Successive Convex Programming Research Articles

Rapid reconfiguration of gravitational detection spacecraft using high-accuracy successive convex programming

This article aims to address the challenge of achieving fast and high-accuracy reconfiguration of the TianQin constellation, with a focus on developing trajectory optimization algorithms to enhance both computation speed and accuracy in the reconfiguration process within TianQin Gravity Wave (GW) detection constellations. Initially, through perturbation analysis on the TianQin constellation, we formulated a dynamic model based on a virtual formation strategy, incorporating factors such as solar radiation pressure (SRP) and differences in third-body perturbation (DTBP). Subsequently, to meet the dual requirements of rapidly trajectory generation and optimal control accuracy, we proposed a new time-optimal high-accuracy successive convex programming (HASCP) algorithm and theoretically proved its convergence and optimality. Finally, we present simulations focusing on the TianQin gravitational detection spacecraft to validate the efficacy of the algorithm.

State-dependent trust region for successive convex programming for autonomous spacecraft

AbstractSpacecraft trajectory optimization is essential for all the different phases of a space mission, from its launch to end-of-life disposal. Due to the increase in the number of satellites and future space missions beyond our planet, increasing the level of autonomy of spacecraft is a key technical challenge. In this context, traditional trajectory optimization methods, like direct and indirect methods are not suited for autonomous or on-board operations due to the lack of guaranteed convergence or the high demand for computational power. Heuristic control laws represent an alternative in terms of computational power and convergence but they usually result in sub-optimal solutions. Successive convex programming (SCVX) enables to extend the application of convex optimization to non-linear optimal control problems. The definition of a good value of the trust region size plays a key role in the convergence of SCVX algorithms, and there is no systematic procedure to define it. This work presents an improved trust region based on the information given by the nonlinearities of the constraints which is unique for each optimization variable. In addition, differential algebra is adopted to automatize the transcription process required for SCVX algorithms. This new technique is first tested on a simple 2D problem as a benchmark of its performance and then applied to solve complex astrodynamics problems while providing a comparison with indirect, direct, and standard SCVX solutions.

Joint Active-Passive Beamforming and User Association in IRS-Assisted mmWave Cellular Networks

Intelligent reflecting surfaces (IRSs) are a promising technology for future-generation wireless networks by extending coverage region to blind spots and increasing mmWave propagation paths in non-line of sight environments. User association (UA) in dense millimeter wave (mmWave) networks is vital to characterizing connections among base stations (BSs) and mobile users for load balancing, interference management, and maximizing network utility. However, it has yet to be examined thoroughly in a multi-IRS-aided network. This paper presents a new UA scheme that takes cell interference into account for a multi-cell mmWave cellular network aided with multiple IRSs. We formulate a network spectral efficiency maximization problem by jointly optimizing active beamforming (AB) at the BSs, passive beamforming (PB) at the IRSs, and user-BS association with consideration of the impact of IRSs. We then propose a computationally efficient iterative algorithm based on alternating optimization (AO) to resolve this intractable mixed-integer non-convex problem. A fractional programming technique is used to optimize active beamforming at the BSs and passive beamforming at the IRSs, and a penalization method combined with successive convex programming is applied for UA optimization, which is shown to reach the optimal solution. Simulation results show significant performance improvements obtained by the proposed algorithm, providing higher spectral efficiency compared to several benchmark algorithms, while having a low computational complexity.

Multi-phase and dual aero/propulsive rocket landing guidance using successive convex programming

This paper aims to suggest a new landing guidance algorithm for reusable launch vehicles (RLVs) to enable generation of fuel-efficient trajectories based on successive convex programming. To this end, a dual aero/propulsive landing guidance problem is first formulated to fully exploit the additional moment generated by the aerodynamic control to reduce the propulsion demand required for attitude control. As the result of the aerodynamic landing phase could greatly affect the fuel-optimal trajectory during the vertical landing phase, the formulation is further extended to the multi-phase optimal guidance problem using state-triggered constraints. The proposed guidance strategy is then obtained by solving the formulated optimal control problem based on the successive convex optimization framework using an interior point method The main contribution of this study lies in forming new RLV landing guidance problems to get an optimal trajectory and transforming the corresponding nonconvex problem into a convex optimization problem by introducing appropriate combinations for convexification techniques. Additionally, this paper introduces several practical constraints, such as the maximum slew rate of aerodynamic control fins and nozzle angles, which are not considered in previous works. In this paper, the performance of the proposed method with the potential for online computation is investigated through numerical simulations.

