A group of subsystems/agents that collaborate autonomously through physical interactions and/or communications (forming a networked system/multi-agent system) could achieve objectives that are beyond the capability of an individual subsystem/agent. Moreover, such networked systems could offer better efficiency, fault tolerance, and flexibility due to their distributed operations, parallelized executions, function redundancy, and reconfigurability in the face of changes. Most importantly, many critical real-world systems, like power networks, supply chain networks, platoons, etc., can be modeled as networked systems. Consequently, there has been a steady growth in research interest in networked systems both from academia and industry.
One of the significant concerns in engineering such networked systems is the design of the cooperative controllers and the interconnection topology while guaranteeing compositionality and scalability. Here, compositionality implies that when certain subsystems are added to or subtracted from the existing network, there is no need to redesign the controllers and the topology globally, but only need to modify the affected components locally. On the other hand, scalability describes how the properties of the networked system, e.g., passivity indices, stability margins, etc., scale with respect to the system dimensions. When these two properties are retained, the subsystems can work cooperatively as a team and are free to join or leave the existing networks without any influence on the properties of the entire network. Besides, for large-scale networks, not only the controllers but also the topology plays a crucial role, as improper topologies may lead to performance deterioration, high delays, high communication costs, and even instability. In this regard, topology synthesis techniques are usually required to obtain an optimal topology with the least communication cost and the optimal system metrics, e.g., a robustness measure with respect to uncertainties, security-aware metrics, and stability margins.
Based on the above observations, in this project, we study the problem of compositional and scalable controller and topology co-design. In our prior work, we have developed several critical fundamental results to address this problem in a more generalized setting. The ongoing research explores establishing more specialized results necessary to address this problem for real-world networked systems like vehicular platoons, power networks, and supply chain networks.
