Recent Advancements in PDE Control of Battery Management and Swarm Robotics

This talk presents two recent PDE control applications using backstepping. The first part focuses on improving state-of-charge (SoC) and state-of-health (SoH) estimation in lithium-ion batteries, which are essential for electrified transportation and energy storage. We propose PDE observers to estimate lithium concentration in the electrolyte across the negative electrode, positive electrode, and separator, using reverse sensitivity analysis to identify the optimal measurable parameter. Enhanced PDE observers for solid-phase lithium concentration in the electrodes provide more accurate SoC and SoH estimates. The second part introduces a distributed encirclement control strategy for PDE-based multi-agent systems, combining both in-domain and boundary control to ensure collision avoidance. We present a three-dimensional framework where backstepping controllers guide boundary agents (leaders) to move agents toward targets, reform their formation, and maintain encirclement. In-domain control is applied for rotating and adjusting the formation.