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AIAA Aviation Forum and Exposition

作者： McDonald, Spencer T. Wang, Zhenbo Univ Tennessee Dept Mech Aerosp & Biomed Engn Knoxville TN 37996 USA

ISBN: (数字)9781624105890

ISBN: (纸本)9781624105890

In this paper, a real-time optimization approach is proposed to generate three-dimensional trajectories for unmanned aerial vehicles (UAVs) to rendezvous into a predefined aerial orbit with time of arrival constraints. The proposed rendezvous strategy and solution method are novel with wide applications such as surveillance, observation, aerial mapping, and package delivery. The primary contributions of this work include the formulation of the rendezvous problem as an optimal control problem and the transformation of the original problem into a convex optimization problem through change of coordinate systems and linear approximation of the dynamics. Additionally, the time of arrival constraint is handled by splitting the rendezvous trajectory into two segments: the constant-velocity segment and the constant-acceleration segment. By solving the relaxed convex optimization problem, a globally optimal solution can be obtained with guaranteed convergence and real-time performance. Preliminary results show that the proposed rendezvous strategy and the convex optimization-based method have great potential for real-time applications for both single and multiple UAVs.

关键词： Miniature Aerial Vehicles Optimal Control nonlinear programming Real Time Optimization Flight Path Angle Aerial Refueling Heading Angle State Space Representation Orbit Rendezvous Guidance Laws

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Fuzzy reliability-redundancy allocation problem of the overspeed protection system

ENGINEERING REPORTS

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ENGINEERING REPORTS 2020年第8期2卷

作者： Taghiyeh, Sajjad Mahmoudi, Morteza Fadaie, Saber Tohidi, Hossein North Carolina State Univ Edwards P Fitts Dept Ind & Syst Engn Raleigh NC 27695 USA Iran Univ Sci Technol Sch Ind Engn Tehran Iran Univ Tafresh Dept Ind Engn Tafresh Iran

System reliability is defined as the probability of satisfactory performance of a system under stated conditions for a specified period of time. According to this definition, four parameters, including probability, satisfactory performance, specific conditions, and time should be exactly characterized to evaluate the system reliability accurately. However, due to the uncertainty involved in real situations, it is hardly possible to assess the aforementioned parameters precisely. In this article, two general and distinct approaches, including Zadeh's extension principle and modification of fuzzy parametric programming (FPP), are proposed to take into account such uncertainty in a famous reliability problem called the overspeed protection system. According to Zadeh's extension principle, a pair of nonlinear programming problems is formulated to compute..-level cuts of fuzzy system reliability. Themembership function of fuzzy system reliability can then be constructed analytically by numerating different values of... This fuzzy system reliability presents flexibility for further system analysis. In the second approach, from a different point of view, a variant of FPP is improved that provides a crisp value as a system reliability measure. The rewarding point of the latter procedure is to handle the problem in a computationally easier way.

关键词： extension principle fuzzy parametric programming fuzzy sets nonlinear programming redundancy allocation problem system reliability

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Automatic generation of numerical methods for time integration in large-scale MDO

Automatic generation of numerical methods for time integrati...

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AIAA Aviation Forum and Exposition

作者： Gandarillas, Victor Hwang, John T. Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA

ISBN: (数字)9781624105890

ISBN: (纸本)9781624105890

Multidisciplinary Design Optimization (MDO) problems often involve models with ODEs. In gradient-based MDO, the derivatives must be computed across the time-integration process, which is simplified when using a central MDO framework to facilitate integration. To avoid the computational overhead in such a setting when time marching, MDO frameworks have been used to integrate ODEs using a parallel-in-time approach. This approach is used by many researchers in trajectory optimization and allows for integration to be performed across multiple processors. We use nonlinear programming to generate optimal numerical methods so that a parallel-in-time approach is guaranteed to converge. This method integrates an ODE for the largest time span possible for the parallel-in-time approach to converge, longer than existing methods. This method provides access to an effectively infinite number of time integration methods, adaptively choosing the best one for each time step. That is, instead of applying a single numerical method over the entire interval, we generate and apply multiple methods within the same interval of integration. The generated methods are applied to the Rossler Attractor and results show that the solver-based approach converges over a larger time interval using a second order generated method than the Implicit Midpoint Method.

关键词： Numerical Integration Multidisciplinary Design Optimization Trajectory Optimization nonlinear programming Runge Kutta Methods Banach Fixed Point Theorem Python Computing Boundary Value Problems nonlinear Systems

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Time-Optimal Trajectory Generation for Dynamic Vehicles: A Bilevel Optimization Approach

Time-Optimal Trajectory Generation for Dynamic Vehicles: A B...

