Semidefinite Programming Problem Research Articles

Signal propagation speed may not be available in practical localization scenarios. This paper addresses both the moving and stationary source localization problems by using frequency measurements when the signal propagation speed is unavailable. The task is fulfilled by exploiting the Doppler frequency shift coming from the relative motion between the source and a network of mobile sensors. Owing to the complicated nonlinear measurement model and the absence of the knowledge about signal propagation speed, it is difficult to conduct localization. To address this problem, we first transform the measurement model to a tractable form, from which to formulate a constrained weighted least squares (CWLS) problem. Afterwards, we propose two methods to solve the non-convex CWLS problem. The first method relaxes the CWLS problem into a semidefinite programming (SDP) problem by applying semidefinite relaxation (SDR). The second method adopts the alternating estimation procedure by utilizing the prior information about the nominal value of the signal propagation speed. Two subproblems are formulated and solved in an alternate manner, one in estimating the source position and velocity by applying SDR and the other the signal propagation speed by an explicit expression. Furthermore, we conduct the mean square error (MSE) analysis to show that the CWLS solution is able to reach the Cramér-Rao lower bound (CRLB) performance. Simulation results validate the expected performance of the proposed methods.

A data association algorithm for the robust confidence ellipsoid filter

Received signal strength- (RSS-) based localization has attracted considerable attention for its low cost and easy implementation. In plenty of existing work, sensor positions, which play an important role in source localization, are usually assumed perfectly known. Unfortunately, they are often subject to uncertainties, which directly leads to effect on localization result. To tackle this problem, we study the RSS-based source localization with sensor position uncertainty. Sensor position uncertainty will be modeled as two types: Gaussian random variable and unknown nonrandom variable. For either of the models, two semidefinite programming (SDP) methods are proposed, i.e., SDP-1 and SDP-2. The SDP-1 method proceeds from the nonconvex problem with respect to the maximum likelihood (ML) estimation and then obtains an SDP problem using proper approximation and relaxation. The SDP-2 method first transfers the sensor position uncertainties to the source position and then obtains an SDP formulation following a similar idea as in SDP-1 method. Numerical examples demonstrate the performance superiority of the proposed methods, compared to some existing methods assuming perfect sensor position information.

In this paper, we discuss mobile source localization using both time of arrival and Doppler frequency shift (TOA-DFS) measurements, where the source moves at a nonuniform velocity. To obtain the position of a mobile source, we first formulate the weighted least squares (WLS) problem by ignoring the second-order noise terms. Due to the non-convexity, we apply the convex relaxation technique to transform the problem into a semi-definite programming problem. However, ignoring the second-order noise terms is only reasonable in the case of small noise levels. In view of this, we then directly establish the maximum likelihood (ML) estimator based on the measurements model without ignoring the second-order noise terms. Since the ML estimator is a non-convex problem, we also propose implementable semidefinite relaxation (SDR) technique to tackle it. Finally, the Cramér-Rao lower bound (CRLB) analysis and results verify that the proposed methods based on the TOA-DFS measurements can significantly enhance localization accuracy.

In this manuscript, we present an energy-efficient alternating optimization framework based on the multi-antenna ambient backscatter communication (AmBSC) assisted cooperative non-orthogonal multiple access (NOMA) for next-generation (NG) internet-of-things (IoT) enabled communication networks. Specifically, the energy-efficiency maximization is achieved for the considered AmBSC-enabled multi-cluster cooperative IoT NOMA system by optimizing the active-beamforming vector and power-allocation coefficients (PAC) of IoT NOMA users at the transmitter, as well as passive-beamforming vector at the multi-antenna assisted backscatter node. Usually, increasing the number of IoT NOMA users in each cluster results in inter-cluster interference (ICI) (among different clusters) and intra-cluster interference (among IoT NOMA users). To combat the impact of ICI, we exploit a zero-forcing (ZF) based active-beamforming, as well as an efficient clustering technique at the source node. Further, the effect of intra-cluster interference is mitigated by exploiting an efficient power-allocation policy that determines the PAC of IoT NOMA users under the quality-of-service (QoS), cooperation, SIC decoding, and power-budget constraints. Moreover, the considered non-convex passive-beamforming problem is transformed into a standard semi-definite programming (SDP) problem by exploiting the successive-convex approximation (SCA) approximation, as well as the difference of convex (DC) programming, where Rank-1 solution of passive-beamforming is obtained based on the penalty-based method. Furthermore, the numerical analysis of simulation results demonstrates that the proposed energy-efficiency maximization algorithm exhibits an efficient performance by achieving convergence within only a few iterations.

