, this paper presents a learning‐based, adaptive‐scenario‐tree model predictive control approach for uncertain nonlinear systems with time‐varying and/or hard‐to‐model dynamics. Bayesian neural networks (BNNs) are used to learn a state‐ and input‐dependent description of model uncertainty, namely the mismatch between a nominal (physics‐based or data‐driven) model of a system and its actual dynamics. We first present a new approach for training robust BNNs (RBNNs) using probabilistic Lipschitz bounds to provide a less conservative uncertainty quantification. Then, we present an approach to evaluate the credible intervals of RBNN predictions and determine the number of samples required for estimating the credible intervals given a credible level. The performance of RBNNs is evaluated with respect to that of standard BNNs and Gaussian process (GP) as a basis of comparison. The RBNN description of plant‐model mismatch with verified accurate credible intervals is employed to generate adaptive scenarios online for scenario‐based MPC (sMPC). The proposed sMPC approach with adaptive scenario tree can improve the robust control performance with respect to sMPC with a fixed, worst‐case scenario tree and with respect to an adaptive‐scenario‐based MPC (asMPC) using GP regression on a cold atmospheric plasma system. Furthermore, closed‐loop simulation results illustrate that robust model uncertainty learning via RBNNs can enhance the probability of constraint satisfaction of asMPC.