In this paper, the reverse order law for the Moore-Penrose inverse of closed linear operators with closed range is investigated by virtue of the Norm-preserving extension of the bounded linear operators. The results g...In this paper, the reverse order law for the Moore-Penrose inverse of closed linear operators with closed range is investigated by virtue of the Norm-preserving extension of the bounded linear operators. The results generalize some results obtained by S Izumino in [12].展开更多
This paper proposes partially norm-preserving filtering for a class of spacecraft in the presence of time-varying, but constant-magnitude maneuver. The augmented state Kalman filter(ASKF) is commonly used to track the...This paper proposes partially norm-preserving filtering for a class of spacecraft in the presence of time-varying, but constant-magnitude maneuver. The augmented state Kalman filter(ASKF) is commonly used to track the maneuvering spacecraft with unknown constant propulsion;however, if the maneuver varies via time, the estimation performance will be degraded. To promote the tracking performance of the ASKF in case of time-invariant,constant-magnitude disturbance, the partially norm-preserving ASKF is developed by applying the norm constraint on the unknown maneuver. The proposed estimator, which is decomposed into two partial estimators and iteratively propagated in turns,projects the unconstrained maneuver estimation onto the Euclidian surface spanned by the norm constraint. The illustrative numerical example is provided to show the efficiency of the proposed method.展开更多
Robust quantum control with uncertainty plays a crucial role in practical quantum technologies.This paper presents a method for solving a quantum control problem by combining neural network and symplecticfinite differ...Robust quantum control with uncertainty plays a crucial role in practical quantum technologies.This paper presents a method for solving a quantum control problem by combining neural network and symplecticfinite difference methods.The neural network approach provides a framework that is easy to establish and train.At the same time,the symplectic methods possess the norm-preserving property for the quantum system to produce a realistic solution in physics.We construct a general high dimensional quantum optimal control problem to evaluate the proposed method and an approach that combines a neural network with forward Euler’s method.Our analysis and numerical experiments confirm that the neural network-based symplectic method achieves significantly better accuracy and robustness against noises.展开更多
文摘In this paper, the reverse order law for the Moore-Penrose inverse of closed linear operators with closed range is investigated by virtue of the Norm-preserving extension of the bounded linear operators. The results generalize some results obtained by S Izumino in [12].
基金supported by the National Natural Science Foundation of China(11872109)the National Key R&D Program of China(2019YFA0706500)。
文摘This paper proposes partially norm-preserving filtering for a class of spacecraft in the presence of time-varying, but constant-magnitude maneuver. The augmented state Kalman filter(ASKF) is commonly used to track the maneuvering spacecraft with unknown constant propulsion;however, if the maneuver varies via time, the estimation performance will be degraded. To promote the tracking performance of the ASKF in case of time-invariant,constant-magnitude disturbance, the partially norm-preserving ASKF is developed by applying the norm constraint on the unknown maneuver. The proposed estimator, which is decomposed into two partial estimators and iteratively propagated in turns,projects the unconstrained maneuver estimation onto the Euclidian surface spanned by the norm constraint. The illustrative numerical example is provided to show the efficiency of the proposed method.
基金supported by the National Natural Science Foundation of China(No.11971458)supported by U.S.Department of Energy under the grant number DE-SC0022253.
文摘Robust quantum control with uncertainty plays a crucial role in practical quantum technologies.This paper presents a method for solving a quantum control problem by combining neural network and symplecticfinite difference methods.The neural network approach provides a framework that is easy to establish and train.At the same time,the symplectic methods possess the norm-preserving property for the quantum system to produce a realistic solution in physics.We construct a general high dimensional quantum optimal control problem to evaluate the proposed method and an approach that combines a neural network with forward Euler’s method.Our analysis and numerical experiments confirm that the neural network-based symplectic method achieves significantly better accuracy and robustness against noises.
