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Australian Control Conference

A Popov approach to performance analysis and coherent guaranteed cost control for uncertain quantum systems

Chengdi Xiang, Ian R. Petersen, Daoyi Dong

Published Nov 1, 2014• 5 citations
Publisher

Abstract

This paper considers a Popov approach to analyze the performance of an uncertain quantum system, which is subjected to quadratic perturbations in the system Hamiltonian. To get improved performance for this quantum system, a coherent guaranteed cost controller is designed by adding a control Hamiltonian. In this case, a performance comparison between the original uncertain quantum system and the uncertain quantum system with added coherent controller is carried out for an illustrative example.

DOI
10.1109/aucc.2014.7358678

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This paper considers a Popov approach to analyze the performance of an uncertain quantum system, which is subjected to quadratic perturbations in the system Hamiltonian. To get improved performance for this quantum system, a coherent guaranteed cost controller is designed by adding a control Hamiltonian. In this case, a performance comparison between the original uncertain quantum system and the uncertain quantum system with added coherent controller is carried out for an illustrative example.
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 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 paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general class of perturbations to the system Hamiltonian. Then, the special case of a nominal linear quantum system is considered with quadratic perturbations to the system Hamiltonian. In this case, a robust stability condition is given in terms of a frequency domain condition which is of the same form as the standard Popov stability condition.
This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general class of perturbations to the system Hamiltonian. Then, the special case of a nominal linear quantum system is considered with quadratic perturbations to the system Hamiltonian. In this case, a robust stability condition is given in terms of a frequency domain condition which is of the same form as the standard Popov stability condition.