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

快速增长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，但也带来了新的根本性问题。特别是，如果要将能源消耗和带宽要求降至最低，就必须质疑永久反馈的中心范例。将计算和网络流量限制在受控系统实际需要注意的情况下，而不是永久地执行传感器和控制计算，显然是可取的。这是基于事件的控制的核心思想。该项目提出了一种基于事件的模型预测控制(MPC)方法。在预测控制中，一个数学优化问题被周期性地求解，以确定被控系统的最优未来控制序列。最优控制序列需要定期更新，因为除其他原因外，还需要对干扰进行校正。因为花在解决基本优化问题上的计算工作量很高，所以尽可能避免它们是很有吸引力的。因此，基于事件的方案对MPC特别有吸引力。现有方法利用了在MPC中不仅计算控制信号而且计算控制信号序列。这里提出的方法基于一种不同的新思想：预测控制逐点操作，即针对系统的当前状态(其状态空间中的一个点)解决优化问题。到目前为止，人们忽略了逐点解蕴含着当前状态周围状态空间(凸多面体)中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，其形式与卡尔曼S提出的线性二次型调节器的最优解相同。(建议的方法不是显式MPC的变体。不需要解决参数最优化问题。)从点解可以确定最优状态反馈律及其有效区域，而几乎不需要额外的计算代价。该方法只需按需解决计算量大的预测控制问题，当被控系统离开当前最优状态反馈律的有效区域时，才会发生导致重新计算的事件；基于事件的预测控制方法可通过将精简(廉价、小、轻、节能)的本地嵌入式系统与仅按需调用的计算能力强大的中心节点相结合来实现。局部节点只需计算最优状态反馈律，其形式与线性二次型调节器的卡尔曼S解的形式相同。当其有效区域为左(凸多面体)时，局部节点向中心节点请求新的状态反馈律。因此，中央节点必须能够解决MPC问题。由于只按需调用，因此中心节点可以向多个本地节点提供服务。

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.