Convex Second-order Cone Research Articles

Energy Management System for an Islanded Microgrid With Convex Relaxation

Conventional energy generation sources mainly provide energy supply to remote areas nowadays. However, because of growing concerns over greenhouse gas emissions, the integration of renewable energy sources is mandatory to meet power demands and reduce climatic effects. The advancements in renewable generation sources and battery storage systems pave the way for microgrids (MGs). As a result, MGs are becoming a viable solution for power supply shortage problems in remote-area applications, such as oceanic islands. In this paper, an islanded MG, which consists of PV system, tidal turbine (TT), diesel generator (DG), and Li-ion battery, is considered for Ouessant island in Brittany region in France. The economic operation of the MG is achieved by including battery degradation cost, levelized costs of energy of the PV system and TT, operating and emission costs of DG, and network constraints. The developed model leads to a non-linear and non-convex problem, which unfortunately can converge to a local optimum solution. The problem has, therefore, been relaxed and converted to a convex second-order cone model to achieve an optimal decision strategy for islanded MG operations with a global or near-global solution. Numerical simulations are carried out to prove the effectiveness of the proposed strategy in reducing the operating and emission costs of the islanded MG. It is shown that the developed convex energy management system formulation has an optimality gap of less than 1% with reduced computational cost.

Second-order cone interior-point method for quasistatic and moderate dynamic cohesive fracture

Cohesive fracture is among the few techniques able to model complex fracture nucleation and propagation with a sharp (nonsmeared) representation of the crack. Implicit time-stepping schemes are often favored in mechanics due to their ability to take larger time steps in quasistatic and moderate dynamic problems. Furthermore, initially rigid cohesive models are typically preferred when the location of the crack is not known in advance, since initially elastic models artificially lower the material stiffness. It is challenging to include an initially rigid cohesive model in an implicit scheme because the initiation of fracture corresponds to a nondifferentiability of the underlying potential. In this work, an interior-point method is proposed for implicit time stepping of initially rigid cohesive fracture. It uses techniques developed for convex second-order cone programming for the nonconvex problem at hand. The underlying cohesive model is taken from Papoulia (2017) and is based on a nondifferentiable energy function. That previous work proposed an algorithm based on successive smooth approximations to the nondifferential objective for solving the resulting optimization problem. It is argued herein that cone programming can capture the nondifferentiability without smoothing, and the resulting cone formulation is amenable to interior-point algorithms. A further benefit of the formulation is that other conic inequality constraints are straightforward to incorporate. Computational results are provided showing that certain contact constraints can be easily handled and that the method is practical.

Secure Transmission for Interference Networks: User Selection and Transceiver Design

Interference is usually regarded as a detrimental factor that degrades the performance of a wireless network. However, when it is used properly, the security of transmission can be effectively improved. In this paper, user selection and transceiver design are proposed to guarantee the secure transmission in a multiple-input multiple-output interference network with an eavesdropper. First, user selection is performed to select the most suitable user to transmit confidential information according to the topology and path loss in each time slot among all users. Then, based on user selection, the transceivers of the users are jointly designed to maximize the secrecy rate of the selected user while guaranteeing a minimum transmission rate for other users. Due to the nonconvexity of the optimization problem, it is transformed into a convex second-order cone programming with the help of successive approximations. An alternate iteration algorithm is proposed to obtain the optimal solution. The fairness of the user selection is considered, and a modified scheme is proposed to share the opportunity of secure transmission among users. Finally, simulation results are presented to show the effectiveness and efficiency of the proposed schemes.

A new neural network framework for solving convex second-order cone constrained variational inequality problems with an application in multi-finger robot hands

ABSTRACTIn this paper, we consider a new neural network model to simply solve the convex second-order cone constrained variational inequality problem. Based on a smoothing method, the variational inequality (VI) problem is first converted to a convex second-order cone programming (CSOCP). Using a high-performance model, the obtained convex programming problem is solved. According to Karush-Kuhn-Tucker conditions of convex optimisation, the equilibrium point of the proposed neural network is proved to be equivalent to the optimal solution of the CSOCP problem. By employing Lyapunov function approach, it is also shown that the presented neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the original optimisation problem. The capability of the method is demonstrated by several numerical results.

