A Homotopy Approach to Coherent Quantum LQG Control Synthesis Using Discounted Performance Criteria

This paper is concerned with linear-quadratic-Gaussian (LQG) control for a field-mediated feedback connection of plant and coherent (measurement-free) controller. The controller are multimode open quantum harmonic oscillators governed by linear stochastic differential equations. objective to make the closed-loop system internally stable minimize infinite-horizon quadratic cost variables output subject physical realizability (PR) constraints. LQG (CQLQG) problem, which has been active research interest over ten years, does not admit solution in form separation principle independent Riccati equations known its classical counterpart. We apply variational techniques family discounted CQLQG problems parameterized an effective time horizon. yields homotopy algorithm, initialized PR (but necessarily stabilizing) aims at locally optimal stabilizing original problem limit.