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IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

作者： Tang, Gao Sun, Weidong Hauser, Kris Duke Univ Durham NC 27706 USA Univ Illinois Dept Comp Sci Urbana IL 61801 USA XYZ Robot Inc Shanghai Peoples R China

ISBN: (纸本)9781728140049

This paper presents a general framework to find time-optimal trajectories for dynamic vehicles like drones and autonomous cars. Hindered by its nonlinear objective and complex constraints, this problem is hard even for state-of-the-art nonlinear programming (NLP) solvers. The proposed framework addresses the problem by bilevel optimization. Specifically, the original problem is divided into an inner layer, which computes a time-optimal velocity profile along a fixed geometric path, and an outer layer, which refines the geometric path by a Quasi-Newton method. The inner optimization is convex and efficiently solved by interior-point methods. A novel variable reordering method is introduced to accelerate the optimization of the velocity profile. The gradients of the outer layer can be derived from the Lagrange multipliers using sensitivity analysis of parametric optimization problems. The method is guaranteed to return a feasible solution at any time, and numerical experiments on a ground vehicle with friction circle dynamics model show that the proposed method performs more robustly than general NLP solvers.

关键词： nonlinear programming

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REACHABLE DOMAIN OF CONTINUOUS LOW-THRUST TRAJECTORIES WITH LINEARIZED DYNAMIC MODEL 29th

REACHABLE DOMAIN OF CONTINUOUS LOW-THRUST TRAJECTORIES WITH ...

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29th AAS/AIAA Space Flight Mechanics Meeting

作者： Wang, Zhaowei Jiang, Fanghua Tsinghua Univ Sch Aerosp Engn Beijing 10084 Peoples R China

ISBN: (纸本)9780877036593

An analytical method is improved for reachable domain of noncircular orbit propelled by low thrust within fixed allowable transfer time, using the linearized differential equations of relative motion. The projection of the relative reachable domain for noncircular and non-coplanar orbits can be obtained by numerical calculation of the derived analytical expressions. A geometrical construction technique based on the envelope theory of family of surfaces is developed to determine the envelope of the reachable domain. A nonlinear programming approach is also applied to solve the reachable domain problem effectively, which comes to be equivalent to the former method. Two numerical examples demonstrate the usefulness of the proposed methods and show that the reachable domains consist well with the ones obtained by numerical optimal control method.

关键词： nonlinear programming

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Memory Based Hybrid Dragonfly Algorithm (MHDA): a New Technique for Determining Model Parameter in Vertical Electrical Sounding (VES) Data 7

Memory Based Hybrid Dragonfly Algorithm (MHDA): a New Techni...

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7th Biannual International Conference on Mathematics and Natural Sciences (ICMNS)

作者： Ramadhani, I. Minarto, E. Sungkono Inst Teknol Sepuluh Nopember Dept Phys Kampus ITS Sukolilo Surabaya 60111 Indonesia

Vertical Electrical Sounding (VES) data inversion is a nonlinear inversion problem because several models can fit to the observed data. Therefore, a new approach based on nonlinear optimization technique is implemented which is called Memory based Hybrid Dragonfly Algorithm (MHDA). It is proposed to solve drawback of Dragonfly Algorithm (DA), i.e. low convergence rate which is caused by high exploration behaviour of DA. The drawback can lead to the local optimum solutions. MHDA successfully balances exploration and exploitation behaviours of DA to obtain global optimum solution. In this research, initially, MHDA is tested for the noise contaminated synthetic VES data to assess its performance. Subsequently, MHDA is applied for the field VES data. In both results, MHDA is able to provide Posterior Distribution Model (PDM) which is obtained from exploration process. All accepted models of PDM have lower misfit value than specified tolerance value in the inversion process. The PDM can be used to estimate solution via median value of PDM. Additionally, the uncertainty estimation of obtained solution can be determined from standard deviation value of PDM. The inversion results of synthetic and field VES data indicate that MHDA is an innovative technique to solve VES data inversion problem.

关键词： nonlinear programming

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A Scaled Gradient Projection Method for Minimization over the Stiefel Manifold 18th

A Scaled Gradient Projection Method for Minimization over th...

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18th Mexican International Conference on Artificial Intelligence (MICAI)

作者： Oviedo, Harry Dalmau, Oscar CIMAT AC Ctr Invest Matemat Guanajuato Mexico

ISBN: (纸本)9783030337490;9783030337483

In this paper we consider a class of iterative gradient projection methods for solving optimization problems with orthogonality constraints. The proposed method can be seen as a forward-backward gradient projection method which is an extension of a gradient method based on the Cayley transform. The proposal incorporates a self-adaptive scaling matrix and the Barzilai-Borwein step-sizes that accelerate the convergence of the method. In order to preserve feasibility, we adopt a projection operator based on the QR factorization. We demonstrate the efficiency of our procedure in several test problems including eigen-value computations and sparse principal component analysis. Numerical comparisons show that our proposal is effective for solving these kind of problems and presents competitive results compared with some state-of-art methods.

关键词： nonlinear programming Gradient projection method Orthogonality constraints Stiefel manifold

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Landing a Fixed-Wing UAV on a Moving Platform: A Pseudospectral Optimal Control Approach

Landing a Fixed-Wing UAV on a Moving Platform: A Pseudospect...

