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Chinese Control Conference (CCC)

Design of observer-based LQG controller via simulated annealing algorithm

Dong He, Zibo Miao

Published Jul 26, 2021• 0 citations
Publisher

Abstract

This paper is concerned with designing linear quadratic Gaussian (LQG) controller based on coherent quantum observer. In more concrete terms, we aim to design a stabilizing coherent quantum controller, which possesses the property of a coherent quantum observer, for a linear quantum plant in order to minimize a mean-square cost for the closed-loop quantum feedback system. In contrast to previous established work, we give a numerical approach to solving this problem via simulated annealing algorithm. Moreover, an illustrative example of designing locally optimal coherent quantum LQG controller are provided in order to demonstrate the algorithm performance proposed in the paper.

DOI
10.23919/ccc52363.2021.9549307

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Abstract. This paper considers a risk-sensitive optimal control problem for a field-mediated interconnection of a quantum plant with a coherent (measurement-free) quantum controller. The plant and the controller are multimode open quantum harmonic oscillators governed by linear quantum stochastic differential equations, which are coupled to each other and driven by multichannel quantum Wiener processes modeling the external bosonic fields. The control objective is to internally stabilize the closed-loop system and minimize the infinite-horizon asymptotic growth rate of a quadratic-exponential functional which penalizes the plant variables and the controller output. We obtain first-order necessary conditions of optimality for this problem by computing the partial Fréchet derivatives of the cost functional with respect to the energy and coupling matrices of the controller in the frequency domain and state space. An infinitesimal equivalence between the risk-sensitive and weighted coherent quantum LQG control problems is also established. In addition to variational methods, we employ spectral factorizations and infinite cascades of auxiliary classical systems. Their truncations are applicable to numerical optimization algorithms (such as the gradient descent) for coherent quantum risk-sensitive feedback synthesis.
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