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The proceedings of the IEEE Conference on Control Applications/The proceedings of the ... IEEE Conference on Control Applications

Guaranteed cost dynamic coherent control for a class of uncertain linear quantum systems

Chengdi Xiang, Ian R. Petersen, Daoyi Dong

Published Sep 1, 2015• 3 citations
Publisher

Abstract

This paper concerns a class of uncertain linear quantum systems subject to quadratic perturbations in the system Hamiltonian. A dynamic quantum controller is added to improve the control performance. A rank constrained LMI method is proposed as a numerical procedure to design a guaranteed cost dynamic coherent controller for this class of uncertain quantum systems.

DOI
10.1109/cca.2015.7320610

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This paper concerns a class of uncertain linear quantum systems subject to quadratic perturbations in the system Hamiltonian. A dynamic quantum controller is added to improve the control performance. A rank constrained LMI method is proposed as a numerical procedure to design a guaranteed cost dynamic coherent controller for this class of uncertain quantum systems.
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.
This technical note extends applications of the quantum small gain and Popov methods from existing results on robust stability to performance analysis results for a class of uncertain quantum systems. This class of systems involves a nominal linear quantum system and is subject to quadratic perturbations in the system Hamiltonian. Based on these two methods, coherent guaranteed cost controllers are designed for a given quantum system to achieve improved control performance. An illustrative example also shows that the quantum Popov approach can obtain less conservative results than the quantum small gain approach for the same uncertain quantum system.
This paper considers a class of uncertain linear quantum systems subject to uncertain perturbations in the system Hamiltonian. We present a method to design a coherent robust H-infinity controller so that the closed loop system is robustly stable and achieves a prescribed level of disturbance attenuation with all the admissible uncertainties. An illustrative example shows that for the given system, the method presented in this paper has improved performance over the existing quantum H-infinity control results without considering uncertainty.