计算机科学
模型预测控制
概率逻辑
树(集合论)
贝叶斯概率
人工神经网络
预测区间
高斯过程
机器学习
控制理论(社会学)
人工智能
高斯分布
控制(管理)
数学
量子力学
物理
数学分析
作者
Yajie Bao,Kimberly J. Chan,Ali Mesbah,Javad Mohammadpour Velni
摘要
Summary 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.
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