Distributed OPF for PET-Based AC/DC Distribution Networks With Convex Relaxation and Linear Approximation

A power electronic transformer (PET) can flexibly regulate the power flow of a network and facilitate the integration of distributed energy resources via AC/DC networks. With the continuous expansion of the scale of multiregional interconnection networks, the traditional centralized optimization method faces great challenges. This paper proposes a distributed convex optimal power flow (OPF) model by leveraging the hierarchical structural characteristics of PET enabled AC/DC distribution networks. An analytical target cascading method is introduced to divide the centralized OPF problem into several subproblems that can make the subnetworks operate individually and coordinate with each other. The PET flexibility is also harnessed to reduce network power loss and voltage deviation. To improve the computational efficiency and algorithm convergence, the convex relaxation and linear approximation methods are proposed. This allows us to transform the original nonconvex nonlinear problem into a successive convex programming problem, which can be easily solved by an iterative solution algorithm. Simulation results verify the feasibility and efficiency of the proposed approach.

Performance Assessment of Convex Low-Thrust Trajectory Optimization Methods

Different discretization and trust-region methods are compared for the low-thrust fuel-optimal trajectory optimization problem using successive convex programming. In particular, the differential and integral formulations of the adaptive pseudospectral Legendre–Gauss–Radau method, an arbitrary-order Legendre–Gauss–Lobatto technique based on Hermite interpolation, and a first-order-hold discretization are considered. The number of discretization points and segments is varied. Moreover, two hard-trust-region methods and a soft-trust-region strategy are compared. It is briefly discussed whether these methods, if implemented on relevant hardware, would fulfill the general requirements for onboard guidance. A perturbed cubic interpolation and the propagation of the nonlinear dynamics are used to generate initial guesses of varying quality. Interplanetary transfers to a near-Earth asteroid, Venus, and asteroid Dionysus are chosen to assess the overall performance.

Joint Communication and Computation Resource Scheduling of a UAV-Assisted Mobile Edge Computing System for Platooning Vehicles

Connected and autonomous vehicles (CAVs) are recently envisioned to provide a tremendous social impact, while they put forward a much higher requirement for both vehicular communication and computation capacities to process resource-intensive applications. In this paper, we study unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) for a platoon of wireless power transmission (WPT)-enabled vehicles. Our objective is to maximize the system-wide computation capacity under both communication and computation resource constraints. We incorporate the coupled effects of the platooning vehicles and the flying UAV, air-to-ground (A2G) and ground-to-air (G2A) communications, onboard computing and energy harvesting into a joint scheduling optimization model of communication and computation resources. To tackle the resulting optimization problem, we propose a successive convex programming method based on a second-order convex approximation, in which feasible search directions are obtained by solving a sequence of quadratic programming subproblems and used to generate feasible points that can approach a local optimum. We also theoretically prove the feasibility and convergence of the proposed method. Moreover, simulation results are provided to validate the effectiveness of our proposed method and demonstrate its superior performance over other conventional schemes.

Energy Efficiency Maximization for UAV-Enabled Hybrid Backscatter-Harvest-Then-Transmit Communications

Wireless powered communication via backscatter and/or harvest-then-transmit (HTT) has been considered a promising solution to connecting nodes in the Internet-of-things (IoT) networks. However, the harvested energy at an IoT node is heavily limited by the distance between the node and the power beacon (PB) due to the high propagation loss. In this paper, we propose to employ an unmanned aerial vehicle (UAV) as a mobile PB to provide energy signals on demand to the IoT nodes, which convey their information to a reader via backscattering or active transmission using the harvested energy. We maximize the total energy efficiency (EE) of all the IoT nodes powered by the UAV by jointly optimizing the UAV’s transmit power and trajectory, the IoT nodes’ backscatter reflection coefficients and their transmit power for active transmission, and the time allocation between backscattering and active transmission. To solve the formulated non-linear fractional programming problem, we use the generalized fractional programming theory and a block coordinated decent method to decompose it into two sub-problems: one optimizes the communication resource allocation under a fixed UAV trajectory, and the other optimizes the UAV trajectory for given communication resource allocation. We then devise a Dinkelbach-based iterative algorithm to solve the two sub-problems by employing a Lagrangian dual method and a successive convex programming technique, respectively and iteratively. Simulation results show that our proposed iterative algorithm converges very fast, and the optimized UAV-enabled hybrid backscatter-HTT communication achieves a much higher EE of all the IoT nodes than the benchmark schemes including the UAV-enabled backscatter, UAV-enabled HTT, and hybrid BackCom-HTT with a fixed PB.

