Robust and stochastic economic model predictive control

模型预测控制（MPC），也称为滚动时域控制，是一种控制策略，它包括重复求解（在线）有限时域最优控制问题，然后将相应解的第一部分应用于所考虑的系统。它的主要优点和广泛成功的原因包括可以明确地将状态和输入约束以及一些性能标准纳入控制器设计。文献中的大多数结果考虑稳定MPC计划，其中的控制目标是稳定的一些先验给定的设定点（或更一般的参考信号）。另一方面，近年来，经济MPC方案受到越来越多的关注，其中控制目标是优化一些通用性能标准，其不需要与稳定MPC中的特定稳态相关。这种经济MPC方案在许多不同的应用中是重要的，并且由于更一般的控制目标，它们需要与稳定MPC不同的分析方法和概念。由于在大多数实际应用中存在建模不确定性和干扰，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，例如约束满足和性能估计。在稳定MPC的背景下，这个问题的各种不同的解决方法都可以在鲁棒和随机设置。另一方面，对于经济MPC，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初步尝试。拟议项目的主要目标是为这一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的MPC方案，其中所需的闭环保证（例如递归可行性、约束满足和（平均）性能保证）可以得到严格证明。我们考虑了两种情况，其中没有关于扰动的进一步信息是已知的（即，鲁棒经济MPC方案）以及关于干扰的附加（随机）信息可用的情况，其可用于性能改进（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并转移到经济环境中，并开发了由于问题的更一般性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.