多速率分段线性系统预测控制的显式设计

蒋亚丽; 邹媛媛; 牛玉刚

doi:10.3724/SP.J.1004.2013.00631

多速率分段线性系统预测控制的显式设计

doi: 10.3724/SP.J.1004.2013.00631

1.
华东理工大学化工过程先进控制与优化技术教育部重点实验室上海 200237;
2.
系统控制与信息处理教育部重点实验室上海 200240

详细信息

通讯作者:
邹媛媛

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- 被引次数: 0
出版历程
- 收稿日期: 2012-05-15
- 修回日期: 2012-08-14
- 刊出日期: 2013-05-20

Explicit Model Predictive Control for Multi-rate Piecewise Linear Systems

1.
Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237;
2.
Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai 200240

摘要

摘要: 针对输出采样周期是输入更新周期N倍的多速率分段线性(Piecewise linear, PWL)系统, 本文提出了保证稳定性的显式预测控制器设计方法. 首先, 基于动态规划原理将预测控制优化问题分解为多个单级优化问题; 然后, 根据分段线性系统各子模型以及目标函数的具体形式, 进一步将各单级优化问题分为若干个子问题, 再利用多参数二次规划(Multiparametric quadratic programming, MP-QP)方法求解;最后,通过比较各子问题的解从而得到系统的最优显式控制律. 在设计过程中, 将系统的最大正不变集作为优化问题的终端约束集, 从而保证了系统的稳定性. 仿真结果表明本文提出的显式预测控制方法能够有效降低多速率分段线性系统的在线计算时间, 在保证系统稳定性的同时, 满足其对输入更新速度的要求.
- 分段线性系统,多速率采样,显式预测控制,动态规划
Abstract: This paper studies the explicit model predictive control for piecewise linear (PWL) systems with the output sampling period several times larger than the input updating period. First, based on dynamic programming, the model predictive control optimization problem is decomposed into multi-stage optimization problems with one-step optimal horizon. Further, optimization problem of each stage is separated into sub-problems according to the sub-models of the piecewise linear system and the form of objective function. After that, by utilizing multiparametric quadratic programming (MP-QP) technique and comparing the solutions of all the sub-problems, the optimal explicit control laws are obtained. Besides, the maximal positively invariant set of the piecewise linear system is chosen as the terminal constraint set of the optimization problem such that the stability can be ensured. The numerical example shows that the proposed explicit model predictive control can reduce online computation and satisfy the demand of the multi-rate piecewise linear system with fast updating speed of input.
- Piecewise linear system, multi-rate control system, explicit model predictive control, dynamic programming

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参考文献(1)

[1]

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