An Alternating Iteration Algorithm for a Parameter-Dependent Distributionally Robust Optimization Model

Based on a successive convex programming method, an alternating iteration algorithm is proposed for solving a parameter-dependent distributionally robust optimization. Under the Slater-type condition, the convergence analysis of the algorithm is obtained. When the objective function is convex, a modified algorithm is proposed and a less-conservative solution is obtained. Lastly, some numerical tests results are illustrated to show the efficiency of the algorithm.

Chance-Constrained Covariance Steering in a Gaussian Random Field via Successive Convex Programming

The problem of optimizing affine feedback laws that explicitly steer the mean and covariance of an uncertain system state in the presence of a Gaussian random field is considered. Spatially dependent disturbances are successively approximated with respect to a nominal trajectory by a sequence of jointly Gaussian random vectors. Sequential updates to the nominal control inputs are computed via convex optimization that includes the effect of affine state feedback, the perturbing effects of spatial disturbances, and chance constraints on the closed-loop state and control. The developed method is applied to solve for an affine feedback law to minimize the 99th percentile of required to complete an aerocapture mission around a planet with a randomly disturbed atmosphere.

An Effective Spatial Modulation Based Scheme for Indoor VLC Systems

We propose an enhanced spatial modulation (SM)-based scheme for indoor visible light communication systems. This scheme enhances the achievable throughput of conventional SM schemes by transmitting higher order complex modulation symbol, which is decomposed into three different parts. These parts carry the amplitude, phase, and quadrant components of the complex symbol, which are then represented by unipolar pulse amplitude modulation (PAM) symbols. Superposition coding is exploited to allocate a fraction of the total power to each part before they are all multiplexed and transmitted simultaneously, exploiting the entire available bandwidth. At the receiver, a two-step decoding process is proposed to decode the active light emitting diode index before the complex symbol is retrieved. It is shown that at higher spectral efficiency values, the proposed modulation scheme outperforms conventional SM schemes with PAM symbols in terms of average symbol error rate (ASER), and hence, enhancing the system throughput. Furthermore, since the performance of the proposed modulation scheme is sensitive to the power allocation factors, we formulated an ASER optimization problem and propose a sub-optimal solution using successive convex programming (SCP). Notably, the proposed algorithm converges after only few iterations, whilst the performance with the optimized power allocation coefficients outperforms both random and fixed power allocation.

Delay-Aware Stochastic Resource Management for Mobile Edge Computing Systems via Constrained Reinforcement Learning

We design a joint radio and computational resource allocation policy for a multi-user mobile edge computing system, such that the expected power consumption is minimized while satisfying long-term delay constraints. The problem is formulated as a constrained Markov decision process (CMDP) that is efficiently solved by the proposed constrained reinforcement learning (CRL) algorithm, called successive convex programming based policy optimization (SCPPO). SCPPO solves a convex objective/feasibility surrogate problem at each update and it can provably converge to a Karush-Kuhn-Tucker (KKT) point of the original CMDP problem almost surely under some mild conditions. Moreover, SCPPO adopts an application-specific policy architecture and employs a data-efficient estimation strategy that can reuse old experiences, such that SCPPO can realize fast learning with low computational complexity.

Powered soft landing guidance method for launchers with non-cluster configured engines

This paper proposes a guidance method for the powered soft landing of a launcher with non-cluster configured engines, for which it is difficult to maintain a low thrust-to-weight ratio (TWR) preferable for rocket recovery. For rockets in service with one or two engines rather than a cluster of engines in the boosters, it is a challenge to deeply throttle the engines to a low level, especially lower than 30%, and if one of the two engines is shut down to reduce the thrust, the attitude control is also difficult due to thrust asymmetry. The theoretical analysis and simulations show that the higher the TWR is, the smaller the feasible region for a soft landing becomes. The analysis also reveals that the bang–bang solutions of fuel-optimal methods are vulnerable to uncertainties and disturbances. A thrust regulation rate constraint is proposed or convexified to reconstruct the landing problem under high TWRs. An initial guess based on mean thrust and relaxing the initial velocity constraint is proposed, making both the adaptive collocation method and the successive convex programming applicable for real-time landing planning. Simulations under TWRs larger than four show that the proposed methods ensure a safe landing and are more adaptive than fuel-optimal solutions when facing disturbances and uncertainties.

