基于事件触发机制的正系统分布式模型预测控制

Practical control systems often contain non-negative quantities. Positive system can accurately describe a control system composed of non-negative quantities such as the dynamic of water quantities in pipe networks, the congestion control process in traffic, and so on. Most of existing results on positive systems only aim to obtain the stability of the systems, but they ignore the advanced property of the presented approaches and the practicability of the obtained results. Thus, the applications of these results may lead to high cost and high resource waste. Considering these issues, this project will solve the problem of distributed model predictive control of positive systems by means of the matrix decomposition and linear programming approaches. First, by virtue of the stability theory and dynamic properties of positive systems, the distributed model predictive control of positive systems is proposed. Second, a distributed model predictive control is proposed for positive systems with disturbance. A cone invariant set is constructed to guarantee the feasibility of the corresponding algorithms. This project will establish a new distributed model predictive control approach of positive systems and apply the obtained results to city water systems.

实际系统常常包含非负量，正系统能精确刻画由非负量构成的系统，如水务管网中的水量动态、交通拥塞控制过程等。现有正系统的研究仅以稳定为最终目标，忽视了所采用方法的先进性和所获结论的实效性，其应用易导致高成本和资源浪费。为此，本项目拟借助矩阵分解和线性规划方法，提出正系统的分布式模型预测控制方法，重点开展如下研究：(1) 基于正系统的稳定性理论和动力学特点，提出正系统分布式模型预测控制方法；(2) 构造线性Lyapunov函数，引入锥不变集，提出外扰正系统分布式模型预测控制方法。本项目拟建立一套有别于传统的分布式模型预测控制方法，并将其应用到水务系统中。

实际系统常常包含非负量，正系统能精确刻画由非负量构成的系统，如水务管网中的水量动态、交通拥塞控制过程等。现有正系统的研究仅以稳定为最终目标，忽视了所采用方法的先进性和所获结论的实效性，其应用易导致高成本和资源浪费。为此，本项目以正系统为研究对象，借助线性规划，引入事件触发机制，提出正系统的事件触发控制和分布式模型预测控制方法，重点开展了如下三方面研究：(i) 基于区间不确定系统控制方法，提出正系统的事件触发控制方法；(ii) 构造线性Lyapunov函数，引入锥不变集，提出正系统的分布式模型预测控制方法；(iii) 引入混合增益线性性能指标，解决带扰动正系统的分布式模型预测控制问题。