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arXiv 2021年

作者： Zhang, Jingwen Lin, Xuan Hong, Dennis W. Department of Mechanical and Aerospace Engineering University of California Los AngelesCA90095 United States

— In order to achieve autonomous vertical wall climbing, the transition phase from the ground to the wall requires extra consideration inevitably. This paper focuses on the contact sequence planner to transition between flat terrain and vertical surfaces for multi-limbed climbing robots. To overcome the transition phase, it requires planning both multicontact and contact wrenches simultaneously which makes it difficult. Instead of using a predetermined contact sequence, we consider various motions on different environment setups via modeling contact constraints and limb switchability as complementarity conditions. Two safety factors for toe sliding and motor over-torque are the main tuning parameters for different contact sequences. By solving as a nonlinear program (NLP), we can generate several feasible sequences of foot placements and contact forces to avoid failure cases. We verified feasibility with demonstrations on the hardware SiLVIA, a six-legged robot capable of vertically climbing between two walls by bracing itself in-between using only friction. © 2021, CC0.

关键词： nonlinear programming

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Fast cluster detection in networks by first-order optimization

arXiv

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arXiv 2021年

作者： Bomze, Immanuel M. Rinaldi, Francesco Zeffiro, Damiano ISOR VCOR & ds:UniVie Universität Wien Austria Dipartimento di Matematica "Tullio Levi-Civita" Università di Padova Italy

Cluster detection plays a fundamental role in the analysis of data. In this paper, we focus on the use of sdefective clique models for network-based cluster detection and propose a nonlinear optimization approach that efficiently handles those models in practice. In particular, we introduce an equivalent continuous formulation for the problem under analysis, and we analyze some tailored variants of the Frank-Wolfe algorithm that enable us to quickly find maximal s-defective cliques. The good practical behavior of those algorithmic tools, which is closely connected to their support identification properties, makes them very appealing in practical applications. The reported numerical results clearly show the effectiveness of the proposed *** Codes 05C35, 05C50, 65K05, 90C06, 90C30, 90C35 Copyright © 2021, The Authors. All rights reserved.

关键词： nonlinear programming

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Database Building and Interpolation for an Online Safe Flight Envelope Prediction System

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2019年第5期42卷 1166-1174页

作者： Zhang, Y. de Visser, C. C. Chu, Q. P. Delft Univ Technol Fac Aerosp Engn Control & Simulat Sect Kluyverweg 1 NL-2629 HS Delft Netherlands

A study addresses offline construction of the database. The main focus and contribution of this study are database building and interpolation for the Database-Driven Safe Flight Envelope Prediction System (DEFEND) system. More importantly, through complexity analysis, the database approach is shown to be feasible for onboard real-time implementation within the aircraft control laws. Reachability analysis as the method to compute safe flight envelopes, as the theory provides a set-valued insight into safety and control design of dynamic systems. One advantage of this method is that all possible trajectories can be computed from all available control strategies and initial states, which naturally meets the safety guarantees. The computed results are called reachable sets, which are defined as a set of states that reach a certain target set within a certain time horizon and current control authority. Two sets of envelopes are computed using the level-set method toolbox. One is the pitching envelope, referred to the motion in the longitudinal plane with horizontal tail damage. The other is the rolling envelope, referred to the motion in the lateral plane with wing tip loss.

关键词： Mean Aerodynamic Chord Control Surfaces Aerodynamic Characteristics True Airspeed Earth Reference Frame Optimal Control nonlinear programming Cessna Citation II Horizontal Stabilizers Structural Damage

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Fuel-Optimal Rocket Landing with Aerodynamic Controls

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2019年第1期42卷 65-77页

作者： Liu, Xinfu Beijing Inst Technol Sch Aerosp Engn Beijing 100081 Peoples R China

Aerodynamic forces are not negligible for a reusable rocket returning back to Earth. How the aerodynamic controls and propulsion should be coordinated to realize fuel-optimal precise landing is addressed in this paper. To this end, a model-based optimal control problem is formulated with the rocket's angle of attack and thrust as control inputs, and constraints on the controls are included to reflect the capabilities of the vehicle. Precise landing requires the (highly nonlinear and nonconvex) problem to be solved onboard in real time. This ability of online computation is becoming increasingly desired in aerospace guidance and control for autonomous missions. Hence, this paper presents how to solve the rocket landing problem via convex optimization that has guaranteed polynomial-time complexity. Specifically, a novel methodology of handling the rocket nonlinear dynamics is introduced, and a relaxation technique used to convexify nonconvex constraints is theoretically proved to be valid. High efficiency of the proposed method, with potential for online computation, is demonstrated by numerical examples and comparisons with other methods.

