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Proceedings of the ... American Control Conference/Proceedings of the American Control Conference

Finite horizon H∞ control for a class of linear quantum measurement delayed systems: A dynamic game approach

Aline I. Maalouf, Ian R. Petersen

Published Jun 1, 2011• 5 citations
Publisher

Abstract

In this paper, a finite horizon H∞control problem is solved for a class of linear quantum systems using a dynamic game approach for the case of delayed measurements. The methodology adopted involves an equivalence between the quantum problem and an auxiliary classical stochastic problem. Then, the finite horizon H∞control problem for the class of linear quantum systems under consideration is solved for the case of delayed measurements by solving the finite horizon H∞control problem for an equivalent stochastic H∞control problem using some results from a corresponding deterministic problem following a dynamic game approach.

DOI
10.1109/acc.2011.5990635

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In this paper, a finite horizon H∞control problem is solved for a class of linear quantum systems using a dynamic game approach for the case of delayed measurements. The methodology adopted involves an equivalence between the quantum problem and an auxiliary classical stochastic problem. Then, the finite horizon H∞control problem for the class of linear quantum systems under consideration is solved for the case of delayed measurements by solving the finite horizon H∞control problem for an equivalent stochastic H∞control problem using some results from a corresponding deterministic problem following a dynamic game approach.
Finite Horizon H∞H^\inftyH∞ Control for a Class of Linear Quantum Measurement Delayed Systems: A Dynamic Game Approach
In this paper, a finite horizon H∞H^\inftyH∞ control problem is solved for a class of linear quantum systems using a dynamic game approach for the case of delayed measurements. The methodology adopted involves an equivalence between the quantum problem and an auxiliary classical stochastic problem. Then, the finite horizon H∞H^\inftyH∞ control problem for the class of linear quantum systems under consideration is solved for the case of delayed measurements by solving the finite horizon H∞H^\inftyH∞ control problem for an equivalent stochastic H∞H^\inftyH∞ control problem following a dynamic game approach.
In this paper, the finite horizon H∞control problem is solved for a class of linear quantum systems using a dynamic game approach. The methodology adopted involves an equivalence between the quantum problem and an auxiliary classical stochastic problem. Then, by solving the finite horizon H∞control problem for the equivalent stochastic problem using results from a corresponding deterministic problem following a dynamic game approach, the finite horizon H∞control problem for the class of linear quantum systems under consideration is solved.
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.