Solution of Optimal Control Problem for High Speed Ascent and Reentry Vehicles

Abstract

Advancements to a general-purpose computational framework is described for solving constrained nonlinear optimal control problems. The framework consists of the following three modules that operate synergistically to improve the accuracy and computational efficiency that can be achieved when solving constrained optimal control problems. The first module is a new class of efficient discretization methods called hp-adaptive Gaussian quadrature methods that transcribe the continuous optimal control problem to a finite-dimensional nonlinear optimization problem. The hp-adaptive methods have the feature that both the degree of the polynomial approximation and the number of mesh intervals can be adjusted to improve the accuracy in the approximation of the solution to the optimal control problem. The second module is a new approach to nonlinear optimization that employs conjugate gradient-based methods with a dual active set method to efficiently solve the non- linear optimization problem associated with the hp-adaptive method. The third module is a novel approach to algorithmic differentiation that produces an efficient derivative source code through a method that combines operator overloading with source transformation. The algorithmic differentiation provides the most accurate derivative possible for use with the gradient-based nonlinear optimization method. Each module in the framework is described and results are shown that demonstrate the effectiveness of the approach. The advancements described in this report include a new hp-adaptive mesh refinement method, a benchmarking study that provides comparisons between various hp-adaptive mesh refinement methods that have been developed in support of this framework, the demonstration of the framework on a high-speed ascent and entry problems, and further advancements to the optimization algorithms and convergence theory of the hp-adaptive methods.

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Document Details

Document Type
Technical Report
Publication Date
May 18, 2018
Accession Number
AD1063085

Entities

People

  • Anil V. Rao
  • William Hager

Organizations

  • University of Florida

Tags

Communities of Interest

  • Space
  • Weapons Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Aerodynamic Heating
  • Air Force
  • Air Force Facilities
  • Algorithms
  • Boundary Value Problems
  • Calculus Of Variations
  • Computations
  • Computer Programs
  • Convergence
  • Detection
  • Differential Equations
  • Efficiency
  • Engineering
  • Equations
  • Flight Paths
  • Fourier Series
  • Gaussian Quadrature
  • Launch Vehicles
  • Linear Programming
  • Mathematical Programming
  • Nonlinear Programming
  • Optimization
  • Standards
  • Test Sets
  • Vehicles

Readers

  • Distributed Systems and Data Platform Development
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)