关键词： Rocket Trajectories Fuels Lift Coefficient Aerodynamic Force nonlinear programming Trajectory Optimization nonlinear Dynamics Earth Flight Path Angle Numerical Algorithms

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First- And second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition

arXiv

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arXiv 2021年

作者： Andreani, Roberto Haeser, Gabriel Mito, Leonardo M. Héctor Ramírez, C. Silveira, Thiago P. Department of Applied Mathematics University of Campinas SP Campinas Brazil Department of Applied Mathematics University of São Paulo SP São Paulo Brazil Universidad de Chile Santiago Chile

The well known constant rank constraint qualification [Math. Program. Study 21:110-126, 1984] introduced by Janin for nonlinear programming has been recently extended to a conic context by exploiting the eigenvector structure of the problem. In this paper we propose a more general and geometric approach for defining a new extension of this condition to the conic context. The main advantage of our approach is that we are able to recast the strong second-order properties of the constant rank condition in a conic context. In particular, we obtain a second-order necessary optimality condition that is stronger than the classical one obtained under Robinson's constraint qualification, in the sense that it holds for every Lagrange multiplier, even though our condition is independent of Robinson's *** Codes 90C46, 90C30, 90C22 Copyright © 2021, The Authors. All rights reserved.

关键词： nonlinear programming

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Modeling design and control problems involving neural network surrogates

arXiv

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arXiv 2021年

作者： Yang, Dominic Balaprakash, Prasanna Leyffer, Sven University of California at Los Angeles Los Angeles United States Argonne National Laboratory Lemont United States

We consider nonlinear optimization problems that involve surrogate models represented by neural networks. We demonstrate first how to directly embed neural network evaluation into optimization models, highlight a difficulty with this approach that can prevent convergence, and then characterize stationarity of such models. We then present two alternative formulations of these problems in the specific case of feedforward neural networks with ReLU activation: as a mixed-integer optimization problem and as a mathematical program with complementarity constraints. For the latter formulation we prove that stationarity at a point for this problem corresponds to stationarity of the embedded formulation. Each of these formulations may be solved with state-of-the-art optimization methods, and we show how to obtain good initial feasible solutions for these methods. We compare our formulations on three practical applications arising in the design and control of combustion engines, in the generation of adversarial attacks on classifier networks, and in the determination of optimal flows in an oil well network. © 2021, CC BY.

关键词： nonlinear programming

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Comprehensive approach for distribution system planning with uncertainties

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IET GENERATION TRANSMISSION & DISTRIBUTION 2019年第24期13卷 5467-5477页

作者： Seta, Felipe da Silva de Oliveira, Leonardo W. de Oliveira, Edimar J. Fed Ctr Technol Educ Dept Elect Engn Angra Dos Reis RJ Brazil Fed Univ Juiz Fora UFJF Dept Elect Engn Juiz De Fora MG Brazil

This study presents a comprehensive approach for the distribution system expansion planning (DSEP) that considers investment, operation, carbon dioxide emission and reliability costs, as well as uncertainties over load demand and wind-based distributed generation. A restoration strategy is taken into account for obtaining the energy not supplied under the 'N - 1' criterion and the corresponding reliability cost over a planning horizon. The problem is modelled as mixed-integer non-linear programming by using the artificial immune system algorithm. Also, two methods to represent uncertainties are applied and compared: an interval technique through an interval power flow and a scenario-based approach. Network constraints are considered, as the limits of current, voltage and power from substations, as well as the obtaining of radial and connected topology. The novelty of the proposed interval DSEP consists of handling the uncertainties over operation in an efficient manner through a single step, instead of the several deterministic evaluations of the scenario-based approach. Numerical results are presented for well known test systems, which show the potentials of the proposed approach.

