Systematic Control Algorithms and Computational Tools for Complex Distributed Systems

该奖项的研究目标是开发严格的控制算法和复杂性降低工具，用于在一般图结构上相互连接的高性能系统，其中控制器传感和驱动拓扑继承自工厂的拓扑。该研究将提供一个新的算子理论框架，可以捕获由异构、非平稳线性参数变化（NSLPV）子系统模型组成的复杂分布式系统，这些子系统模型在潜在的无限图上相互连接，子系统之间和内部包含延迟。利用该框架，分布式系统的状态空间方程可以用一种类似于标准状态空间方程的紧算子形式表示，并且在单个标准状态空间系统上的许多鲁棒控制结果的推导和证明可以适用于在任意图上互连的NSLPV系统。研究结果将包括用于稳定和可稳定/可检测分布式系统的模型简化技术，以及用于控制设计的凸方法，包括处理互联结构实时变化和不确定初始条件的新型确定性方法。简化的计算算法也将被设计用于最终的周期性分布式系统。如果成功，该研究将应用于广泛的复杂分布式工程系统。感兴趣的具体应用是移动传感器网络和多车辆系统的协同控制，例如在危险环境或灾区操作的地面机器人或无人驾驶飞行器（uav）。本科生将通过众多项目参与研究计划。与弗吉尼亚理工大学工程多样性增强中心合作，基于这项研究的适合年龄的模块，以及无人机飞行控制系统的实践经验，将在夏令营中为初中和高中学生提供，包括女性和少数民族。此外，一个交叉列出的研究生课程的控制软件设计将被开发，它明确地解决控制系统的实施问题和相关问题。

The research objective of this award is to develop rigorous control algorithms and complexity reduction tools for high-performance systems interconnected over general graph structures, where the controller sensing and actuation topology is inherited from that of the plant. The research will provide a new operator theoretic framework that can capture complex distributed systems composed of heterogeneous, non-stationary linear parameter-varying (NSLPV) subsystem models interconnected over potentially infinite graphs, with delays incorporated between and within the subsystems. Using this framework, the state-space equations of the distributed system can be represented in a compact operator form which is reminiscent of standard state-space equations, and many derivations and proofs of robust control results on single standard state-space systems can be adapted to NSLPV systems interconnected over arbitrary graphs. The results will include model reduction techniques for stable and stabilizable/detectable distributed systems and convex methods for control design, encompassing novel deterministic approaches to handling real-time changes in the interconnection structure and uncertain initial conditions. Simplified computational algorithms will also be devised for eventually periodic distributed systems.If successful, the research will apply to a broad class of complex distributed engineering systems. Specific applications of interest are mobile sensor networks and cooperative control of multi-vehicle systems, such as ground robots or uninhabited aerial vehicles (UAVs), operating in hazardous environments or disaster zones. Undergraduate students will be involved in the research program through numerous projects. In collaboration with the Center for the Enhancement of Engineering Diversity at Virginia Tech, age-appropriate modules based on this research, along with hands-on experience with UAV flight control systems, will be provided in summer camps for middle and high school students, including women and minorities. In addition, a cross-listed graduate course on control software design will be developed, which addresses explicitly the implementation issues of control systems and related problems.