Control theory focuses on steering the behavior of dynamical systems– often modeled by ordinary or partial differential equations– through the application of suitable external inputs. Its goals include driving the system toward a desired state, optimizing performance, or ensuring robustness in the presence of uncertainties. Stabilization, a closely related area, concerns designing strategies that prevent undesirable or unstable dynamics, guaranteeing that solutions remain near or converge toward equilibrium states. 

For systems governed by PDEs, these objectives involve a deep understanding of qualitative properties of solutions, energy methods, variational techniques, unique continuation principles, and Carleman estimates. Recent years have witnessed substantial progress driven by new analytical tools, the study of models inspired by real-world phenomena, and the emergence of nonclassical frameworks such as nonlocal operators, multi-agent systems, and hybrid network dynamics. 

This minisymposium brings together several contributions that reflect these advances in control and stability theory for problems arising in concrete applications. The talks address infinite-horizon optimal control with state constraints, stability and displacement monotonicity methods for mean field game systems, and novel controllability results for mixed and nonlocal operators motivated by peridynamics. Other presentations focus on inverse problems and geometric reconstruction techniques, as well as innovative approaches to stabilization and controllability in flexible networked structures. 

By gathering diverse perspectives, the minisymposium aims to foster interaction between researchers working on the theoretical foundations of control and stability and those motivated by applied challenges, highlighting emerging problems and promising directions for future investigation.