Coherent strong observers for a class of linear quantum stochastic systems with unknown inputs

In this paper, we extend our previous research on design of coherent observers for open quantum systems (as quantum plants) to the case where there exist unknown inputs in the quantum plants. The unknown inputs represent unmodeled dynamics or disturbances which are prevalent in reality in quantum systems. Since no prior knowledge for the unknown inputs is assumed, the quantum version of Luenberger observers or Kalman filters are not adequate in such a scenario. We thus employ linear quantum stochastic systems and an inner model to tackle this problem. In addition, in order to preserve the coherence in the information flow due to quantum mechanics, any measurement of the quantum system is ruled out, which brings in new challenges compared to the classical counterpart. To be more specific, we develop coherent strong observers for open quantum harmonic oscillators with unknown inputs involved, showing a detailed procedure regarding synthesis of coherent strong observers for such systems that accomplish the task of simultaneously estimating system variables together with the unknown inputs, which is also illustrated by a simulation example. The results in this paper enrich our exploration on observer design for quantum systems under various circumstances, and thus pave the way towards more systematic and comprehensive analysis concerning coherent estimation.