Physics – Quantum Physics
Scientific paper
2011-05-09
Physics
Quantum Physics
22 pages, 1 figure; a brief version of this paper has been accepted for publication in the Proceedings of the Australian Contr
Scientific paper
The paper is concerned with the coherent quantum Linear Quadratic Gaussian (CQLQG) control problem for time-varying quantum plants governed by linear quantum stochastic differential equations over a bounded time interval. A controller is sought among quantum linear systems satisfying physical realizability (PR) conditions. The latter describe the dynamic equivalence of the system to an open quantum harmonic oscillator and relate its state-space matrices to the free Hamiltonian, coupling and scattering operators of the oscillator. Using the Hamiltonian parameterization of PR controllers, the CQLQG problem is recast into an optimal control problem for a deterministic system governed by a differential Lyapunov equation. The state of this subsidiary system is the symmetric part of the quantum covariance matrix of the plant-controller state vector. The resulting covariance control problem is treated using dynamic programming and Pontryagin's minimum principle. The associated Hamilton-Jacobi-Bellman equation for the minimum cost function involves Frechet differentiation with respect to matrix-valued variables. The gain matrices of the CQLQG optimal controller are shown to satisfy a quasi-separation property as a weaker quantum counterpart of the filtering/control decomposition of classical LQG controllers.
Petersen Ian R.
Vladimirov Igor G.
No associations
LandOfFree
A Dynamic Programming Approach to Finite-horizon Coherent Quantum LQG Control does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Dynamic Programming Approach to Finite-horizon Coherent Quantum LQG Control, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Dynamic Programming Approach to Finite-horizon Coherent Quantum LQG Control will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-333236