Attitude control for a full-scale flexible electric solar wind sail spacecraft on heliocentric and displaced non-Keplerian orbits

Safety verification for Regime-Switching Jump Diffusions via barrier certificates

Context. The presence of time delays occurs in many complex dynamical systems, particularly in the areas of modern communication and information technologies, such as the problem of stabilizing networked control systems and high-speed communication networks. In many cases, time-delays lead to a decrease in the efficiency of such systems and even to the loss of stability. In the last decade, many interesting solutions using the Lyapunov-Krasovskii functional have been proposed for stability analysis and synthesis of a stabilizing regulator for discrete-time dynamic systems with unknown but bounded state-delays. The presence of nonlinear constraints on the amplitude of controls such as saturation further complicates this problem and requires the development of new approaches and methods.
 Objective. The purpose of this study is to develop a procedure for calculating the control gain matrix of state feedback that ensures the asymptotic stability of the analyzed system, as well as a procedure for calculating the maximum permissible value of the state-delay under which the stability of the closed-loop system can be ensured for a given set of admissible initial conditions.
 Method. The paper uses the method of descriptor transformation of the model of a closed-loop system and extends the invariant ellipsoids method to systems with unknown but bounded state-delays. The application of the Lyapunov-Krasovskii functional and the technique of linear matrix inequalities made it possible to reduce the problem of calculating the control gain matrix to the problem of semi-definite programming, which can be solved numerically. An iterative algorithm for solving the bilinear matrix inequality is proposed for calculating the maximum permissible value of the time-delay.
 Results. The results of numerical modeling confirm the effectiveness of the proposed approach in the problems of stabilizing discrete-time systems under the conditions of state-delays and nonlinear constraints on controls, which allows to recommend the proposed method for practical use for the problem of stability analysis and synthesis of stabilizing regulator, as well as for calculating the maximum permissible value of time-delay.
 Conclusions. An approach is proposed that allows extending the invariant ellipsoids method to discrete-time dynamic systems with unknown but bounded state-delays for solving the problem of system stabilization using static state feedback based on the application of the Lyapunov-Krasovskii functional. The results of numerical modeling confirm the effectiveness of the proposed approach in the presence of the saturation type nonlinear constraints on the control signals.

In this paper, we propose a secure multi-user uplink communicaion scheme against a mobile aerial eavesdropper (AE) in Integrated Sensing and Communication (ISAC) systems, where the ISAC base station transmits radar signals to track and jam the AE. For tracking mobile AE, we adopt an extended Kalman filter technique to predict AE's motion state. Based on the tracking information we formulate an optimization problem to jointly design radar signal and receiver beamformer for improving the secrecy performance. To deal with the non-convex constraints and the coupled variables, we propose an alternating optimization based algorithm via iteratively solving a Fractional Programming (FP) problem and a Semidefinite Program (SDP) problem. Numerical results show that the proposed algorithm can achieve higher secrecy capacity and better fairness, compared to the state-of-the-art techniques.

On the regularization and optimization in quantum detector tomography

Optimal linear array orientation design for 3D direct position determination via semi-Definite relaxation

The space, air and ground integrated network (SAGIN) will greatly promote the development of the Internet of Things (IoT). Green IoT will be an important part of SAGIN. Ambient backscatter communication (AmBC) is a potential solution for green SAGIN IoT. To improve the achievable sum rate (ASR) of the AmBC system, we propose a reconfigurable intelligent surface (RIS) assisted AmBC system. In the single-BD AmBC scenario, we firstly give the phase shifts that maximize the gain of the reflection link of the AmBC system, and then give the optimal reflection coefficient. The proposed scheme does not need to solve the convex semidefinite program (SDP) problem, and has the characteristics of low computational complexity. In the multi-BD AmBC scenario, we first propose a multi-BD phase shifts initialization strategy to ensure the stability of the proposed scheme. Then, we give the optimal reflection coefficient and phase shifts based on iterative method. Simulations show that the RIS-assisted AmBC scheme is superior to the non-RIS-assisted AmBC scheme.

Because of their capability of providing seamless connectivity, low-Earth-orbit (LEO) satellites will play a vital role in integrated satellite–terrestrial paradigms. However, high-speed satellite motion brings frequent handovers, during which redundant transmission and even loss of data easily occur. In this letter, we propose a handover-aware downlink beamforming design. To mitigate the impact of inter-satellite handover, we reduce the blocklength of coverage-edge users, aiming at completing transmission within the remaining visible time (RVT). Hence, the capacity of these users should be evaluated in the finite-block length (FBL) regime. After obtaining a surrogate of the FBL capacity function with a low-complexity method, we formulate the beamforming optimization model as a semidefinite programming (SDP) problem and solve it with CVX. The simulation results show that the proposed scheme can reach a 99.35% transmission success rate before inter-satellite handover.

We propose a mathematical framework for designing robust networks of coupled phase-oscillators by leveraging a vulnerability measure proposed by Tyloo et al. that quantifies the impact of a small perturbation at an individual phase-oscillator's natural frequency to the system's global synchronized frequencies. Given a complex network topology with specific governing dynamics, the proposed framework finds an optimal allocation of edge weights that minimizes such vulnerability measure(s) at the node(s) for which we expect perturbations to occur by solving a tractable semi-definite programming problem. We specify the mathematical model to high voltage electric grids where each node corresponds to a voltage phase angle associated with a bus and edges correspond to transmission lines. Edge weights are determined by the susceptance values along the transmission lines. In this application, frequency synchronization is increasingly challenged by the integration of renewable energy, yet is imperative to the grid's health and functionality. Our framework helps to alleviate this challenge by optimizing the placement of renewable generation and the susceptance values along the transmission lines.

