复杂明渠灌溉系统圣维南模型的预测控制研究

项目名称： 复杂明渠灌溉系统圣维南模型的预测控制研究

项目编号： No.61473317

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 岑丽辉

作者单位： 中南大学

项目金额： 82万元

中文摘要： 直接从圣维南方程出发研究明渠灌溉系统的预测控制，不仅能充分考虑系统的双曲型偏微分方程特性又能兼顾具有稳定性保证的有限时域优化控制，但其研究刚刚起步，还缺乏有效的理论分析和设计方法。本项目将以Riemann不变和Lyapunov方法为基本工具，借鉴边界反馈控制理论、无穷维系统理论和预测控制定性综合理论，提出基于圣维南动力学模型的具有稳定性保证的预测控制方案和策略。采用无穷算子，给出圣维南方程初边值混合问题的抽象形式，建立带终端约束集的预测控制统一描述；研究基于边界条件线性化的预测控制器构造方法、边界状态终端约束集设计方法，提出基于圣维南方程的预测控制算法；采用边界条件显式化方法，对复杂构形系统给出具有边界反馈控制特征的预测控制设计框架，研究面向复杂构形系统圣维南方程的分布式预测控制方法。本项目不仅是拟线性双曲型偏微分方程优化控制理论的新进展，且对节水灌溉和缓解水资源短缺矛盾具有重要意义。

中文关键词： 圣维南方程；预测控制；明渠灌溉系统；分布式控制

英文摘要： The study on the predictive control of open irrigation systems starting directly from the Saint-Venant equations takes both the property of hyperbolic partial differential equations and the optimal control in finite horizon with stability guarantee into account. Currently, this study is just started and lacks efficient theoretical methods for design and analysis. Based on the Riemann invariants and Lyapunov approach, the predictive control approach with stability guarantee for the Saint-Venant equations will be proposed, by combination of the boundary feedback control theory, infinite-dimensional theory and predictive control qualitative theory. By using the infinitesimal operator, the Saint-Venant mixed initial-boundary value problem will be converted to its abstract form. The formulation of the predictive control problem will be established. The construction method of the predictive controllers based on the linearization of the boundary conditions and the design of the terminal constraint set of the boundary states will be explored. The predictive control algorithms based on the Saint-Venant equations will also be developed. By using the explicit conversion of the boundary conditions, the distributed predictive control for open irrigation systems with complex topologies is investigated and the framework of the predictive control with the characteristic of the boundary feedback control will be presented. This work is not only a new development for optimal control theory of quasi-linear hyperbolic partial differential equations, but also significant for saving irrigation water and relieving the scarcity of water resources.

英文关键词： Saint-Venant equations;Predictive control;Open irrigation systems;Distributed control