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Power Flow Optimization for Smart Microgrids by SDP Relaxation on Linear Networks

IEEE TRANSACTIONS ON SMART GRID 2013年第2期4卷 751-762页

作者： Erseghe, Tomaso Tomasin, Stefano Univ Padua Dipartimento Ingn Informaz I-35131 Padua Italy

In a smart microgrid currents injected by distributed energy resources (DERs) and by the point of common coupling can be adapted to minimize the energy cost. Design and quality constraints usually make the problem grow fast with the number of nodes in the network. In this paper we provide a solution to the optimization problem having a significantly reduced complexity with respect to existing techniques. The efficiency of the proposed solution stems by modeling the smart microgrid as a linear network where loads are approximated as impedances. This simplification allows avoiding explicit use of power flow equations, and having a number of equation proportional to the number of DERs rather than to the total number of nodes (loads and DERs). The optimal power flow problem is then solved by a semidefinite programming (SDP) relaxation, which provides the initial point for the search of a feasible solution by a sequential convex programming procedure based on a local linear approximation of non-convex constraints. Numerical results show the merits of the proposed approach for typical smart microgrid scenarios.

关键词： Energy efficiency optimal power flow semidefinite programming sequential convex programming smart microgrid

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Spectrum Allocation and Power Control for Non-Orthogonal Multiple Access in HetNets

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2017年第9期16卷 5825-5837页

作者： Zhao, Jingjing Liu, Yuanwei Chai, Kok Keong Nallanathan, Arumugam Chen, Yue Han, Zhu Queen Mary Univ London London E1 4NS England Univ Houston Houston TX 77004 USA Kyung Hee Univ Dept Comp Sci & Engn Seoul South Korea

In this paper, a novel resource allocation design is investigated for non-orthogonal multiple access (NOMA) enhanced heterogeneous networks (HetNets), where small cell base stations (SBSs) are capable of communicating with multiple small cell users (SCUs) via the NOMA protocol. With the aim of maximizing the sum rate of SCUs while taking the fairness issue into consideration, a joint problem of spectrum allocation and power control is formulated. In particular, the spectrum allocation problem is modeled as a many-to-one matching game with peer effects. We propose a novel algorithm where the SBSs and resource blocks interact to decide their desired allocation. The proposed algorithm is proved to converge to a twosided exchange-stable matching. Furthermore, we introduce the concept of 'exploration' into the matching game for further improving the SCUs' sum rate. The power control of each SBS is formulated as a non-convex problem, where the sequential convex programming is adopted to iteratively update the power allocation result by solving the approximate convex problem. The obtained solution is proved to satisfy the Karush-Kuhn-Tucker conditions. We unveil that: 1) the proposed algorithm closely approaches the optimal solution within a limited number of iterations;2) the 'exploration' action is capable of further enhancing the performance of the matching algorithm;and 3) the developed NOMA-enhanced HetNets achieve a higher SCUs' sum rate compared with the conventional OMA-based HetNets.

关键词： Fairness heterogeneous networks (HetNets) matching game non-orthogonal multiple access (NOMA) sequential convex programming sum rate

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Matrix Structure Driven Interior Point Method for Quadrotor Real-Time Trajectory Planning

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IEEE ACCESS 2019年 7卷 90941-90953页

作者： Xu, Guangtong Long, Teng Wang, Zhu Cao, Yan Beijing Inst Technol Sch Aerosp Engn Beijing 100081 Peoples R China Minist Educ Key Lab Dynam & Control Flight Vehicle Beijing 100081 Peoples R China