In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More precisely, we present a procedure to obtain a sequence of explicit approximations of the weakly efficient solution set of the problem in question. Each approximation is the intersection of the sublevel set of a single polynomial and the feasible set. To this end, we make use of the achievement function associated with the considered problem and construct polynomial approximations of it over the feasible set from above. Remarkably, the construction can be converted to semidefinite programming problems. Several nontrivial examples are designed to illustrate the proposed new scheme.

Mutual localization provides a consensus of reference frame as an essential basis for cooperation in multi-robot systems. Previous works have developed certifiable and robust solvers for relative transformation estimation between each pair of robots. However, recovering relative poses for robotic swarm with partially mutual observations is still an unexploited problem. In this letter, we present a complete algorithm for it with optimality, scalability and robustness. Firstly, we fuse all odometry and bearing measurements in a unified minimization problem among the Stiefel manifold. Furthermore, we relax the original non-convex problem into a semi-definite programming (SDP) problem with a strict tightness guarantee. Then, to hold the exactness in noised cases, we add a convex (linear) rank cost and apply a convex iteration algorithm. We compare our approach with local optimization methods on extensive simulations with different robot amounts under various noise levels to show our global optimality and scalability advantage. Finally, we conduct real-world experiments to show the practicality and robustness.

Achieving consensus behavior robust to time delay in multiagent systems has attracted much attention. This work is concerned with optimizing the convergence rate of the consensus algorithm in such systems with time delays. Previous approaches optimize either the robustness to time delay or the convergence rate separately, while imposing a limit on the other. Eigenratio optimization is another method, which does not necessarily result in a unique set of weights. Here, the problem is treated in its general form as a multiobjective optimization problem. It is shown that the corresponding Pareto frontier depends solely on the optimal condition number of the Laplacian, and it includes the optimal answer of previously adopted approaches as special cases. A notion of optimal consensusability is then defined, which allows a particular point on the Pareto Frontier with special properties to be identified. The resulting optimization problem is shown to be convex, as is solved by reformulating it as a standard semidefinite programming problem. The optimal weights for individual topologies, clique lifted graphs, and different types of subgraphs are provided, where for the latter, the optimal weights have shown to be independent of the rest of topology. Through numerical simulations, the tradeoff between robustness and convergence rate is demonstrated.

Orientation estimation is an important task in three-dimensional cryo-EM image reconstruction. By applying the common line method, the orientation estimation task can be formulated as a least squares (LS) problem or a least un-squared deviation (LUD) problem with orthogonality constraint. However, the non-convexity of the orthogonality constraint introduces numerical difficulties to the orientation estimation. The conventional approach is to reformulate the orthogonality constrained minimization problem into a semi-definite programming problem using convex relaxation strategies. In this paper, we consider a direct way to solve the constrained minimization problem without relaxation. We focus on the weighted LS problem because the LUD problem can be reformulated into a sequence of weighted LS problems using the iteratively re-weighted LS approach. As a classical approach, the projected gradient descent (PGD) method has been successfully applied to solve the convex constrained minimization problem. We apply the PGD method to the minimization problem with orthogonality constraint and show that the constraint set is a generalized prox-regular set, and it satisfies the norm compatibility condition. We also demonstrate that the objective function of the minimization problem satisfies the restricted strong convexity and the restricted strong smoothness over a constraint set. Therefore, the sequence generated by the PGD method converges when the initial conditions are satisfied. Experimental results show that the PGD method significantly outperforms the semi-definite relaxation methods from a computation standpoint, and the mean square error is almost the same or smaller.

Abstract To improve the effect of web page information extraction, this paper proposes an improved information extraction method of mixed text density grids. Under various power constraints of the relay node itself, this paper proposes a design scheme of joint beamforming and artificial noise based on safety and rate maximisation. Furthermore, with the help of semidefinite relaxation techniques and first‐order approximations, it can be approximated as a semidefinite programming problem that is easy to solve. In addition, this paper uses an iterative algorithm based on a continuous convex approximation to process data to improve the accuracy of web page data extraction. The experimental results show that the information extraction method based on improved mixed text density webpages proposed in this paper has a good information extraction effect.

This paper presents an iterative algorithm to compute a Robust Control Invariant (RCI) set, along with an invariance-inducing control law, for Linear Parameter-Varying (LPV) systems. As real-time measurements of the scheduling parameters are typically available, we allow the RCI set description and the invariance-inducing controller to be scheduling parameter dependent. Thus, the considered formulation leads to parameter-dependent conditions for the set invariance, which are replaced by sufficient Linear Matrix Inequalities (LMIs) via Polya’s relaxation. These LMI conditions are then combined with a novel volume maximization approach in a Semidefinite Programming (SDP) problem, which aims at computing the desirably large RCI set. Besides ensuring invariance, it is also possible to guarantee performance within the RCI set by imposing a chosen quadratic performance level as an additional constraint in the SDP problem. Using numerical examples, we show that the presented iterative algorithm can generate RCI sets for large parameter variations where commonly used robust approaches fail.