CPS: Small: A Convex Framework for Control of Interconnected Systems over Delayed Networks

近年来，蜂窝和WiFi网络在部署半自主物理系统机队方面出现了爆炸性增长，这些系统包括无人机(UAV)、自动驾驶车辆和气象站，以执行包裹递送、作物收获和天气预报等任务。蜂窝和WiFi网络的使用极大地降低了与这些形式的嵌入式技术相关的成本、能源和维护，但也增加了延迟、丢包和信号丢失等新的挑战。由于这些新的挑战，以及我们对不可靠通信如何影响性能的了解有限，当前用于管理无线网络上的物理系统的协议速度慢、效率低，并且可能不稳定。在这个项目中，我们开发了一个新的计算框架，用于设计可证明快速、高效和安全的协议，用于控制半自主物理系统的舰队。本项目所考虑的系统是动态的，由耦合的常微分方程组定义，并通过反馈连接到控制器，反馈互连具有多个静态时滞、多个时变时滞或在离散时间采样。对于这些系统，我们希望在传感器测量数量有限的情况下设计最优和鲁棒的反馈控制器。具体地说，我们试图设计一类在计算上有效的、可扩展到大量子系统的算法，并且在给定动态、通信链路和不确定性的模型的情况下，该算法将返回一个可证明稳定的、对模型不确定性稳健的、且在相关性能度量中可证明为最优的控制器。为了完成这一任务，我们利用了一个新的对偶结果，它允许无限维系统的控制器综合问题凸化。这一结果允许将最优和鲁棒动态输出反馈控制器综合问题转化为一组凸线性算子不等式的可行性。然后，我们使用半定规划来对可行算子集进行参数化，从而在几乎没有保守性的情况下检验这些不等式的可行性。类似地，估值器设计和最优控制器综合被转化为半定规划问题，并用于解决采样数据和输入时滞系统的问题。算法将可扩展到至少20个状态，控制器将在轮式机器人车辆车队上进行现场测试。

Recent years have seen an explosion in the use of cellular and wifi networks to deploy fleets of semi-autonomous physical systems, including unmanned aerial vehicles (UAVs), self-driving vehicles, and weather stations to perform tasks such as package delivery, crop harvesting, and weather prediction. The use of cellular and wifi networks has dramatically decreased the cost, energy, and maintenance associated with these forms of embedded technology, but has also added new challenges in the form of delay, packet drops, and loss of signal. Because of these new challenges, and because of our limited understanding of how unreliable communication affects performance, the current protocols for regulating physical systems over wireless networks are slow, inefficient, and potentially unstable. In this project we develop a new computational framework for designing provably fast, efficient and safe protocols for the control of fleets of semi-autonomous physical systems. The systems considered in this project are dynamic, defined by coupled ordinary differential equations, and connected by feedback to a controller, with a feedback interconnection which has multiple static delays, multiple time-varying delays, or is sampled at discrete times. For these systems, we would like to design optimal and robust feedback controllers assuming a limited number of sensor measurements are available. Specifically, we seek to design a class of algorithms which are computationally efficient, which scale to large numbers of subsystems, and which, given models of the dynamics, communication links, and uncertainty, will return a controller which is provably stable, robust to model uncertainty, and provably optimal in the relevant metric of performance. To accomplish this task, we leverage a new duality result which allows the problem of controller synthesis for infinite-dimensional systems to be convexified. This result allows the problem of optimal and robust dynamic output-feedback controller synthesis to be reformulated as feasibility of a set of convex linear operator inequalities. We then use semidefinite programming to parametrize the set of feasible operators and thereby test feasibility of the inequalities with little to no conservatism. In a similar manner, estimator design and optimal controller synthesis are recast as semidefinite programming problems and used to solve the problems of sampled-data and systems with input delay. The algorithms will be scalable to at least 20 states and the controllers will be field-tested on a fleet of wheeled robotic vehicles.