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.
