Application of Direct Transcription to Commercial Aircraft Trajectory Optimization

Betts, John T.; Cramer, Evin

doi:10.2514/3.56670

Cited by 83 publications

(32 citation statements)

References 12 publications

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“…Discretization-based estimation approaches have been widely studied in diverse fields such as chemical engineering [24][25][26] and aerospace engineering [27][28][29] (see [30] for a comprehensive review) but less so in computational biology. A major factor that has hindered wider adoption is the lack of easy-to-use computational frameworks that facilitate access to non-expert users.…”

Section: Interior-point Methodsmentioning

confidence: 99%

Scalable Nonlinear Programming Framework for Parameter Estimation in Dynamic Biological System Models

Shin

Venturelli

Zavala

2018

Preprint

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We present a nonlinear programming (NLP) framework for the scalable solution of parameter estimation problems that arise in dynamic modeling of biological systems. Such problems are computationally challenging because they often involve highly nonlinear and stiff differential equations as well as many experimental data sets and parameters. The proposed framework uses cutting-edge modeling and solution tools which are computationally efficient, robust, and easy-to-use. Specifically, our framework uses a time discretization approach that: i) avoids repetitive simulations of the dynamic model, ii) enables fully algebraic model implementations and computation of derivatives, and iii) enables the use of computationally efficient nonlinear interior point solvers that exploit sparse and structured linear algebra techniques. We demonstrate these capabilities by solving estimation problems for synthetic human gut microbiome community models. We show that an instance with 156 parameters, 144 differential equations, and 1,704 experimental data points can be solved in less than 3 minutes using our proposed framework (while an off-the-shelf simulation-based solution framework requires over 7 hours). We also create large instances to show that the proposed framework is scalable and can solve problems with up to 2,352 parameters, 2,304 differential equations, and 20,352 data points in less than 15 minutes. Competing methods reported in the computational biology literature cannot address problems of this level of complexity. The proposed framework is flexible, can be broadly applied to dynamic models of biological systems, and enables the implementation of sophisticated estimation techniques to quantify parameter uncertainty, to diagnose observability/uniqueness issues, to perform model selection, and to handle outliers. Author summaryConstructing and validating dynamic models of biological systems spanning biomolecular networks to ecological systems is a challenging problem. Here we present a scalable computational framework to rapidly infer parameters in complex dynamic models of biological systems from large-scale experimental data. The framework was applied to infer parameters of a synthetic microbial community model from large-scale time series data. We also demonstrate that this framework can be used to analyze parameter uncertainty, to diagnose whether the experimental data are sufficient to PLOS 1/28 uniquely determine the parameters, to determine the model that best describes the data, and to infer parameters in the face of data outliers. PLOS

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Section: Interior-point Methodsmentioning

confidence: 99%

Scalable Nonlinear Programming Framework for Parameter Estimation in Dynamic Biological System Models

Shin

Venturelli

Zavala

2018

Preprint

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“…The fundamental prior research work on aircraft trajectory optimization within the current ATM concept was presented in [17]. The flight of an aircraft was modeled as a collection of phases and procedures in which continuity of the state variables was imposed in order to link phases, permitting discontinuities in control variables and flight-path angle.…”

Section: Hybrid Optimal Control Approach To Commercial Aircraft Trajementioning

confidence: 99%

Hybrid Optimal Control Approach to Commercial Aircraft Trajectory Planning

Soler

Olivares

Staffetti

2010

Journal of Guidance, Control, and Dynamics

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“…In [6,7], an unmanned air vehicle flight mission is solved considering the route as a given sequence of waypoints. In [5,8], the minimum fuel trajectory problem for commercial aircraft is discussed for a given sequence of However, due to an increasing sophistication of both manned and unmanned space missions, and due to the complex nature of the airspace structure in atmospheric flights, decision variables may be needed for better modeling of trajectory optimization problems [12]. Therefore, integer or binary variables are introduced to model decision-making processes in optimal control problems.…”

mentioning

confidence: 99%

“…Thus, different flight models can be used for different phases, resulting in a multistage or multiphase trajectory optimization problem [5], which can be typically formulated as multiphase optimal control problems. Many instances have been solved for practical applications in aerospace engineering.…”

mentioning

confidence: 99%

Multiphase Mixed-Integer Optimal Control Approach to Aircraft Trajectory Optimization

Bonami

Olivares

Soler

et al. 2013

Journal of Guidance, Control, and Dynamics

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In this paper, an approach to aircraft trajectory optimization is presented in which integer and continuous variables are considered. Integer variables model decision-making processes, and continuous variables describe the state of the aircraft, which evolves according to differential-algebraic equations. The problem is formulated as a multiphase mixed-integer optimal control problem. It is transcribed into a mixed-integer nonlinear programming problem by applying a fifth degree Gauss-Lobatto direct collocation method and is then solved using a nonlinear-programming-based branch-and-bound algorithm. The approach is applied to the following en route flight planning problem: Given an aircraft point mass model, a wind forecast, an airspace structure, and the relevant flying information regions with their associated overflying costs, find the control inputs that steer the aircraft from the initial fix to the final fix, following a route of waypoints while minimizing the fuel consumption and overflying costs during the flight. The decision-making process arises in determining the optimal sequence of waypoints. The optimal times at which the waypoints are to be overflown are also to be determined. Numerical results are presented and discussed, showing the effectiveness of the approach.

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Application of Direct Transcription to Commercial Aircraft Trajectory Optimization

Cited by 83 publications

References 12 publications

Scalable Nonlinear Programming Framework for Parameter Estimation in Dynamic Biological System Models

Scalable Nonlinear Programming Framework for Parameter Estimation in Dynamic Biological System Models

Hybrid Optimal Control Approach to Commercial Aircraft Trajectory Planning

Multiphase Mixed-Integer Optimal Control Approach to Aircraft Trajectory Optimization

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