Guaranteed Cost Dynamic Coherent Control for Uncertain Linear Quantum Systems

TL;DR

This paper develops guaranteed cost control methods for uncertain linear quantum systems, proposing static and dynamic coherent controllers designed via LMIs, with the dynamic controller showing improved performance in simulations.

Contribution

It introduces two novel LMI-based methods for designing static and dynamic coherent controllers for uncertain quantum systems, with a focus on performance guarantees.

Findings

Dynamic quantum controller outperforms static controller in simulations.

Proposed methods effectively handle quadratic Hamiltonian perturbations.

Numerical results validate the control design approaches.

Abstract

This paper concerns a class of uncertain linear quantum systems subject to quadratic perturbations in the system Hamiltonian. A small gain approach is used to evaluate the performance of the given quantum system. In order to get improved control performance, we propose two methods to design a coherent controller for the system. One is to formulate a static quantum controller by adding a controller Hamiltonian to the given system, and the other is to build a dynamic quantum controller which is directly coupled to the given system. Both controller design methods are given in terms of LMIs and a non-convex equality. Hence, a rank constrained LMI method is used as a numerical procedure. An illustrative example is given to demonstrate the proposed methods and also to make a performance comparison with different controller design methods. Results show that for the same uncertain quantum system, the dynamic quantum controller can offer an improvement in performance over the static quantum controller.