Tag - Control theory

Marco Cirant: On the long time behaviour of equilibria in a Kuramoto Mean Field Game

20th February, 2024

In a recent work, R. Carmona, Q. Cormier and M. Soner proposed a mean field game based on the classical Kuramoto model, originally motivated by systems of chemical and biological oscillators. Such MFG model exhibits several stationary equilibria, and the question of their ability to capture long time limits of dynamic equilibria is largely open. I will discuss in the talk how to show that, up to translations, there are two possible stationary equilibria only - the incoherent and the synchronised one - provided that the interaction parameter is large enough. Finally, I will present some local stability properties of the synchronised equilibrium.

Sophie Shermer: Robust control of quantum systems

25th May, 2023

Robust control is a well-established field in classical control theory that addresses the need for designing controllers capable of maintaining desired system performance despite uncertainties and disturbances. Approaches like H∞ control and μ-synthesis have been widely used in robust control for classical systems. However, these techniques face challenges when applied to quantum control systems due to the non-linear and time-domain nature of the latter, as well as the problem of marginal stability.

Stability is generally considered a crucial property of control systems and often a prerequisite for robust control, but in the context of quantum control systems, stability is often not desirable. This motivates the exploration of achieving robust performance without stabilization, i.e., maintaining control at the edge of stability. To achieve this, conventional measures for robust performance need to be adapted to the quantum setting.

In this talk we will investigate the applicability of classical robust performance measures to quantum control systems. We explore the limitations of techniques such as singular value analysis, log-sensitivity, and robustness infidelity measures based on the Wasserstein distance. These measures provide insights into the system's sensitivity to uncertainties and disturbances, but they may not be sufficient for fully capturing the complexities of quantum control systems.

Achieving robust performance without stabilization and quantifying it will require innovative approaches tailored to the specific characteristics of quantum systems. Further research is needed to develop new techniques and metrics that can effectively address the robustness requirements of quantum control systems.