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Event-based model predictive control with piecewise optimal state feedback laws

具有分段最优状态反馈定律的基于事件的模型预测控制

基本信息

批准号：
280904794
负责人：
Professor Dr.-Ing. Martin Mönnigmann
金额：
--
依托单位：
Lehrstuhl für Regelungstechnik und Systemtheorie
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 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/280904794?language=en
关键词：
Event based model predictive control

项目摘要

Rapidly growing digital networks and ever growing computing power provide new possibilities for control and automation technology, but also give rise to new fundamental problems. In particular the central paradigm of permanent feedback must be questioned, if energy consumption and bandwidth requirements are to be minimized. Instead of permanently performing sensor and control computations, it is obviously desirable to limit computation and network traffic to instances when a controlled system actually needs attention. This is the central idea of event-based control.The proposed project addresses an event-based approach to model predictive control (MPC). In MPC, a mathematical optimization problem is solved periodically to determine the optimal future control sequence for the controlled system. The optimal control sequence needs to be updated periodically, because, among other reasons, disturbances need to be corrected for. Because the computational effort spent on solving underlying optimization problems is high, it is attractive to avoid them whenever possible. Consequently, event-based schemes are particularly attractive for MPC. Existing approaches exploit that not only a control signal but a control signal sequence is calculated in MPC. The approach proposed here is based on a different, new idea: Predictive control operates point-by-point, i.e. the optimization problem is solved for the current state of the system (a point in its state space). It has so far been overlooked that the point-wise solution implies the optimal feedback law on an entire region in the state space (a convex polytope) around the current state. In fact, the optimal feedback law is a state feedback law that has the same simple form as Kalman´s seminal optimal solution to the linear-quadratic regulator. (The proposed approach is not a variant of explicit MPC. No parametric optimizations need to be solved.)The optimal state feedback law and the region of its validity can be determined at practically no extra computational cost from the point-wise solution. The computationally expensive MPC problem only needs to be solved on demand, and the event causing the re-computation occurs when the controlled system leaves the region of validity of the current optimal state feedback law.The resulting event-based MPC method can be implemented by combining a lean (cheap, small, light, energy-efficient) local embedded system and a computationally powerful central node that is only called on demand. The local node only needs to evaluate optimal state feedback laws of the same simple form as Kalman´s solution to the linear-quadratic regulator. When its region of validity is left (a convex polytope), the local node requests a new state feedback law from the central node. The central node must therefore be capable of solving MPC problems. Because it is only called on demand, the central node can provide its service to multiple local nodes.

快速发展的数字网络和不断增长的计算能力为控制和自动化技术提供了新的可能性，但也引发了新的基本问题。特别是，如果要最小化能耗和带宽要求，则必须质疑永久反馈的中心范式。显然，希望将计算和网络流量限制在受控系统实际需要关注的实例中，而不是永久地执行传感器和控制计算。这是基于事件的控制的中心思想。所提出的项目解决了基于事件的模型预测控制（MPC）方法。在 MPC 中，定期求解数学优化问题以确定受控系统的最优未来控制序列。最佳控制序列需要定期更新，因为除其他原因外，还需要校正干扰。由于解决底层优化问题所花费的计算量很大，因此尽可能避免它们是很有吸引力的。因此，基于事件的方案对于 MPC 特别有吸引力。现有方法不仅利用MPC计算控制信号，而且还计算控制信号序列。这里提出的方法基于一个不同的新想法：预测控制逐点运行，即针对系统的当前状态（其状态空间中的一个点）求解优化问题。迄今为止，人们忽视了逐点解意味着当前状态周围状态空间（凸多面体）整个区域的最优反馈律。事实上，最优反馈律是一种状态反馈律，其简单形式与卡尔曼线性二次调节器的开创性最优解相同。（所提出的方法不是显式 MPC 的变体。不需要解决参数优化问题。）最佳状态反馈定律及其有效性区域可以通过逐点解决方案确定，几乎不需要额外的计算成本。计算成本高的 MPC 问题只需要按需解决，当受控系统离开当前最优状态反馈律的有效区域时，就会发生导致重新计算的事件。由此产生的基于事件的 MPC 方法可以通过将精益（廉价、小型、轻量、节能）本地嵌入式系统与仅按需调用的计算能力强大的中央节点相结合来实现。本地节点只需要评估与线性二次调节器的卡尔曼解相同简单形式的最优状态反馈定律。当离开其有效区域（凸多面体）时，本地节点向中央节点请求新的状态反馈律。因此，中心节点必须能够解决 MPC 问题。因为它只是按需调用，所以中心节点可以向多个本地节点提供其服务。