Systematic Control Algorithms and Computational Tools for Complex Distributed Systems

该奖项的研究目标是为通过一般图形结构互联的高性能系统开发严格的控制算法和降低复杂性的工具，其中控制器传感和执行拓扑继承自工厂的拓扑结构。这项研究将提供一个新的算子理论框架，它可以捕获由异质、非平稳线性变参数(NSLPV)子系统模型组成的复杂分布式系统，这些模型在潜在无限图上相互连接，子系统之间和子系统内包含延迟。利用该框架，分布式系统的状态空间方程可以表示成类似于标准状态空间方程的紧致算子形式，并且单个标准状态空间系统的鲁棒控制结果的许多推导和证明可以适用于任意图上互联的NSLPV系统。结果将包括稳定和可稳定/可检测的分布式系统的模型降阶技术和控制设计的凸方法，包括处理互连结构和不确定初始条件的实时变化的新的确定性方法。对于最终周期性的分布式系统，还将设计简化的计算算法。如果成功，这项研究将适用于更广泛的复杂分布式工程系统。令人感兴趣的具体应用是移动传感器网络和多车辆系统的协作控制，例如在危险环境或灾区运行的地面机器人或无人驾驶飞行器(UAV)。本科生将通过许多项目参与研究计划。与弗吉尼亚理工大学加强工程多样性中心合作，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，将在初中生和高中生夏令营中提供，包括女性和少数族裔。此外，还将开发一门交叉列出的控制软件设计研究生课程，明确讨论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.