Robust and stochastic economic model predictive control

模型预测控制(MPC)，又称滚动域控制，是一种重复地在线求解有限域最优控制问题，然后将相应解的第一部分应用于所考虑的系统的控制策略。它的主要优点和广泛成功的原因包括可以将状态和输入约束以及一些性能准则显式地结合到控制器设计中。文献中的大多数结果都考虑了稳定预测控制方案，其中控制目标是使某个先验给定的设定点(或更一般的参考信号)镇定。另一方面，近年来，经济型预测控制方案受到了越来越多的关注，其控制目标是某种一般性能指标的最优化，而不需要像稳定化预测控制那样与特定的稳态有关。这种经济的预测控制方案在许多不同的应用中具有重要意义，而且由于控制目标更一般，它们需要不同于稳定预测控制的分析方法和概念。由于在大多数实际应用中，建模的不确定性和扰动都是存在的，因此开发MPC方案具有内在的重要性，即使存在这些扰动，也可以为其建立闭环系统保证，例如约束满足和性能估计。在稳定化预测控制的背景下，这个问题的各种不同的求解方法在稳健和随机环境下都是可用的。另一方面，对于经济货币政策而言，这在很大程度上是一个悬而未决的问题，迄今在这方面的初步尝试很少。拟议项目的主要目标是为这一开放研究领域做出贡献。特别是，我们的目标是为不确定系统开发经济的MPC方案，对于这些系统，期望的闭环系统保证，如递归可行性、约束满足和(平均)性能保证，可以得到严格的证明。我们既考虑了不知道关于扰动的进一步信息的情况(即，稳健的经济MPC方案)，也考虑了关于扰动的附加(随机)信息可用于性能改进的情况(即，随机经济MPC方案)。为此，该项目审查了稳定稳健和随机货币政策的某些方法是否以及如何可以推广并转移到经济环境中，并开发了由于问题的更一般性质而需要的新方法和概念。

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.