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作者： Sowell, Sam Taheri, Ehsan Johns Hopkins Univ Appl Phys Lab Laurel MD 20723 USA Auburn Univ Dept Aerosp Engn Auburn AL 36849 USA

ISBN: (数字)9781624107115

ISBN: (纸本)9781624107115

Solving practical optimal control problems (OCPs) that consist of multiple state, path, and control equality and inequality constraints can become challenging, but is necessary for improving the performance of modern engineering systems. A general and popular approach to solve practical OCPs is to transcribe the original continuous-time OCP into a nonlinear programming (NLP) problem that can be solved with a variety of mature NLP solvers. These direct optimization methods are differentiated by the adopted transcription scheme. A variety of different software programs that utilize direct methods exist, such as SOCS, OTIS, PSOPT, DIDO, and GPOPS-II. In this paper, we introduce an open-source, MATLAB-based optimization software, the Tiger Optimization Software (TOPS). TOPS employs several Legendre-Gauss pseudospectral transcriptions and is compatible with advanced NLP solvers such as IPOPT and SNOPT. In addition, TOPS is compatible with the open-source automatic differentiation software ADiGator to improve convergence performance of the NLP solvers. TOPS also features automatic mesh refinement and is compatible with a wide variety of OCP formulations. The goal of this paper is to outline the direct method employed by TOPS and showcase its capabilities using a small suite of OCPs and spacecraft trajectory optimization problems.

关键词： MATLAB Pontryagin's Minimum Principle sparse sequential quadratic programming Spacecraft Trajectory Optimization Adaptive Mesh Refinement Earth Potentially Hazardous Asteroids Gauss Pseudospectral Method Canonical Units Minimum Orbit Intersection Distance

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Hermite-Legendre-Gauss-Lobatto Direct Transcription in Trajectory Optimization

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2009年第4期32卷 1392-1395页

作者： Williams, Paul Delft Univ Technol Fac Aerosp Engn NL-2600 AA Delft Netherlands

The purpose of this Note is to provide an alternative framework for arbitrary higher-order methods suitable for implementation on digital computers and in a reusable form. The optimal control problem is approximated by a discrete nonlinear programming problem (NLP) by expanding the state trajectories using local Hermite interpolating polynomials. For high accuracy, the collocation points are selected from the family of Gauss-Lobatto points. This also allows the integral performance index to be approximated via Gauss-Lobatto quadrature rules. For optimal control problems of the Bolza form, the natural choice of quadrature points are the Legendre-Gauss-Lobatto (LGL) points, because they are derived on the basis of a unity weight function, giving the highest accuracy for polynomial integrands. The generalization of the approach is referred to as the Hermite-Legendre-Gauss-Lobatto (HLGL) approach throughout the remainder of this Note.

关键词： Pontryagin's Maximum Principle Nonlinear programming Bank Angle Lagrange Multipliers FORTRAN Legendre Pseudospectral Method Flight Path Angle Angle of Attack Earth sparse sequential quadratic programming

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HYBRID OPTIMAL CONTROL OF MOTORIZED TRAVELING SALESMEN AND BEYOND

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IFAC Proceedings Volumes 2002年第1期35卷 439-444页

作者： Markus Glocker Oskar von Stryk Simulation and Systems Optimization Group Technische Universität Darmstadt Alexanderstr. 10 64283 Darmstadt Germany http://www.sim.informatik.tu-darmstadt.de

Numerical methods for optimal control of hybrid dynamical systems are considered where the discrete dynamics and the nonlinear continuous dynamics are tightly coupled. A decomposition approach for numerically solving general mixed-integer continuous optimal control problems (MIOCPs) is discussed. In the outer optimization loop a branch-and-bound binary tree search is used for the discrete variables. The multiple-phase optimal control problems for the continuous state and control variables in the inner optimization loop are solved by a sparse direct collocation transcription method. A genetic algorithm is applied to improve the performance of the branch-and-bound approach by providing a good initial upper bound on the MIOCP performance index. Results are presented for motorized traveling salesmen problems, new benchmark problems in hybrid optimal control.

关键词： nonlinear hybrid dynamical systems mixed-integer optimal control branch-and-bound direct collocation transcription sparse sequential quadratic programming motorized traveling salesmen genetic algorithm

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PATH-CONSTRAINED TRAJECTORY OPTIMIZATION USING sparse sequential quadratic-programming

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1993年第1期16卷 59-68页

作者： BETTS, JT HUFFMAN, WP Boeing Computer Services Seattle WA

One of the most effective numerical techniques for the solution of trajectory optimization and optimal control problems is the direct transcription method. This approach combines a nonlinear programming algorithm with discretization of the trajectory dynamics. The resulting mathematical programming problem is characterized by matrices that are large and sparse. Constraints on the path of the trajectory are then treated as algebraic inequalities to be satisfied by the nonlinear program. This paper describes a nonlinear programming algorithm that exploits the matrix sparsity produced by the transcription formulation. Numerical experience is reported for trajectories with both state and control variable equality and inequality path constraints.

关键词： Trajectory Optimization sparse sequential quadratic programming Nonlinear programming Lagrange Multipliers Control Derivatives Algorithm Performance Three Degrees of Freedom Boundary Value Problems Aerodynamic Heating Cholesky Factorization

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APPLICATION OF DIRECT TRANSCRIPTION TO COMMERCIAL AIRCRAFT TRAJECTORY OPTIMIZATION

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1995年第1期18卷 151-159页

作者： BETTS, JT CRAMER, EJ Boeing Computer Services Seattle WA

One of the most effective numerical techniques for the solution of trajectory optimization and optimal control problems is the direct transcription method, This approach combines a nonlinear programming algorithm with a discretization of the trajectory dynamics, When the resulting mathematical programming problem is solved using a sparse sequential quadratic programming algorithm, the technique produces solutions very rapidly and has demonstrated considerable robustness when applied to atmospheric acid orbital trajectories, This paper describes the application of the direct transcription technique to the optimal design of a commercial aircraft trajectory, subject to realistic constraints on the aircraft flight path, A primary result of the paper is to demonstrate that the transcription formulation leads to a very natural treatment of realistic Federal Aviation Administration (FAA) imposed path constraints within a high fidelity simulation, A second important result is to demonstrate that modeling tabular data using smooth approximations significantly improves the speed of convergence.

关键词： Trajectory Optimization Commercial Aircraft Nonlinear programming Federal Aviation Administration sparse sequential quadratic programming Aerodynamic Drag Calibrated Airspeed Flight Path Angle Lift Coefficient Applied Mathematics

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APPLICATION OF sparse NONLINEAR-programming TO TRAJECTORY OPTIMIZATION

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1992年第1期15卷 198-206页

作者： BETTS, JT HUFFMAN, WP Boeing Computer Services Seattle Washington 98124

The most effective numerical techniques for the solution of trajectory optimization and optimal control problems combine a nonlinear iteration procedure with some type of parametric approximation to the trajectory dynamics. Early methods attempted to parameterize the dynamics using a small number of variables because the iterative search procedures could not successfully solve larger problems. With the development of more robust nonlinear programming algorithms, it is now feasible and desirable to consider formulations of the trajectory optimization problem incorporating a large number of variables and constraints. The purpose of this paper is to address the manner in which a trajectory is parameterized and the design of the nonlinear programming algorithm to effectively deal with this formulation.

关键词： Nonlinear programming Trajectory Optimization sparse sequential quadratic programming Numerical Integration Angle of Attack Vehicle Trajectories Aerodynamics Computing Space Shuttle Orbiter Re Entry Trajectories

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