Performance Analysis for Distributed and Multiobjective Model Predictive Control — The role of Pareto fronts, multiobjective dissipativity and multiple equilibria

分布式多目标模型预测控制的性能分析 â 帕累托前沿、多目标耗散性和多重均衡的作用

• 批准号: 244602989
• 负责人: Professor Dr. Lars Grüne
• 金额: --
• 依托单位: Lehrstuhl für Angewandte Mathematik
• 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 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/244602989?language=en
• 关键词: Performance; Analysis; Distributed; Multiobjective; Model

Model predictive control is a control method which computes a feedback law by iteratively solving optimal control problems on finite time horizons. This proposal considers problem formulations in which these optimal control problem are not given in standard form but in which game theoretic or other generalized optimization settings are considered. The motivation for considering such generalized settings is primarily triggered by the growing interest in controlling large networks of systems in a distributed way, often by taking into account more than one optimization criterion. In such settings in general one cannot assume that a central optimal solution to the finite horizon optimal control problem can be found; instead, concepts like, e.g., Nash equilibria and Pareto optimality enter the picture. Smart grid applications form a particular class of such problems and while this proposal is not focused on a particular application area, smart grid control problems will serve as benchmark problems for evaluating our methods. Given such a situation, the central theme to be addressed in this project can be summarized in a single question: Given a distributed and/or multiobjective MPC scheme in which the solution to the finite horizon problem in each sampling instant satisfies some optimality property, can we conclude that the closed loop solution generated by the MPC scheme also enjoys a similar optimality property, at least in an approximate way? So, if for instance we can ensure that in each step an iterative algorithm (involving negotiations between a number of subsystems) can ensure that we reach a Nash equilibrium, under which conditions and for which optimality criteria can we ensure that the MPC closed loop is also (close to) a Nash equilibrium?In this project we will investigate both MPC schemes with and without stabilizing terminal constraints as well as economic MPC. In our analysis, dynamical properties of optimal finite horizon trajectories like turnpike properties are expected to play an important role. As these can be concluded from suitable dissipativity and controllability properties, the extension of such concepts to distributed and game theoretic contexts will have to be investigated. Moreover, numerical tools will be developed which allow to verify our theoretical results but also serve as a tool to build theoretical intuition and to identify reasonable assumptions on the systems under consideration.The project shall be carried out in close cooperation with the companion project "Fairness and Efficiency in Distributed Economic Model Predictive Control" proposed by Prof. Dr.-Ing. Frank Allgöwer, Universität Stuttgart. Both proposals address similar problem formulations, with this project concentrating on conceptual questions and their numerical verification and Prof. Allgöwer's proposal focusing on a constructive and algorithmic approach. As such, the projects ideally complement each other.

模型预测控制是一种通过在有限时间范围内迭代求解最优控制问题来计算反馈律的控制方法。该建议考虑的问题配方中，这些最优控制问题没有给出标准形式，但在博弈论或其他广义优化设置被认为是。考虑这种广义设置的动机主要是由于人们对以分布式方式控制大型系统网络的兴趣日益浓厚，通常是通过考虑一个以上的优化标准。在这样的设置中，通常不能假设可以找到有限时域最优控制问题的中心最优解;相反，诸如，纳什均衡和帕累托最优进入画面。智能电网的应用形成了一类特殊的问题，而这个建议是不是集中在一个特定的应用领域，智能电网控制问题将作为评估我们的方法的基准问题。在这种情况下，在这个项目中要解决的中心主题可以概括为一个问题：给定一个分布式和/或多目标MPC方案，其中在每个采样时刻的有限时域问题的解决方案满足一些最优性属性，我们可以得出结论，由MPC方案产生的闭环解决方案也享有类似的最优性属性，至少在一个近似的方式？因此，例如，如果我们可以确保在每一步中，迭代算法（涉及许多子系统之间的协商）可以确保我们达到纳什均衡，那么在哪些条件下以及在哪些最优性标准下，我们可以确保MPC闭环也是（接近）纳什均衡？在这个项目中，我们将调查MPC计划与不稳定终端的限制，以及经济MPC。在我们的分析中，动力学性质的最佳有限水平轨道像收费公路性质预计将发挥重要作用。由于这些可以得出结论，从适当的耗散性和可控性，这些概念的扩展到分布式和博弈论的背景下，将不得不进行调查。此外，还将开发数值工具，以验证我们的理论结果，同时也作为建立理论直觉和确定所考虑系统的合理假设的工具。该项目将与教授博士提出的配套项目“分布式经济模型预测控制的公平性和效率”密切合作。Ing. Frank Allgöwer，斯图加特大学。这两项建议都涉及类似的问题表述，本项目侧重于概念问题及其数值验证，而Allgöwer教授的建议侧重于建设性的算法方法。因此，这些项目在理想情况下是相辅相成的。