sequential convex programming (SCP) has been recently employed in various trajectory planning problems, including entry flight, planetary landing, and aircraft formation. In SCP, convex programming subproblems are sequentially solved to obtain the optimum of original nonconvex problems. For SCP-based quadrotor trajectory planning, this paper proposes a matrix-structure-driven interior point method (MSD-IPM) to improve the efficiency of solving search directions in convex programming. In MSD-IPM, primal-dual systems for solving search directions are derived from the Karush-Kuhn-Tucher (KKT) conditions of quadrotor trajectory planning subproblems. Then, the successive elimination technique is used to solve the inverse of large-scale coefficient matrices of primal-dual systems by more efficient operations on small-scale matrices. In successive elimination, the positive definiteness of several small-scale matrices is used to enhance the numerical stability of computing search directions, and the specific diagonal structures of small-scale matrices are exploited to efficiently compute the search directions. The complexity analysis shows that the efficiency of the proposed method is about one order of magnitude higher than that of the standard IPM. The comparative studies on simulation experiments demonstrate that the MSD-IPM generally outperforms several well-known optimizers (e.g., MOSEK, SDPT3, and SeDuMi) in terms of efficiency and robustness. Finally, the indoor trajectory tracking experiments indicate that the proposed method can generate smooth trajectories for real-world applications.

关键词： Quadrotor trajectory planning sequential convex programming interior point method matrix structure exploitation

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Autonomous parafoil precision landing using convex real-time optimized guidance and control

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CEAS SPACE JOURNAL 2023年第2期15卷 371-384页

作者： Leeman, Antoine Preda, Valentin Huertas, Irene Bennani, Samir European Space Agcy Directorate Technol Engn & Qual GNC AOCS 1 NL-2201 AZ Noordwijk Netherlands European Space Agcy Directorate Technol Engn & Qual Pointing Div 1 NL-2201 AZ Noordwijk Netherlands Swiss Fed Inst Technol Inst Dynam Syst & Control Zurich Switzerland

To overcome the limitations of current parafoil precision landing capabilities, an efficient real-time convex optimized guidance and control strategy is presented. The parafoil guidance problem is non-convex in essence and it can be solved with a sequence of convex problems, each of those converging in polynomial time to a feasible solution of the approximated original problem. Our approach shows reliable and fast numerical convergence through in-flight recalculation of time of flight and a new optimal trajectory to cope with time-varying dynamics. The efficiency of our strategy is demonstrated via a comparative analysis of the existing X-38 in-flight demonstrated guidance and control system. Exhaustive Monte Carlo simulations show performance improvements of about one order of magnitude. The concept proposed is simple, yet general, as it scales to any atmospheric parafoil landing system and allows efficient implementation relying only on the turn rate saturation information for the parafoil model.

关键词： Parafoil convex programming Guidance and control Landing Real time Trajectory optimization sequential convex programming

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Autonomous Rendezvous and Docking Implementation for Small Satellites Using Model Predictive Control

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2024年第3期47卷 539-547页

作者： Fear, Andrew Lightsey, E. Glenn Georgia Inst Technol Dept Aerosp Engn Atlanta GA 30332 USA

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Global convergence of a nonlinear programming method using convex approximations

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NUMERICAL ALGORITHMS 2001年第3期27卷 265-289页

作者： Zillober, C Univ Bayreuth Inst Math D-95440 Bayreuth Germany

The method of moving asymptotes (MMA) and its globally convergent extension SCP (sequential convex programming) are known to work well for certain problems arising in structural optimization. In this paper, the methods are extended for a general mathematical programming framework and a new scheme to update certain penalty parameters is defined, which leads to a considerable improvement in the performance. Properties of the approximation functions are outlined in detail. All convergence results of the traditional methods are preserved.

关键词： convex approximations sequential convex programming method of moving asymptotes global convergence

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A Combined convex Approximation-Interior Point Approach for Large Scale Nonlinear programming

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OPTIMIZATION AND ENGINEERING 2001年第1期2卷 51-73页

作者： Zillober, Christian Univ Bayreuth Math Inst D-95440 Bayreuth Germany

The method of moving asymptotes (MMA) and its globally convergent extension SCP (sequential convex programming) are known to work well in the context of structural optimization. The two main reasons are that the approximation scheme used for the objective function and the constraints fits very well to these applications and that at an iteration point a local optimization model is used such that additional expensive function and gradient evaluations of the original problem are avoided. The subproblems that occur in both methods are special nonlinear convex programs and have traditionally been solved using a dual approach. This is now replaced by an interior point approach. The latter one is more suitable for large problems because sparsity properties of the original problem can be preserved and the separability property of the approximation functions is exploited. The effectiveness of the new method is demonstrated by a few examples dealing with problems of structural optimization.

