Nonlinear Optimal Trajectories Using Successive Linearization

Abstract

A method of designing trajectories for maneuvering reentry vehicles is developed in this paper. Optimal control theory using linear perturbation guidance and a quadratic penalty function is employed to design trajectories for these vehicles. The vehicle equations of motion are represented by a five- dimension state vector. The problem is formulated by linearizing about a reference trajectory. A linear servomechanism problem, rather than a regulator problem, is solved, leading to a Riccati matrix differential equation and an auxiliary vector differential equation which are solved backwards in time. Successive linearization consists of iteratively generating new trajectories by linearizing about a reference trajectory created from a prior iteration. The cost function is adjusted between iterations to shape the trajectory. Qualitative guidelines for selecting these cost functions are given. Test cases are shown, with emphasis on designing a trajectory to intercept a target point.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jun 28, 1977
Accession Number
ADA046068

Entities

People

  • C. Hecht

Organizations

  • The Aerospace Corporation

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Control Theory
  • Coordinate Systems
  • Corporations
  • Differential Equations
  • Dynamic Pressure
  • Equations
  • Equations Of Motion
  • Flight Paths
  • Guidance
  • Perturbation Theory
  • Perturbations
  • Reentry Vehicles
  • Servomechanisms
  • Trajectories
  • Vehicles

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Operations Research