Trajectory and Resource Optimization in OFDM-Based UAV-Powered IoT Network

The Internet of Things (IoT) is playing an increasingly vital role in multiple industries and our everyday life. A pressing practical problem of IoT devices (IoT-Ds) is their explosive growth of connectivity which leads to large energy consumption. One of the most promising solutions to achieve a sustainable green IoT network is unmanned aerial vehicle (UAV) enabled wireless power transfer (WPT) due to its flexibility, mobility and cost advantage. In this paper, we propose an UAV-powered IoT network based on Orthogonal Frequency Division Multiplexing (OFDM). In the proposed network, two ground nodes (GNs) are powered by two UAVs through down link WPT. In the uplink, the data collected by GNs are transmitted to the corresponding UAVs with the harvested energy by utilizing orthogonal subcarriers, which can effectively avoid the interference. UAVs' trajectories and resource allocation are optimized to maximize the sum average transmission rate of two GNs while ensuring the minimum average transmission rate of each GN. In this paper, we utilize successive convex programming (SCP) technique to solve the proposed optimization problem. Simulation results show that our proposed scheme achieves larger sum average transmission rate than the benchmark schemes.

Resource and trajectory optimization in UAV-powered wireless communication system

The unmanned aerial vehicle (UAV) is a promising enabler of Internet of Things (IoT) owing to its highly flexible features. Combined with wireless power transfer (WPT) techniques, a UAV can provide energy for IoT nodes, which can extend the lifetime of energy constrained communication systems. This paper studies resource and trajectory optimization in UAV-powered wireless communication systems, which consists of two UAVs and two ground nodes (GNs). The system works in a way that the two UAVs alternately charge the two GNs through wireless power transfer and two GNs also alternately send their information to the corresponding UAV with the harvested energy, which can effectively reduce the interference while receiving the information of GNs. Aiming to maximize the minimum throughput of two GNs, wireless resource and UAVs’ trajectories are jointly optimized with the constraints of UAV collision avoidance, flying speed, and transmit power. Successive convex programming (SCP) and block coordinate descent (BCD) are utilized to solve the optimization problem. Simulation results show that the proposed scheme achieves larger minimum throughput than the benchmark scheme.

Power allocation for D2D aided cooperative NOMA system with imperfect CSI

Non-orthogonal multiple access (NOMA) has become one of the promising technologies for 5G, which can improve the spectrum resource utilization and system throughput along with the support of effective resource allocation algorithms. Most previous works on NOMA-enhanced cooperative relay systems assume perfect channel state information (CSI), which degrades the performance of their schemes severely when used in imperfect CSI environment. In this article, a power allocation algorithm in D2D aided cooperative NOMA communications with imperfect CSI is proposed. In the proposed algorithm, the probabilistic non-convex optimization problem is transformed into a non-probabilistic convex optimization problem by evaluating the channel gains and using the successive convex programming (SCP) which approximately gives the lower bound of the maximum transmission rate. In the SCP enhanced power allocation algorithm (SCPPAA), we iteratively obtain the sub-optimal power allocation coefficients for the optimization problem by Lagrangian dual multiplier method and Karush–Kuhn–Tucker conditions. This program is divided into two layers for updating the power allocation coefficients and the multipliers respectively. Numerical results demonstrate that our algorithm has a fast convergence performance and the algorithm in D2D-based cooperative NOMA scheme has significant sum-data-rate advantages compared with it in traditional ways.

