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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。一个最近的变体称为显式MPC（EMPC）与其他MPC方法的不同之处在于，在控制器的运行时间不需要数值优化。由于在运行时不需要迭代算法，EMPC适用于具有非常高的采样频率和严格的实时要求的系统。然而，EMPC仅适用于约束条件少、预测范围短的低阶线性系统。EMPC控制律的计算和快速评价是目前国内外研究的热点。在快速评估方法取得进展之后，第一步，即显式控制律的实际计算是瓶颈。本项目的目标是设计一种新的方法（简称顶点法），用于计算具有线性输入、状态和输出约束的线性系统的显式控制律。具体包括以下三个方面：（1）发展一种鲁棒的复杂显式控制律计算方法：顶点法计算量大。它与现有方法共享这一特性。所提出的方法中所需的计算是，但是，更简单，可以进行更可靠地比现有的方法。假设所提出的项目可以进行，顶点方法将计算要求，但可以应用于更苛刻的MPC问题比目前的方法，由于其简单性和可靠性。此外，顶点方法提供了显式的控制律的形式，这是特别适合于最近提出的方法来快速评估EMPC法律。(2)明确的法律的概括性描述的基础：虽然该项目的第一阶段专门处理线性系统，规范形式和等价类的顶点的描述是长期的兴趣，因为它在原则上适合于描述非线性MPC问题的显式控制律的结构。顶点法是基于分叉奇点理论的中心思想，这是一个非线性理论的起源。(3)通过结合显式和在线MPC来加速在线MPC：该项目的一部分研究了一种新的方法来利用在线MPC中显式控制律的结构。在控制器运行时不使用实际的显式控制律，而是使用其结构来简化在线MPC问题。中心思想不是存储关于对于每个x（t）哪些约束是活动的信息，而是关于哪些约束是不活动的信息。后一种信息可以用多面体存储。这些多面体一般不是凸的，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EMPC中计算工作量和存储的指数增长相反。