Controllability of Networks Under Sparsity Constraints
Speaker: Geethu Joseph
Abstract: This talk explores how graph-based approaches, combined with sparsity constraints, can optimize the controllability of network systems in large-scale applications. Network systems form the backbone of modern control theory, driving sectors such as biological networks, social networks, energy, healthcare, and finance. These systems are commonly represented using weighted graph structures, where nodes correspond to system components and edges represent interactions. Graphs in this context come in two forms: those with fully known edges and weights, and those with partially known edges and unknown weights. This talk explores the controllability of these two types of graphs through the lens of sparsity. First, we examine the controllability of systems modeled by graphs with known weights. We look at controlling such systems using sparse actuation, where only a small subset of sensors or actuators is selected due to resource constraints. We discuss how classical control theory and compressed sensing converge to optimize control strategies in large-scale networks. In the second part, we shift to structured systems represented by graphs with unknown weights. We define the notion of strong structural controllability and discuss sparse control of structured systems. We also briefly explore methods for sparsely modifying the input matrix to achieve strong structural controllability.
On the Optimality of Sparse Feedback Control under Architecture-Dependent Communication Delays
Speaker: Luca Ballotta
Abstract: Distributed control of multi-agent and large-scale systems is a well-established paradigm to tradeoff control performance for practical feasibility and costs. However, the profound connection between distributed architecture and control performance is often elusive in realistic scenarios. In this talk, I investigate the effects of communication delays that increase with the number of links in a distributed controller architecture. Specifically, I consider a distributed consensus task with stochastic and deterministic dynamics where the control design respectively minimizes the steady-state variance and maximizes the speed of convergence. Contrary to the common belief that more complex controllers provide better performance, these scenarios yield that the optimal controllers may exhibit sparse communication, shedding new light on optimal control design under real-world communication.