An ADMM-Based Approach to Robust Array Pattern Synthesis

In most existing robust array beam pattern synthesis studies, the bounded-sphere model is used to describe the steering vector (SV) uncertainties. In this letter, instead of bounding the norm of SV perturbations as a whole, we explore the amplitude and phase perturbations of each SV element separately, thereby obtaining a tighter SV uncertainty model. Based on this model, we formulate the robust array pattern synthesis problem from the perspective of the min-max optimization, which aims to minimize the maximum side lobe response, while preserving the main lobe response. However, this problem is difficult due to the infinitely many non-convex constraints. As a remedy, we employ the worst-case criterion and recast the problem as a convex second-order cone program (SOCP). To solve the SOCP, we further develop an alternating direction method of multipliers (ADMM)-based algorithm, which is computationally efficient with each step being computed in closed form. Numerical simulations demonstrate the efficacy and efficiency of the proposed algorithm.

Distribution Network Restoration in a Multiagent Framework Using a Convex OPF Model

The ever-increasing requirement for reliability and quality of supply suggests to enable the self-healing features of modern distribution networks employing the intelligent measurement, communication, and control facilities of smart grids. In this paper, the concept of multiagent automation in smart grids is applied to build a self-healing framework to be used for restoration service. In this regard, an agent interaction mechanism is designed to build a reduced model of only those parts of the network that could participate in the restoration process. This reduced model is subject to a global optimization method, aiming at restoring a maximum of loads with minimum switching operations. This optimization problem, including power flow constraints is formulated as a convex second-order cone programming and solved using GUROBI solver. The proposed multi-agent systems-based strategy is completely scalable and leads to a global optimum solution (up to the desired accuracy) in a short time, without the need for powerful processors. The simulation studies are carried out on a 70-bus distribution network in case of multiple fault scenarios, using MATLAB/Yalmip toolbox.

A new collaborate neuro-dynamic framework for solving convex second order cone programming problems with an application in multi-fingered robotic hands

A neural network model is constructed on the basis of the duality theory, optimization theory, convex analysis theory and Lyapunov stability theory to solve convex second-order cone programming (CSOCP) problems. According to Karush-Kuhn-Tucker conditions of convex optimization, the equilibrium point of the proposed neural network is proved to be equivalent to the optimal solution of the CSOCP problem. By employing Lyapunov function approach, it is also shown that the presented neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the original optimization problem. Simulation results show that the neural network is feasible and efficient.

An On-Line Optimal Controller for a Commuter Train

This paper proposes an on-board optimal controller that drives a train between two stations in an optimal time efficient, energy efficient, or mixed-objective manner, while adhering to a set of system-specific constraints. To this end, at each step along the track, the train control problem is formulated and solved as a constrained optimization problem over the remainder of the trip, while utilizing the latest train sensor data. The optimization problem is a convex second-order cone program. It incorporates knowledge of the track profile and relevant velocity and propulsion/braking constraints in the computation of the optimal propulsion/braking commands. It features an option to enforce a safety buffer between the train and another leading train on the track. The resulting convex optimization problem can be efficiently solved using a simple numerical solver, ensuring global optimality and robustness of the solution. Real-time performance and simulated closed-loop control results are presented, for a realistic vehicle and advanced trip model on desktop and embedded computer architectures.

Optimal Infrastructure Planning of Active Distribution Networks Complying With Service Restoration Requirements

For a fault occurring in a feeder of an active distribution system, the targeted restoration strategy consists of activating, in a first stage, clusters of nodes supplied each by a unique resource. This resource could be a DG or a tie-switch (tie-line) that provides power from a neighboring feeder. To reinforce the security of supply, in a second stage, each DG cluster is connected to a tie-switch cluster to form a so-called large cluster. Therefore, the problem presented in this paper aims at determining the optimal numbering, sizing, and location of potential distributed energy resources as well as the optimal border of the associated clusters. It is formulated in term of a convex second-order cone optimization problem where the objective is to find the best trade-off between picking up as many loads as possible whatever the fault location and the investment plus the maintenance costs. This problem has been solved in the case of a modified IEEE 34-bus system considering different potential infrastructure scenarios.

A novel gradient-based neural network for solving convex second-order cone constrained variational inequality problems

In this paper, we apply a gradient neural network model to efficiently solve the convex second-order cone constrained variational inequality problem. According to a smoothing method, the variational inequality problem is first reduced to a convex second order cone programming (CSOCP). Using a capable neural network, the obtained convex programming problem is solved. The stability in the sense of Lyapunov and globally convergence of the proposed neural network model are also provided. The effectiveness of the scheme is established by several numerical examples.