关键词： power distribution planning distributed power generation investment load flow artificial immune systems power distribution economics nonlinear programming power distribution faults integer programming power distribution reliability mixed-integer nonlinear programming artificial immune system algorithm interval technique interval power flow scenario-based approach interval DSEP known test systems distribution system expansion planning carbon dioxide emission reliability costs uncertainties overload demand wind-based distributed generation restoration strategy planning horizon

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Efficient linear network model for TEP based on piecewise McCormick relaxation

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IET GENERATION TRANSMISSION & DISTRIBUTION 2019年第23期13卷 5404-5412页

作者： Goodarzi, Shahin Gitizadeh, Mohsen Abbasi, Ali Reza Shiraz Univ Technol Dept Elect & Elect Engn Shiraz Iran Fasa Univ Fac Engn Dept Elect Fasa Iran

This study presents a novel scheme for transmission expansion planning (TEP) based on piecewise McCormick relaxation. The model presented considers investment and operation cost and identifies the transmission lines to be built. Since the AC power flow equations are inherently non-convex and non-linear, the resulting TEP model will be a highly complex optimisation problem, in which the optimal global solution is not guaranteed to be found by the existing techniques. This study aims to transform the non-linear model of the power network into a novel linear one. The model proposed is much more precise compared with the DC approach, while the global solution is guaranteed to be found by the off-the-shelf solvers. This accurate transformation from a non-convex and non-linear AC-TEP formulation into a linear-TEP model enables the planner to get more insight into the power flow of the power system. The TEP problem is formulated as a mixed-integer linear programming problem and is solved using the efficient commercial solvers. The results of the case studies show the tractability and exactness of the proposed model as well as its superiority over the state-of-the-art schemes.

关键词： power transmission planning linear programming nonlinear programming integer programming investment concave programming load flow power transmission economics power transmission lines nonconvex AC-TEP formulation nonlinear AC-TEP formulation off-the-shelf solvers power network nonlinear model optimal global solution complex optimisation problem AC power flow equations transmission lines operation cost investment transmission expansion planning piecewise McCormick relaxation efficient linear network model efficient commercial solvers mixed-integer linear programming problem TEP problem power system linear-TEP model

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CONOPT solver embedded in GAMS for optimal power flow

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JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 2019年第4期11卷 1-15页

作者： Calasan, Martin P. Nikitovic, Lazar Mujovic, Sasa Univ Montenegro Fac Elect Engn Podgorica Montenegro Univ Montenegro Maritime Fac Kotor Montenegro

This paper addresses the optimal power flow (OPF) issue by using the CONOPT solver for nonlinear programming embedded in the Generalized Algebraic Modeling System (GAMS) software package. The research is performed on both standard IEEE 30-bus test systems and their modified version. The system modification has been done in order to assess the impact of the integrated renewable energy sources, primarily wind energy sources, on the OPF. The obtained results strongly confirm the GAMS/CONOPT efficiency for solving the OPF problem. GAMS/CONOPT always converges to the same optimal solution contrary to many well-known optimization techniques. Additionally, the GAMS/CONOPT requested computation time considerably outperforms that of the other techniques in the field (in all analyzed cases, in the worst situation, more than 30 times). These performances promote GAMS/CONOPT as a very successive tool for solving the real-time OPF problem.

关键词： load flow nonlinear programming wind power

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An adaptive sequential wavelet-based algorithm developed for dynamic optimization problems

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COMPUTERS & CHEMICAL ENGINEERING 2019年 121卷 465-482页

作者： Santos, Lizandro de Sousa Secchi, Argimiro Resende Prata, Diego Martinez Biscaia Jr, Evaristo Chalbaud Univ Fed Fluminense Sch Engn Dept Chem Engn & Petr Rua Passo Patria 156 BR-24210240 Niteroi RJ Brazil Univ Fed Rio de Janeiro PEQ COPPE Chem Engn Program Ctr Tecnol Av Horcicio Macedo 2030Bloco GSala G-116 BR-21941914 Rio De Janeiro RJ Brazil

In this paper we present an adaptive wavelet algorithm (WAA) tailored for dynamic optimization problems (DOP). The main feature of the WAA is the automatic computation of time-domain discretization, generating a self-adapting control parameterization, which depends on the nonlinear characteristics of the mathematical model. For this, the control variables are analyzed and treated at different wavelet levels. First, we have demonstrated the advantages of WAA over heuristic adaptive procedures, proposed in the last years. Second, the results of the proposed strategy are illustrated through the solution of ten case studies. According to the results, the computation cost could be reduced by about 56% on average. Besides, the average NLP size reduction was approximately 49.94%, showing that one of the most considerable advantages of the algorithm is the adaptive discretization without prior information of the control profile. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Dynamic optimization nonlinear programming Wavelets Thresholding Control vector parameterization

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