Robust and stochastic economic model predictive control

鲁棒随机经济模型预测控制

• 批准号: 279734922
• 负责人: Professor Dr.-Ing. Frank Allgöwer
• 金额: --
• 依托单位: Institut für Regelungstechnik (IRT)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/279734922?language=en
• 关键词: Robust; stochastic; economic; model; predictive

Model predictive control (MPC), also called receding horizon control, is a control strategy which consists of repeatedly solving (online) a finite horizon optimal control problem and then applying the first part of the corresponding solution to the considered system. Its main advantages and reasons for its widespread success include the possibility to explicitly incorporate state and input constraints as well as some performance criterion into the controller design. Most of the results available in the literature consider stabilizing MPC schemes, where the control objective is the stabilization of some a priori given setpoint (or more general reference signal). On the other hand, in recent years economic MPC schemes have received an increasing amount of attention, where the control objective is the optimization of some general performance criterion, which need not be related to a specific steady-state as in stabilizing MPC. Such economic MPC schemes are of importance in many different applications, and they require different analysis methods and concepts than stabilizing MPC due to the more general control objective. As in most practical applications modeling uncertainties as well as disturbances are present, it is of intrinsic importance to develop MPC schemes for which closed-loop guarantees such as constraint satisfaction and performance estimates can be established despite the presence of these disturbances. In the context of stabilizing MPC, various different solution methods to this problem are available both in a robust and stochastic setting. On the other hand, for economic MPC, this is to a very large extent an open problem and only very few first attempts in this direction were made so far. The main goal of the proposed project is to contribute to this open research area. In particular, we aim at developing economic MPC schemes for uncertain systems for which desired closed-loop guarantees such as recursive feasibility, constraint satisfaction and (average) performance guarantees can be rigorously proven. We consider both the cases where no further information on the disturbances is known (i.e., robust economic MPC schemes) as well as cases where additional (stochastic) information on the disturbance is available, which can be used for performance improvement (i.e., stochastic economic MPC schemes). To this end, the project examines whether and how certain approaches from stabilizing robust and stochastic MPC can be extended and transferred to an economic setting, and develops novel methods and concepts which are needed due to the more general nature of the problem.

模型预测控制（MPC），也称为后退水平控制，是一种通过反复求解（在线）有限水平最优控制问题，然后将相应解的第一部分应用于被考虑系统的控制策略。它的主要优点和广泛成功的原因包括可以显式地将状态和输入约束以及一些性能标准纳入控制器设计中。文献中可用的大多数结果都考虑稳定MPC方案，其中控制目标是稳定一些先验给定的设定值（或更一般的参考信号）。另一方面，近年来经济性MPC方案受到越来越多的关注，其中控制目标是某些一般性能标准的优化，而不需要像稳定MPC那样与特定的稳态相关。这种经济的MPC方案在许多不同的应用中都很重要，但由于控制目标更一般，与稳定MPC相比，它们需要不同的分析方法和概念。由于在大多数实际应用中建模不确定性和干扰都是存在的，因此开发MPC方案具有内在的重要性，尽管存在这些干扰，但仍可以建立闭环保证，如约束满足和性能估计。在稳定MPC的背景下，在鲁棒和随机环境下，该问题有各种不同的求解方法。另一方面，对于经济MPC来说，这在很大程度上是一个开放的问题，到目前为止，在这个方向上只有很少的第一次尝试。拟建项目的主要目标是为这个开放的研究领域做出贡献。特别是，我们的目标是为不确定系统开发经济MPC方案，其中期望的闭环保证，如递归可行性，约束满足和（平均）性能保证可以严格证明。我们考虑了没有关于干扰的进一步信息已知的情况（即，鲁棒经济MPC方案）以及关于干扰的额外（随机）信息可用的情况，这些信息可用于性能改进（即，随机经济MPC方案）。为此，该项目研究了稳定稳健和随机MPC的某些方法是否以及如何扩展和转移到经济环境中，并开发了由于问题的更普遍性质所需要的新方法和概念。