Pole placement design for quantum systems via coherent observers

Abstract

Abstract-We previously extended Luenberger's approach for observer design to the quantum case, and developed a class of coherent observers which tracks linear quantum stochastic systems in the sense of mean values. In light of the fact that the Luenberger observer is commonly and successfully applied in classical control, it is interesting to investigate the role of coherent observers in quantum feedback. As the first step in exploring observer-based coherent control, in this paper we study pole-placement techniques for quantum systems using coherent observers, and in such a fashion, poles of a closed-loop quantum system can be relocated at any desired locations. In comparison to classical feedback control design incorporating the Luenberger observer, here direct coupling between a quantum plant and the observer-based controller are allowed to enable a greater degree of freedom for the design of controller parameters. A separation principle is presented, and we show how to design the observer and feedback independently to be consistent with the laws of quantum mechanics. The proposed scheme is applicable to coherent feedback control of quantum systems, especially when the transient dynamic response is of interest, and this issue is illustrated in an example.

Isolated Loops in Quantum Feedback Networks

“…This we recognize as the SLH model where the input is trivially reflected -and so equals the output -while the Hamiltonian is modified exactly as in (34).…”

Nonlinear Optimal Feedback Control of the Two-Level Open Non-Markovian Stochastic Quantum System

“…To overcome this issue, an estimator is required to estimate the state of the system by using the output values of the quantum system, and then the estimated state is used to design the state feedback control laws [8]. Some work have been presented for the feedback control based on estimate of linear stochastic quantum system [9,10]. When the quantum system has some nonlinearities, such as the bilinearities, to design a state feedback controller for the bilinear stochastic quantum systems is a challenging work.…”

Bilinear Hamiltonian interactions between linear quantum systems via feedback

“…In this work, a direct or Hamiltonian interaction between the LQSSs is always meant to be bilinear, see Subsection 2.3. Such interactions have been considered in [21,26,27,28,29] for the applications mentioned above.…”

“…In this work, a direct or Hamiltonian interaction between the LQSSs is always meant to be bilinear, see Subsection 2.3. Such interactions have been considered in [21,26,27,28,29] for the applications mentioned above.Contrary to the Hamiltonian interactions between physical systems, like atoms or subatomic particles, that occur naturally, such interactions between engineered LQSSs must themselves be engineered. In [21, Subsection 6.4], a scheme for the implementation of a direct interaction between two one degree-of-freedom LQSSs (generalized harmonic oscillators) is proposed.…”