Analytic optimal pose tracking control in close-range proximity operations with a non-cooperative target

This paper investigates an analytical optimal pose tracking control problem for chaser spacecraft during the close-range proximity operations with a non-cooperative space target subject to attitude tumbling and unknown orbital maneuvering.Firstly,the relative translational motion between the orbital target and the chaser spacecraft is described in the Line-of-Sight(LOS)coordinate frame along with attitude quaternion dynamics.Then,based on the coupled 6-Degree of Freedom(DOF)pose dynamic model,an analytical optimal control action consisting of constrained optimal control value,application time and its duration are proposed via exploring the iterative sequential action control algorithm.Meanwhile,the global closed-loop asymptotic stability of the proposed predictive control action is presented and discussed.Compared with traditional proximity control schemes,the highlighting advantages are that the application time and duration of the devised controller is applied discretely in light of the influence of the instantaneous pose configuration on the pose tracking performance with less energy consumptions rather than at each sample time.Finally,three groups of illustrative examples are organized to validate the effectiveness of the proposed analytical optimal pose tracking control scheme.

Angles-only initial relative orbit determination algorithm for noncooperative spacecraft proximity operations

This research furthers the development of a closed-form solution to the angles-only initial relative orbit determination problem for non-cooperative target close-in proximity operations when the camera offset from the vehicle center-of-mass allows for range observability.In previous work,the solution to this problem had been shown to be non-global optimal in the sense of least square and had only been discussed in the context of Clohessy–Wiltshire.In this paper,the emphasis is placed on developing a more compact and improved solution to the problem by using state augmentation least square method in the context of the Clohessy–Wiltshire and Tschauner–Hempel dynamics,derivation of corresponding error covariance,and performance analysis for typical rendezvous missions.A two-body Monte Carlo simulation system is used to evaluate the performance of the solution.The sensitivity of the solution accuracy to camera offset,observation period,and the number of observations are presented and discussed.

Proximity point algorithm for low-rank matrix recovery from sparse noise corrupted data

The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can be exactly solved via convex optimization by minimizing a combination of the nuclear norm and the 11 norm. In this paper, an algorithm based on the Douglas-Rachford splitting method is proposed for solving the RPCA problem. First, the convex optimization problem is solved by canceling the constraint of the variables, and ~hen the proximity operators of the objective function are computed alternately. The new algorithm can exactly recover the low-rank and sparse components simultaneously, and it is proved to be convergent. Numerical simulations demonstrate the practical utility of the proposed algorithm.

A Splitting Primal-dual Proximity Algorithm for Solving Composite Optimization Problems

Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is associated with many interesting challenges encoun- tered in the image restoration and image reconstruction fields. We developed a splitting primal-dual proximity algorithm to solve this problem. Furthermore, we propose a preconditioned method~ of which the iterative parameters are obtained without the need to know some particular operator norm in advance. Theoretical convergence theorems are presented. We then apply the proposed methods to solve a total variation regularization model, in which the L2 data error function is added to the L1 data error function. The main advantageous feature of this model is its capability to combine different loss functions. The numerical results obtained for computed tomography （CT） image recon- struction demonstrated the ability of the proposed algorithm to reconstruct an image with few and sparse projection views while maintaining the image quality.

An Efficient Proximity Point Algorithm for Total-Variation-Based Image Restoration

In this paper,we propose a fast proximity point algorithm and apply it to total variation(TV)based image restoration.The novel method is derived from the idea of establishing a general proximity point operator framework based on which new first-order schemes for total variation(TV)based image restoration have been proposed.Many current algorithms for TV-based image restoration,such as Chambolle’s projection algorithm,the split Bregman algorithm,the Berm´udez-Moreno algorithm,the Jia-Zhao denoising algorithm,and the fixed point algorithm,can be viewed as special cases of the new first-order schemes.Moreover,the convergence of the new algorithm has been analyzed at length.Finally,we make comparisons with the split Bregman algorithm which is one of the best algorithms for solving TV-based image restoration at present.Numerical experiments illustrate the efficiency of the proposed algorithms.

Impact Force Localization and Reconstruction via ADMM-based Sparse Regularization Method

In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although l_(1) regularization can be used to obtain sparse solutions,it tends to underestimate solution amplitudes as a biased estimator.To address this issue,a novel impact force identification method with l_(p) regularization is proposed in this paper,using the alternating direction method of multipliers(ADMM).By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators,ADMM can address the challenge effectively.To mitigate the sensitivity to regularization parameters,an adaptive regularization parameter is derived based on the K-sparsity strategy.Then,an ADMM-based sparse regularization method is developed,which is capable of handling l_(p) regularization with arbitrary p values using adaptively-updated parameters.The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure.Additionally,an investigation into the optimal p value for achieving high-accuracy solutions via l_(p) regularization is conducted.It turns out that l_(0.6)regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic l_(1) regularization method.The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.

