Efficient calculation of explicit model predictive control laws using topological equivalence classes of critical points

使用临界点的拓扑等价类有效计算显式模型预测控制律

基本信息

批准号：
234842388
负责人：
Professor Dr.-Ing. Martin Mönnigmann
金额：
--
依托单位：
Lehrstuhl für Regelungstechnik und Systemtheorie
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2013
资助国家：
德国
起止时间：
2012-12-31 至 2016-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/234842388?language=en
关键词：
Efficient calculation explicit model predictive

项目摘要

Model predictive control (MPC) methods are established. A more recent variant known as explicit MPC (EMPC) differs from other MPC approaches in that no numerical optimization is required at runtime of the controller. Because no iterative algorithms are required at runtime, EMPC is suitable for systems with very high sampling frequencies and strict realtime requirements. EMPC can only be applied, however, to low order linear systems with few constraints and short prediction horizons. Both, the calculation of EMPC control laws, and the fast evaluation of these laws, are currently investigated by researchers worldwide. Today the first step, the actual calculation of the explicit laws, is the bottleneck, after methods for the fast evaluation have recently made progress.It is the goal of the project to devise a new method (the vertex-method for short) for the calculation of explicit control laws for linear systems with linear input, state and output constraints. Three aspects of this goal can be detailed as follows: (1) Development of a robust method for the calculation of complex explicit control laws: The vertex-method is computational demanding. It shares this trait with existing approaches. The calculations required in the proposed method are, however, simpler and can be carried out more reliably than for the existing methods. Assuming the proposed project can be carried out, the vertex-method will be computational demanding but can be applied to more demanding MPC problems than current methods due to its simplicity and reliability. Moreover, the vertex-method provides the explicit control law in a form which is particularly suitable for the recently proposed approaches to the fast evaluation of EMPC laws. (2) Foundations of a generalizable description of explicit laws: While the first period of the project exclusively deals with linear systems, the description of vertices with normal forms and equivalence classes is of long-term interest, because it is in principle suitable to describe the structure of explicit control laws of nonlinear MPC problems. The vertex-method is based on central ideas of the singularity theory of bifurcations, which is a nonlinear theory by origin. (3) Acceleration of online MPC by combining explicit and online MPC: A part of the project investigates a new approach to exploiting the structure of an explicit control law in online MPC. The actual explicit control law is not used at the runtime of the controller, but its structure is used to simplify the online MPC problem. The central ideas is not to store information about which constraints are active for every x(t), but about which constraints are inactive. The latter information can be stored with polytopes. These polytopes are not convex in general, but the number of these polytopes grows only linearly in the size of the control problem, in contrast to the exponential growth of computational effort and storage in EMPC.

建立了模型预测控制（MPC）方法。最近称为显式MPC（EMPC）的变体与其他MPC方法不同，因为在控制器的运行时不需要数值优化。由于运行时不需要迭代算法，因此EMPC适用于具有很高采样频率和严格实时要求的系统。但是，EMPC只能应用于少数约束和短距离预测范围的低阶线性系统。目前，全球研究人员都研究了EMPC控制法律的计算以及对这些法律的快速评估。今天的第一步是，明确定律的实际计算是瓶颈，在快速评估的方法最近取得了进步之后，该项目的目的是设计一种新方法（简短的Vertex方法）来计算使用线性输入，状态和输出约束的线性系统的显式控制法律。该目标的三个方面可以详细说明如下：（1）开发一种可靠的方法来计算复杂的显式控制定律：顶点方法是计算要求。它与现有方法共享这个特征。但是，提出的方法中所需的计算比现有方法更简单，并且可以更可靠地进行。假设可以执行提出的项目，则顶点方法将是计算要求的，但由于其简单性和可靠性，可以将其应用于更苛刻的MPC问题。此外，顶点方法以一种形式提供了明确的控制法，该形式特别适合最近提出的快速评估EMPC法律的方法。（2）对明确法律的可推广描述的基础：虽然该项目的第一阶段专门涉及线性系统，而对具有正常形式和等效类别类别的顶点的描述是长期的，因为它原则上适合描述非线性MPC问题的明确控制定律的结构。顶点方法基于分叉的奇异性理论的中心思想，这是一种非线性理论。（3）通过合并显式和在线MPC加速在线MPC：该项目的一部分研究了一种新方法来利用在线MPC中明确控制法的结构。在控制器的运行时不使用实际的显式控制法，但其结构用于简化在线MPC问题。中心思想不是存储每个X（t）的约束活动的信息，而是在哪些约束中不活动。后一个信息可以用多面体存储。这些多面体通常不是凸，但是这些多面体的数量仅在控制问题的大小上线性增长，与计算工作和储存在EMPC中的指数增长相反。