线性量子随机系统的H-无穷控制
H-Infinity Control of Linear Quantum Stochastic Systems
摘要：
本文的目的是制定和解决一类非交换线性随机系统的H ∞控制器的综合问题，其中包括许多感兴趣的量子技术的例子。该文件包括结果的类这样的系统的量子交换关系被保存（这样的要求必须满足物理量子系统）。一个量子版本的标准（经典）耗散性的结果，并从这个量子版本的严格有界实引理。这使得量子版本的两个Riccati解决方案的H-无穷控制问题。这个结果导致控制器，可以实现使用纯量子，纯经典或量子和经典元素的混合物。这个问题的控制器的物理可实现性进行了详细研究，并给出了必要和充分条件。我们的结果是建设性的意义上，我们提供了明确的公式对应的控制器的哈密顿函数和耦合算子。
英文摘要：
The purpose of this paper is to formulate and solve a H-infinity controller synthesis problem for a class of non-commutative linear stochastic systems which includes many examples of interest in quantum technology. The paper includes results on the class of such systems for which the quantum commutation relations are preserved (such a requirement must be satisfied in a physical quantum system). A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the Strict Bounded Real Lemma is derived. This enables a quantum version of the two Riccati solution to the H-infinity control problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements. This issue of physical realizability of the controller is examined in detail, and necessary and sufficient conditions are given. Our results are constructive in the sense that we provide explicit formulas for the Hamiltonian function and coupling operator corresponding to the controller.
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