Energy Efficiency Maximization for Symbiotic Radio Networks With Multiple Backscatter Devices

Driven by the limited radio spectrum resources and the high energy consumption of wireless devices, symbiotic radio (SR) has recently been proposed to support passive Internet-of-Things (IoT) networks, where a primary transmitter (PT) transmits information to a primary reader (PR), while passive backscatter devices (BDs) modulate their own information on the received primary signal and backscatter the modulated signal to the same PR by adjusting their reflection coefficients. Existing works on SR have mainly studied the case of a single BD while without considering the BD's energy harvesting (EH) ability. In this paper, we aim to maximize the energy efficiency (EE) of an SR system that includes multiple BDs each being able to harvest energy while backscattering, by jointly optimizing the PT transmission power and the BDs' reflection coefficients and time division multiple access (TDMA) time slot durations for both the parasitic SR (PSR) and commensal SR (CSR) cases. To solve the formulated non-convex optimization problems, we propose a Dinkelbach-based iterative algorithm that builds on the block coordinated decent (BCD) method and the successive convex programming (SCP) technique. Simulation results show that the proposed algorithm converges fast, and the system EE is maximized when the BD that can provide the highest EE is allocated the maximum allowed time for backscattering while guaranteeing the throughput requirements for both the primary link and the other backscatter links.

Federated Learning With a Drone Orchestrator: Path Planning for Minimized Staleness

In this paper, we investigate the problem of scheduling transmissions for spatially scattered nodes that contribute to a collaborative federated learning (FL) algorithm via wireless links provided by a drone. In the considered system, the drone acts as an orchestrator, coordinating the transmissions and the learning schedule within a predefined deadline. The actual schedule is reflected in a planned path: as the drone traverses it, it controls the distance and thereby the data rate to each node. Hence, the model is structured such that the drone orchestrator uses the path (trajectory) as its only tool to achieve fairness in terms of learning <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">staleness</i> , which reflects the learning time discrepancy among the nodes. Using the number of learning epochs performed at each learner as a performance indicator, we combine the average number of epochs computed and staleness into a balanced optimization criterion that is agnostic to the underlying FL implementation. We consider two methods for solving the complex trajectory planning optimization problem for static nodes: (1) successive convex programming (SCP) and (2) deep reinforcement learning (RL). Considering the proposed criterion, both methods are compared in three specific scenarios with few nodes. The results show that drone-orchestrated FL outperforms an immobile deployment by providing improvements in the range of 57% to 87.7%. Additionally, RL-guided trajectories are generally superior to SCP provided ones for complex node arrangements.

When Probabilistic Shaping Realizes Improper Signaling for Hardware Distortion Mitigation

Hardware distortions (HWDs) render drastic effects on the performance of communication systems. They are recently proven to bear asymmetric signatures; and hence can be efficiently mitigated using improper Gaussian signaling (IGS), thanks to its additional design degrees of freedom. Discrete asymmetric signaling (AS) can practically realize the IGS by shaping the signals' geometry or probability. In this paper, we adopt the probabilistic shaping (PS) instead of uniform symbols to mitigate the impact of HWDs and derive the optimal maximum a posterior detector. Then, we design the symbols' probabilities to minimize the error rate performance while accommodating the improper nature of HWD. Although the design problem is a non-convex optimization problem, we simplified it using successive convex programming and propose an iterative algorithm. We further present a hybrid shaping (HS) design to gain the combined benefits of both PS and geometric shaping (GS). Finally, extensive numerical results and Monte Carlo (MC) simulations highlight the superiority of the proposed PS over conventional uniform constellation and GS. Both PS and HS achieve substantial improvements over the traditional uniform constellation and GS with up to one order magnitude in error probability and throughput.

Wireless-Powered Machine-to-Machine Multicasting in Cellular Networks

In future cellular networks, it is expected that data traffic will increase significantly due to deployments of large numbers of Internet of Things (IoT) objects. The IoT objects operate underlaying a cellular network, and they use Machine-to-Machine (M2M) communication to transmit multicst messages. We propose to use Radio Frequency (RF) Energy Transmitters (ET) to compensate the IoT objects with the energy consumed in forwarding multicast messages. Our goal is to support multicast service for IoT objects and transmit energy to them such that the total transferred energy by the ETs is minimized. We formulated the problem mathematically as a non-convex Mixed Integer Nonlinear Program (MINLP). Due to the difficulty of solving the problem optimally, we decompose the original problem into two sub-problems using Generalized Bender Decomposition with Successive Convex programming (GBD-SCP). Although this method facilitates finding a solution for the problem, the problem is still hard due to binary variables. Hence, we propose the Constraints Decomposition with SCP and Binary Variable Relaxation (CDR) algorithm to solve the problem more efficiently. Simulation results show that the proposed algorithm achieves a performance close to the GBD-SCP algorithm while the computation time is reduced significantly when the network size is larger.