An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-lsotropicTotalVariation

In this paper,we design an efficient,multi-stage image segmentation framework that incorporates a weighted difference of anisotropic and isotropic total variation(AITV).The segmentation framework generally consists of two stages:smoothing and thresholding,thus referred to as smoothing-and-thresholding(SaT).In the first stage,a smoothed image is obtained by an AITV-regularized Mumford-Shah(MS)model,which can be solved efficiently by the alternating direction method of multipliers(ADMMs)with a closed-form solution of a proximal operator of the l_(1)-αl_(2) regularizer.The convergence of the ADMM algorithm is analyzed.In the second stage,we threshold the smoothed image by K-means clustering to obtain the final segmentation result.Numerical experiments demonstrate that the proposed segmentation framework is versatile for both grayscale and color images,effcient in producing high-quality segmentation results within a few seconds,and robust to input images that are corrupted with noise,blur,or both.We compare the AITV method with its original convex TV and nonconvex TVP(O<p<1)counterparts,showcasing the qualitative and quantitative advantages of our proposed method.

Dual-quaternion-based satellite pose estimation and control with event-triggered data transmission

This paper proposes an event-triggered active disturbance rejection control framework to achieve the simultaneous position and attitude control of a satellite in proximity operations.Firstly,to facilitate the satellite motion description,we derive the relative kinematics and dynamics in terms of dual quaternions with the considerations of internal uncertainties and external disturbances.Then,two kinds of event-triggered mechanisms in the sensor/observer and controller/actuator channels are proposed to reduce the utilization of onboard communication resources and to improve control performance,respectively.The observation error and tracking error of both the attitude and orbit systems are theoretically proven to be asymptotically bounded.Finally,the simulation results show that the proposed method can achieve simultaneous position and attitude tracking between target and chaser satellites with satisfactory control performance and reduced communication rates.

Analysis of loss functions in support vector machines

Support vector machines(SVMs)are a kind of important machine learning methods generated by the cross interaction of statistical theory and optimization,and have been extensively applied into text categorization,disease diagnosis,face detection and so on.The loss function is the core research content of SVM,and its variational properties play an important role in the analysis of optimality conditions,the design of optimization algorithms,the representation of support vectors and the research of dual problems.This paper summarizes and analyzes the 0-1 loss function and its eighteen popular surrogate loss functions in SVM,and gives three variational properties of these loss functions:subdifferential,proximal operator and Fenchel conjugate,where the nine proximal operators and fifteen Fenchel conjugates are given by this paper.

A Variance Reducing Stochastic Proximal Method with Acceleration Techniques

We consider a fundamental problem in the field of machine learning—structural risk minimization,which can be represented as the average of a large number of smooth component functions plus a simple and convex(but possibly non-smooth)function.In this paper,we propose a novel proximal variance reducing stochastic method building on the introduced Point-SAGA.Our method achieves two proximal operator calculations by combining the fast Douglas–Rachford splitting and refers to the scheme of the FISTA algorithm in the choice of momentum factors.We show that the objective function value converges to the iteration point at the rate of O(1/k)when each loss function is convex and smooth.In addition,we prove that our method achieves a linear convergence rate for strongly convex and smooth loss functions.Experiments demonstrate the effectiveness of the proposed algorithm,especially when the loss function is ill-conditioned with good acceleration.

EFFICIENT BOX-CONSTRAINED TV-TYPE-l^1 ALGORITHMS FOR RESTORING IMAGES WITH IMPULSE NOISE

In this paper, we study the restoration of images simultaneously corrupted by blur and impulse noise via variational approach with a box constraint on the pixel values of an image. In the literature, the TV-l^1 variational model which contains a total variation （TV） regularization term and an l^1 data-fidelity term, has been proposed and developed. Several numerical methods have been studied and experimental results have shown that these methods lead to very promising results. However, these numerical methods are designed based on approximation or penalty approaches, and do not consider the box constraint. The addition of the box constraint makes the problem more difficult to handle. The main contribution of this paper is to develop numerical algorithms based on the derivation of exact total variation and the use of proximal operators. Both one-phase and two-phase methods are considered, and both TV and nonlocal TV versions are designed. The box constraint [0, 1] on the pixel values of an image can be efficiently handled by the proposed algorithms. The numerical experiments demonstrate that the proposed methods are efficient in computational time and effective in restoring images with impulse noise.

PAPR Reduction in Massive MU-MIMO-OFDM Systems Using the Proximal Gradient Method

In this paper,we address the issue of peak-to-average power ratio(PAPR)reduction in large-scale multiuser multiple-input multiple-output(MU-MIMO)orthogonal frequency-division multiplexing(OFDM)systems.PAPR reduction and the multiuser interference(MUI)cancellation problem are jointly formulated as an l_(∞)-norm based composite convex optimization problem,which can be solved efficiently using the iterative proximal gradient method.The proximal operator associated with l_(∞)-norm is evaluated using a low-cost sorting algorithm.The proposed method adaptively chooses the step size to accelerate convergence.Simulation results reveal that the proximal gradient method converges swiftly while provid-ing considerable PAPR reduction and lower out-of-band radiation.