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AIAA Aviation Forum and Exposition

作者： Pravitra, Jintasit Clarke, John-Paul Johnson, Eric N. Georgia Inst Technol Sch Aerosp Engn Atlanta GA 30332 USA Penn State Univ Dept Aerosp Engn University Pk PA 16802 USA

ISBN: (数字)9781624105890

ISBN: (纸本)9781624105890

This paper presents a preliminary development on a guidance algorithm capable of landing a fixed-wing UAV on a moving platform. The problem has not been investigated thoroughly by the community where almost all of related works are applications of either helicopters or multirotors. The problem is challenging because it demands position, velocity, and attitude to be matched simultaneously at touchdown. We formulate the problem as a minimum time optimal control problem and solve it using the pseudospectral optimal control method. We found that direct-lift control is a key element to successfully match position, velocity, and attitude simultaneously at touchdown. Our approach can handle steady wind and can also handle mildly maneuvering platform scenario. The algorithm is tested with various initial conditions and also tested in a receding horizon manner. The method is too slow to run in real-time. However, it reveals many challenges unique to this problem that must be overcome in future research.

关键词： Pontryagin's Maximum Principle Unmanned Aerial Vehicle Rotary Wing Guidance Algorithms Helicopters Model Reference Adaptive Control nonlinear programming Fixed Wing Aircraft Joint Precision Approach and Landing System Control Surfaces

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Optimizing the credit term decisions in supply chain finance

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JOURNAL OF PURCHASING AND SUPPLY MANAGEMENT 2019年第2期25卷 146-156页

作者： Li, Haitao Mai, Liuqing Zhang, Wenlong Tian, Xiangyu Univ Missouri Coll Business Adm Supply Chain & Analyt Dept St Louis MO 63121 USA Univ Missouri Coll Business Adm Dept Finance St Louis MO 63121 USA Shanxi Univ Finance & Econ Sch Finance Taiyuan Shanxi Peoples R China Shanxi Univ Finance & Econ Sch Accounting Taiyuan Shanxi Peoples R China

We study a credit term determination problem in the context of a supplier-buyer supply chain. The supplier's credit term decision is simultaneously made with its production and inventory decisions, and most importantly, it is impacted by the buyer's order quantity. We present a new game-theoretic framework to model this problem, which captures the interaction between the supplier's credit term decision and the buyer's order decision in a multi-period setting. An exact method based on nonlinear programming is implemented to obtain the optimal solutions. We apply our methodologies on a real world case. The computational results show that our approach significantly outperforms the heuristics with fixed credit terms, and either a short or a long credit term can be sub-optimal for the supplier in profitability. Our work offers the first data-driven model and solution approach that assists purchasing and supply managers to make optimal dynamic credit term decision in conjunction with production, ordering and inventory decisions in a game-theoretic setting.

关键词： Supply chain finance Credit term Stackelberg game Bilevel programming nonlinear programming

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Construction of Parallel Piecewise-Linear Interval Models for nonlinear Dynamical Objects 9

Construction of Parallel Piecewise-Linear Interval Models fo...

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9th International Conference on Advanced Computer Information Technologies (ACIT)

作者： Voliansky, Roman Sadovoi, Oleksandr Volianska, Nina Sinkevych, Oleksiy Dniprovsk State Tech Univ Dept Elect Engn Kamyanske Ukraine Dniprovsk State Tech Univ Heat Transfer Dept Kamyanske Ukraine Natl Forestry Univ Ukraine Dept IT Lyiv Ukraine

ISBN: (纸本)9781728104492

The paper is devoted to the developing of the methodological framework for modeling of nonlinear dynamical objects. Such a framework allows performing the coordinate transformation and formulating the algorithm of its usage to transform the series mathematical models of the nonlinear dynamical objects into the interval piecewise-defined linear models and then translate them into parallel ones. The above mentioned algorithm is based on reducing domains size where the nonlinearities of studied objects exist. We offer to reduce these domains by defining intervals on which nonlinear functions can be bounded on the bottom and on the top by linear functions. Thus, we suggest replacing nonlinear functions with their top and bottom piecewise-linear boundaries which are determined by minimization of the above-mentioned domains' areas. Previously suggested boundaries are used to define the transfer functions of the considered objects but one can use them for the stability analysis and the synthesis of closed-loop systems with desired dynamic as well. Then, we apply partial fraction decomposition of the transfer functions to perform transformation of the mathematical models into parallel form. Usage of the proposed approach is one of the ways to decrease calculation time and to improve multi-core CPU usage while simulation of nonlinear dynamical objects is being performed as well as to simplify the study of transients and steady-state modes of considered objects and to construct closed-loop control systems for a wide range of the nonlinear dynamical objects.

关键词： modeling and simulation interval methods nonlinear programming series dynamical model parallel dynamical model interval piecewise-linear model transfer function

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