关键词： method of moving asymptotes sequential convex programming interior point method structural optimization convex approximations large scale problems

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TIME DIVISION MULTIPLE ACCESS METHODS IN BI-DIRECTIONAL COOPERATIVE RELAY NETWORKS

TIME DIVISION MULTIPLE ACCESS METHODS IN BI-DIRECTIONAL COOP...

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IEEE 7th Sensor Array and Multichannel Signal Processing Workshop (SAM)

作者： Schad, Adrian Pesavento, Marius Tech Univ Darmstadt Commun Syst Grp D-64283 Darmstadt Germany

ISBN: (纸本)9781467310710

In this paper, we develop a new class of time division multiple access schemes for bi-directional multiuser communications in cooperative amplify-and-forward relay networks. The proposed schemes enable a flexible trade-off between spectral efficiency and suppression of multiuser interference. The relay weights are chosen to maximize the minimum received quality-of-service of all the users under constraints on the individual and the total power at the relays. Simulation results demonstrate that the selection of the scheme has a considerable impact on the achieved throughput of the relay network.

关键词： Amplify-and-forward relaying bi-directional relaying distributed beamforming multiuser peer-to-peer relay networks sequential convex programming

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On Optimal Link Removals for Controllability Degradation in Dynamical Networks 53

On Optimal Link Removals for Controllability Degradation in ...

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53rd IEEE Annual Conference on Decision and Control (CDC)

作者： Fardad, Makan Diwadkar, Amit Vaidya, Umesh Syracuse Univ Dept Elect Engn & Comp Sci Syracuse NY 13244 USA Iowa State Univ Dept Elect & Comp Engn Ames IA 50011 USA

ISBN: (纸本)9781467360906

We consider the problem of controllability degradation in dynamical networks subjected to malicious attacks. Attacks on the networks are assumed to be in the form of the removal of interconnection links. We formulate an optimization problem that seeks sets of links whose removal causes maximal degradation in the rank of the controllability gramian. We apply the alternating direction method of multipliers and sequential convex programming to find local solutions to this combinatorial optimization problem. We provide illustrative examples to demonstrate the utility of our results.

关键词： Alternating direction method of multipliers (ADMM) cyber-physical systems link failure rank minimization sequential convex programming

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A convex Approach to High-fidelity Landing Trajectory Optimization for Advanced Air Mobility

A Convex Approach to High-fidelity Landing Trajectory Optimi...

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AIAA SciTech Forum

作者： Wu, Yufei Deniz, Sabrullah Wang, Zhenbo Huang, Daning Univ Tennessee Dept Mech Aerosp & Biomed Engn Knoxville TN 37996 USA Penn State Univ Dept Aerosp Engn University Pk PA 16802 USA

ISBN: (数字)9781624107115

ISBN: (纸本)9781624107115

Urban Air Mobility (UAM) presents an innovative solution for intra-urban and inter-urban transportation, promising enhanced flexibility, efficiency, and sustainability. However, the integration of UAM into densely populated city environments brings significant challenges, particularly in the precision landing of multi-rotor vehicles amid complex and dynamic urban landscapes. To address this challenge, our paper introduces a novel convex optimization approach to solve the high-fidelity landing problem of electric vertical take-off and landing (eVTOL) vehicles. In our method, we first conceptualize the eVTOL vehicle landing trajectory optimization as a high-dimensional, highly nonconvex optimal control problem. We then implement a series of convenient convexification techniques to transform this problem into a convex form. The core of our approach lies in the application of sequential convex programming (SCP), an advanced method known for its efficacy and real-time performance in handling complex optimization challenges. We conduct a comparative analysis of our SCP-based solution with results obtained from the GPOPS-II solver, a widely recognized general-purpose tool in optimal control. This comparison not only benchmarks the performance of our method but also highlights its potential advantages in solving complicated, dynamic trajectory optimization problems in the context of UAM.

关键词： Optimal Control Problem Advanced Air Mobility Electric Vertical Take off and Landing convex Optimization sequential convex programming Precision Landing Multi Rotor Aerodynamic Coefficients Blade Element Momentum Theory Flight Dynamics

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