Funnel MPC with application to the control of magnetic levitation systems

提出的研究项目的目标是新的控制概念漏斗MPC （FMPC）的发展，数值实现和分析。这个概念以一种创新的方式将自适应跟踪控制、学习和基于优化的方法联系在一起。漏斗控制和模型预测控制（MPC）都是控制工程和数学系统理论的研究热点，它们成功地平衡了理论与应用。FMPC利用两种控制策略的已知优势（例如，符合输出和控制约束，固有的鲁棒性，出色的控制性能）来实现非线性系统通用控制器设计的长期目标。FMPC由三个部分组成：在控制器的基于模型的部分，来自漏斗控制的元素被集成到MPC中，例如，通过将来自漏斗控制器的高增益因素整合到阶段成本的构建中。这确保了输出约束的遵从性，并最终允许通过最优性参数严格证明递归可行性——没有（稳定）终端约束，独立于预测范围的长度。2)。MPC一般不能保证稳健性。因此，将漏斗控制固有的鲁棒性转移到FMPC是一个主要目标。为此，控制回路由一个无模型组件通过与基于模型部分的预测误差的漏斗控制器耦合来扩展。对于这种组合，关于模型不确定性的鲁棒性有待严格证明。通过学习组件对控制回路的第二次扩展，实现了连续的模型自适应以及控制器性能的改进。为此，对未知模型参数进行近似，对系统状态进行估计。同时，鲁棒化的FMPC保证了输出约束的严格满足。此外，正如数值测试所表明的那样，它对系统产生了足够的刺激，从而确保了学习过程所必需的输入-输出数据中的高信息含量。这将在数学上严格地表征，并通过项目中“持续激励”的概念以可验证的方式进行布置。作为一个概念的证明，将考虑磁悬浮列车的控制，其中理论和数值实践之间的定期反馈是有意的。在悬浮控制中，必须保证车辆悬架与导轨之间的规定距离。此外，对于不确定性（例如，车辆的总质量取决于乘客区域的占用）和干扰（例如，风力条件）的鲁棒性至关重要。同时，需要高的控制器性能，包括行驶舒适性。正是这些属性统一在创新概念FMPC。

The objective of the proposed research project is the development, numerical implementation and analysis of the new control concept Funnel MPC (FMPC). This concept ties adaptive tracking control, learning and optimization based methods together in an innovative way.Funnel control and model predictive control (MPC) are both current research areas in control engineering and mathematical systems theory, which successfully balance theory and application. FMPC utilizes known advantages of both control strategies (e.g., compliance with output and control constraints, inherent robustness, excellent control performance) to achieve the long-term goal of a universal controller design for nonlinear systems. FMPC consists of three components:1.) In a model-based part of the controller, elements from funnel control are integrated into MPC, e.g., by incorporating the high-gain factor from the funnel controller in the construction of the stage costs. This ensures compliance with the output constraints and ultimately allows to rigorously prove recursive feasibility via an optimality argument – without (stabilizing) terminal constraints and independent of the length of the prediction horizon. 2.) MPC does not guarantee robustness in general. Hence, it is a main objective to transfer the robustness inherent to funnel control to FMPC. To this end, the control loop is extended by a model-free component via coupling with a funnel controller with respect to the prediction error of the model-based part. For this combination, robustness with respect to model uncertainties is to be proved rigorously.3.) Through a second extension of the control loop by a learning component a continuous model adaptation as well as a concomitant improvement of controller performance is achieved. For this purpose, unknown model parameters are approximated and the system state is estimated. Meanwhile, the robustified FMPC guarantees the strict satisfaction of the output constraints. Additionally, as numerical tests have shown, it induces a sufficient stimulation of the system, which ensures a high information content in the input-output data that is necessary for the learning process. This is to be characterized in a mathematically rigorous and laid out in a verifiable way by the concept of „persistency of excitation“ within the project. As a proof of concept the control of magnetic levitation trains will be considered, where a regular feedback between theory and numerical practice is intended. In levitation control a prescribed distance between vehicle suspension and guideway must be ensured. Furthermore, a robustness with respect to uncertainties (e.g., the total mass of the vehicle depending on the occupancy of the passenger area) and disturbances (e.g., wind conditions) is crucial. At the same time, a high controller performance, including travelling comfort, is desirable. Exactly those properties are unified in the innovative concept FMPC.