基于高斯回归学习的场景优化鲁棒预测控制

doi:10.3785/j.issn.1008-973X.2023.04.006

浙江大学学报(工学版)

2023, Vol. 57

Issue (4): 693-701 DOI: 10.3785/j.issn.1008-973X.2023.04.006

自动化技术、计算机技术

基于高斯回归学习的场景优化鲁棒预测控制

熊伟亮(

),何德峰*(

),王秀丽,周丹

浙江工业大学信息工程学院，浙江杭州 310012

Scenario optimization robust predictive control via Gaussian regression learning

Wei-liang XIONG(

),De-feng HE*(

),Xiu-li WANG,Dan ZHOU

College of Information Engineering, Zhejiang University of Technology, Hangzhou 310012, China

全文: PDF(1863 KB) HTML

摘要：

针对具有未知加性不确定性的约束线性系统，提出基于高斯过程回归学习的场景优化鲁棒模型预测控制算法. 在离线阶段使用高斯回归从经验数据中学习不确定性结构与参数，能够抽取大量随机场景. 在在线控制阶段中，求解抽取场景所构建的有限时域优化问题，将滚动优化得到的控制律作用于系统. 引入松弛变量保证优化问题的可行性，应用随机凸优化理论，证明所提算法使系统以一定的置信度满足松弛机会约束，收敛于终端域. 通过DC-DC转换器和网联车巡航控制仿真实验，验证了本文算法的有效性和优越性.

关键词： 鲁棒模型预测控制; 场景优化; 高斯回归学习; 机会约束; 随机凸优化

Abstract:

A scenario optimization robust model predictive control algorithm based on Gaussian process regression was proposed for constrained linear systems with unknown additive uncertainty. The Gaussian regression was used to learn the uncertainty parameter from the empirical data in the offline stage, so that sufficient scenarios could be obtained. The finite-horizon optimal control problem constructed by extracted scenarios was solved in the online control stage, and the control law obtained by rolling optimization was used to control the system. The relaxation variable was introduced to ensure the feasibility of the optimization problem. Then the random convex optimization theory was used. It was proved that the closed-loop system satisfied the relaxed chance constraint and converged to the terminal set with certain confidence bound. The control simulation experiments of a DC-DC converter and a connected vehicle cruise system illustrated the feasibility and merits of the proposed algorithm.

Key words: robust model predictive control scenario optimization Gaussian regression learning chance constraint random convex optimization

收稿日期: 2022-04-26 出版日期: 2023-04-21

CLC:

TP 273

基金资助: 国家自然科学基金资助项目（62173303）；浙江省属高校基本科研业务费资助项目（RF-C2020003）

通讯作者: 何德峰 E-mail: 17857102644@163.com;hdfzj@zjut.edu.cn

作者简介: 熊伟亮（1999—），男，博士生，从事模型预测控制的研究. orcid.org/0000-0002-2476-8941. E-mail： 17857102644@163.com

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引用本文:

熊伟亮,何德峰,王秀丽,周丹. 基于高斯回归学习的场景优化鲁棒预测控制[J]. 浙江大学学报(工学版), 2023, 57(4): 693-701.

Wei-liang XIONG,De-feng HE,Xiu-li WANG,Dan ZHOU. Scenario optimization robust predictive control via Gaussian regression learning. Journal of ZheJiang University (Engineering Science), 2023, 57(4): 693-701.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2023.04.006 或 https://www.zjujournals.com/eng/CN/Y2023/V57/I4/693

图 1 GP拟合结果及双侧0.8置信区间

表 1 10 000次蒙特卡洛模拟的统计结果

图 2 初始状态的一步可达集合与状态约束集合

图 3 算法1在Pp = 0.1时的10 000条蒙特卡洛状态轨迹

图 4 算法1在Pp = 0.1时10 000条蒙特卡洛输入轨迹

表 2 2种工况下的理想加速度数据

图 5 减速工况下的加速度对比图

图 6 减速工况下的速度对比图

图 7 减速工况下的间距误差对比图

图 8 减速工况下的状态轨迹对比图

图 9 加速工况下的加速度对比图

图 10 加速工况下的速度对比图

图 11 加速工况下的间距误差对比图

图 12 加速工况下的状态轨迹对比图

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