Battery Energy Storage System Control for Intermittency Smoothing Using an Optimized Two-Stage Filter

A new method for the control of a battery energy storage system and its implementation on a 25 kW solar system to compensate solar power intermittency and improve distribution grid power quality is presented in this paper. The novelty of the proposed method is to provide a systematic way to optimize the size of the battery capacity for the desired level of solar power smoothing. This goal is achieved by designing a two-stage filter solution. The first stage is a fast response digital finite impulse response (FIR) filter that makes a trade-off between smoothing of the solar output and battery capacity. This paper proposes an optimal design of a minimum-length, low-group-delay FIR filter by employing convex optimization, discrete signal processing, and polynomial stabilization techniques. The new strategy proposed in this paper formulates the design of a length- $N$ low-group-delay FIR filter as a convex second-order cone programming, which guarantees that all the filter zeros are inside the unit circle (minimum-phase). A quasi-convex optimization problem is formulated to minimize the length of the low-group-delay FIR filter. The second-stage filter is designed to level the battery charging load. The effectiveness and performance of the proposed approach is demonstrated by simulation results and also over a real-case implementation.

NLOS Error Mitigation for TOA-Based Source Localization With Unknown Transmission Time

In this letter, we address the time-of-arrival-based localization problem using an asynchronous sensor network under non-line-of-sight conditions. We formulate a robust least square (RLS) problem to jointly estimate the source location and the transmission time. To tackle the problem that the unknowns in the RLS problem are coupled with each other, we decouple the coupled constraint as the second-order cone constraints by applying some inequalities, and then apply the standard second-order cone relaxation technique to obtain a convex second-order cone program. Simulation results verify the performance of the proposed method.

Multiuser MISO Transceiver Design for Indoor Downlink Visible Light Communication Under Per-LED Optical Power Constraints

Light-emitting diode (LED)-based visible light communication (VLC), combining illumination and communication, is a promising technique for providing high-speed, low-cost indoor wireless services. In indoor environments, multiple LEDs routinely used as lighting sources may also be concomitantly invoked to support wireless services for multiple users, thus forming a multiuser multiple-input-single-output (MU-MISO) system. Since the user terminals detect all the light rays impinging from multiple LEDs, inter-user interference may severely degrade the attainable system performance. Hence, we conceive a transceiver design for indoor VLC MU-MISO systems to suppress the multiuser interference (MUI). In contrast to classic radio-frequency (RF) communication, in VLC, the signals transmitted from the LEDs are restricted by optical constraints, such as the real-valued nonnegativity of the optical signal, the maximum permissible optical intensity, and the constant brightness requirements of the LEDs. Given these practical constraints, we design the optimal transceiver relying on the objective function of minimizing the maximum mean square error (MMSE) between the legitimate transmitted and received signals of the users and show that it can be readily found by solving a convex second-order cone program. Then, we also propose a simplified transceiver design by incorporating zero-forcing (ZF) transmit precoding (TPC) and show that the TPC coefficients can be efficiently found by solving a linear program. The performance of both the optimal and the simplified transceiver is characterized by comprehensive numerical results under diverse practical VLC system setups.

A practical nonlinear dynamic framework for solving a class of fractional programming problems

In this paper, we present a high-performance dynamic optimization scheme to solve a class of fractional programming (FP) problems. The main idea is to convert the FP problem into an equivalent convex second-order cone programming problem. A neural network model based on a dynamic model is then constructed for solving the obtained convex programming problem. By employing a credible Lyapunov function approach, it is shown that the proposed neural network model is stable in the sense of Lyapunov and is globally convergent to an exact optimal solution of the original optimization problem. A block diagram of the model is also given. Several illustrative examples are provided to show the efficiency of the proposed method in this manuscript.

Efficient Solutions to Distributed Beamforming for Two-Way Relay Networks Under Individual Relay Power Constraints

This paper investigates distributed beamforming (DBF) designs for two-way relay networks (TWRNs), where two terminal nodes exchange information through a set of amplify-and-forward (AF) relays. We assume individual relay power constraints and study two important design problems, namely, the max–min fairness (MMF) problem and the weighted sum-rate maximization (WSRM) problem. For the MMF problem, unlike the existing works that usually solve the problem by a bisection method, we propose an efficient optimal solution by solving one convex second-order cone program (SOCP) only. For the WSRM problem, we develop an efficient iterative algorithm based on SOCP reformulation and the successive convex approximation (SCA) technique. For both the MMF and WSRM designs, we further propose a distributed implementation framework where each of the relays can independently compute its beamforming weight using its local channel state information (CSI) and some common parameters broadcasted by a control center. Simulation results are presented to demonstrate the performance advantages of the proposed solutions.

