哈尔滨工业大学（深圳）学术讲座

演讲人Speaker：Ian R. Petersen院士

主持人Host: 苗子博

题目Title: Risk Sensitive Control for Quantum Linear Systems

时间Date: 2023年 11月 29日      Time: 11：00 ~ 13：00

讲座地址Zoom Meeting ID: 829 2029 0840（Password: 415169）

内容摘要Abstract：

We consider the risk sensitive control problem for quantum linear systems. This involves designing a  controller to  minimize a cost functional which is the expectation of the exponential of a quadratic cost for an underlying quantum linear system. Such quantum linear systems arise in areas such as quantum optics and quantum microwave circuits as accurate approximations of true nonlinear quantum behaviours. These technologies have applications in newly emerging quantum technologies such as quantum computing and quantum metrology. The motivation for considering the quantum risk sensitive control problem is similar to the classical case in which the use of risk sensitive controllers leads to robustness of the feedback control system.

Unlike the classical case, the calculation of the quantum risk sensitive cost functional is a challenging problem even in the case of linear quantum systems. Our approach to this problem involves first deriving a  quantum Karhunen-Loeve type expansion for the quantum system variables. This is used in order to obtain a Girsanov type representation for quadratic-exponential functions.  We can then compute the  infinite-horizon risk sensitive cost corresponding to a stable linear quantum system. The resulting frequency-domain formulas express the infinite-horizon risk sensitive cost functional in terms of two spectral functions associated with the quantum system. This result extends a classical formula by Arov and Krein on the evaluation of entropy functionals to the quantum case. The result enables us to consider a numerical solution to a risk-sensitive optimal control problem for a feedback connection of a linear quantum plant with a measurement-based linear classical controller.

个人简介(About the speaker):

Ian R.Petersen自2017年起在澳大利亚国立大学工程学院担任教授。他是IFAC会士、IEEE会士、澳大利亚科学院院士和中科院“国际杰出学者”。1985年到2016年，在新南威尔士大学堪培拉校区工作，担任首席教授。曾担任《IEEE Transactions on Automatic Control》和《SIAM Journal on Control and Optimization》等期刊副主编，目前担任控制领域顶刊《Automatica》Optimization in Systems and Control版面主编，主要研究方向包括鲁棒控制理论，量子控制理论和随机控制理论等。