arXiv subjects

Ian R. Petersen

Publications and source records attributed to Ian R. Petersen.

242 records · Page 14Linked to original sources

arXiv2011

A Dynamic Programming Approach to Finite-horizon Coherent Quantum LQG Control

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.

quant-ph↗

arXiv2011

A Quasi-separation Principle and Newton-like Scheme for Coherent Quantum LQG Control

This paper is concerned with constructing an optimal controller in the coherent quantum Linear Quadratic Gaussian problem. A coherent quantum controller is itself a quantum system and is required to be physically realizable. The use of coherent control avoids the need for classical measurements, which inherently entail the loss of quantum information. Physical realizability corresponds to the equivalence of the controller to an open quantum harmonic oscillator and relates its state-space matrices to the Hamiltonian, coupling and scattering operators of the oscillator. The Hamiltonian parameterization of the controller is combined with Frechet differentiation of the LQG cost with respect to the state-space matrices to obtain equations for the optimal controller. A quasi-separation principle for the gain matrices of the quantum controller is established, and a Newton-like iterative scheme for numerical solution of the equations is outlined.

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arXiv2011

Low Frequency Approximation for a class of Linear Quantum Systems using Cascade Cavity Realization

This paper presents a method for approximating a class of complex transfer function matrices corresponding to physically realizable complex linear quantum systems. The class of linear quantum systems under consideration includes interconnections of passive optical components such as cavities, beam-splitters, phase-shifters and interferometers. This approximation method builds on a previous result for cascade realization and gives good approximations at low frequencies.

eess.SY↗

arXiv2011

Lagrange Stabilization of Pendulum-like Systems: A Pseudo H-infinity Control Approach

This paper studies the Lagrange stabilization of a class of nonlinear systems whose linear part has a singular system matrix and which have multiple periodic (in state) nonlinearities. Both state and output feedback Lagrange stabilization problems are considered. The paper develops a pseudo H-infinity control theory to solve these stabilization problems. In a similar fashion to the Strict Bounded Real Lemma in classic H-infinity control theory, a Pseudo Strict Bounded Real Lemma is established for systems with a single unstable pole. Sufficient conditions for the synthesis of state feedback and output feedback controllers are given to ensure that the closed-loop system is pseudo strict bounded real. The pseudo H-infinity control approach is applied to solve state feedback and output feedback Lagrange stabilization problems for nonlinear systems with multiple nonlinearities. An example is given to illustrate the proposed method.

eess.SY↗

arXiv2011

Singular Perturbation Approximations for a Class of Linear Quantum Systems

This paper considers the use of singular perturbation approximations for a class of linear quantum systems arising in the area of linear quantum optics. The paper presents results on the physical realizability properties of the approximate system arising from singular perturbation model reduction.

eess.SY↗

arXiv2011

A New Stability Result for the Feedback Interconnection of Negative Imaginary Systems with a Pole at the Origin

This paper is concerned with stability conditions for the positive feedback interconnection of negative imaginary systems. A generalization of the negative imaginary lemma is derived, which remains true even if the transfer function has poles on the imaginary axis including the origin. A sufficient condition for the internal stability of a feedback interconnection for NI systems including a pole at the origin is given and an illustrative example is presented to support the result.

math.OC↗

arXiv2009

Sliding mode control of quantum systems

This paper proposes a new robust control method for quantum systems with uncertainties involving sliding mode control (SMC). Sliding mode control is a widely used approach in classical control theory and industrial applications. We show that SMC is also a useful method for robust control of quantum systems. In this paper, we define two specific classes of sliding modes (i.e., eigenstates and state subspaces) and propose two novel methods combining unitary control and periodic projective measurements for the design of quantum sliding mode control systems. Two examples including a two-level system and a three-level system are presented to demonstrate the proposed SMC method. One of main features of the proposed method is that the designed control laws can guarantee desired control performance in the presence of uncertainties in the system Hamiltonian. This sliding mode control approach provides a useful control theoretic tool for robust quantum information processing with uncertainties.

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arXiv2008

Avoiding entanglement sudden-death via measurement feedback control in a quantum network

In this paper, we consider a linear quantum network composed of two distantly separated cavities that are connected via a one-way optical field. When one of the cavity is damped and the other is undamped, the overall cavity state obtains a large amount of entanglement in its quadratures. This entanglement however immediately decays and vanishes in a finite time. That is, entanglement sudden-death occurs. We show that the direct measurement feedback method proposed by Wiseman can avoid this entanglement sudden-death, and further, enhance the entanglement. It is also shown that the entangled state under feedback control is robust against signal loss in a realistic detector, indicating the reliability of the proposed direct feedback method in practical situations.

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