Robust Bearing Estimation in Shallow Water Using Vector Optimization

Correlated multi-paths may cause a biased bearing estimation in shallow water, so most existing methods make fully use of the multi-path nature and the underwater channel property to provide an unbiased bearing estimation. However, an imprecise knowledge of the underwater channel parameters or the array model mismatches will cause performance degradation, especially for the high-resolution methods. Therefore development of robust bearing estimation methods in shallow water is critically important. In this paper, a new approach to robust bearing estimation is proposed in the presence of underwater channel parameter uncertainties or array model mismatches. The proposed method is based on the convex optimization theory, exactly to say, the vector optimization theory, and can be derived by imposing a certain constraint on the Euclidean norm of the source vector. It is shown that the proposed method can be reformulated as a convex secondorder cone program (SOCP) problem and solved efficiently by the well-established interior point method, such as SEDUMI. Computer simulations and experiment analysis show that the proposed method is highly robust against the underwater channel parameter uncertainties and array model mismatches, moreover, demonstrates its excellent performance as compared with existing methods.

Distributed Model Predictive Control of Linear Systems with Stochastic Parametric Uncertainties and Coupled Probabilistic Constraints

This paper investigates the distributed stochastic model predictive control (DSMPC) for multiple constrained dynamically decoupled subsystems subject to stochastic uncertainties in the parameters. To obtain a computationally tractable formulation for real control applications, a spectral method called generalized polynomial chaos expansions (gPCEs) is utilized to propagate the stochastic parametric uncertainties through the system model. By using gPCEs combined with the probabilistic information on the uncertainties, both local probabilistic constraints and coupled probabilistic constraints are converted explicitly into deterministic convex second-order cone constraints. The constraints can achieve satisfaction of coupled probabilistic constraints in a distributed way by permitting a single subsystem to optimize a local cost function at each time step, while “freezing” the plans of others. The proposed gPCEs-based DSMPC algorithm guarantees recursive feasibility with respect to both local and coupled probabilistic constraints and ensures asymptotic stability in all the moments for any choice of update sequence. A numerical example is used to illustrate the effectiveness of the proposed algorithm.

Analysis of smoothing-type algorithms for the convex second-order cone programming

There recently has been much interest in smoothing-type algorithms for solving the linear second-order cone programming (LSOCP). We extend such method to solve the convex second-order cone programming (CSOCP), which is an extension of the LSOCP. In this paper, we first propose a new smoothing function. Based on this function, we establish a smoothing Newton algorithm for solving the CSOCP and prove that the algorithm is globally and locally quadratically convergent under suitable assumptions. For the established algorithm, we use a generalized Armijo-type search rule to generate the step size. Some numerical results are reported which indicate the effectiveness of our algorithm.

Robust Adaptive Beamforming Applied to Planar Array

Capon beamforming has better resolution and interference rejection capability. However, its performance will seriously degrade due to noise, array steering vector error, and other factors. In this paper, a robust Capon beamforming applied to a planar array is described. It is shown that the proposed method is the natural extension of the original Vector Optimization Robust Beamforming algorithm to the case of a planar array, and can be reformulated as a convex second-order cone program and solved by SEDUMI. Computer simulation has shown that the proposed method has better performance than other conventional methods, such as narrower main lobe and lower side lobe.

Efficient Beamforming in Cognitive Radio Multicast Transmission

The optimal beamforming problems for cognitive multicast transmission are quadratic nonconvex optimization problems. The standard approach is to convert the problems into the form of semi-definite programming (SDP) with the aid of rank relaxation and later employ randomization techniques for solution search. However, in many cases, this approach brings solutions that are far from the optimal ones. We consider the problem of minimizing the total power transmitted by the antenna array subject to quality-of-service (QoS) at the secondary receivers and interference constraints at the primary receivers. It is shown that this problem, which is known to be nonconvex NP-hard, can be approximated by a convex second-order cone programming (SOCP) problem. Then, an iterative algorithm in which the SOCP approximation is successively improved is presented. Simulation results demonstrate the superior performance of the proposed approach in terms of total transmitted power and feasibility, together with a reduced computational complexity, as compared to the existing ones, for both the perfect and imperfect channel state information (CSI) cases. It is further shown that the proposed approach can be used to address the max-min fairness (MMF) based beamforming problem.