Skip to content

A Steepest-Ascent Method for Solving Optimum Programming Problems

Authors: Arthur E. Bryson, Walter F. Denham

Published: 1962 (Journal Paper)

Source: Journal of Applied Mechanics

Algorithm: Steepest Ascent

DOI: 10.1115/1.3640537

Summary

One of the foundational papers on gradient-based trajectory optimization, introducing the use of adjoint-equation integration to compute the steepest-ascent direction for optimal control problems with terminal constraints. The adjoint (co-state) approach is the direct predecessor of modern shooting methods and continuous-time policy gradient algorithms.

Abstract

A systematic and rapid steepest-ascent numerical procedure is described for determining optimum programs for nonlinear systems with terminal constraints. The procedure uses the concept of local linearization around a nominal (nonoptimum) path. The effect on the terminal conditions of a small change in the control variable program is determined by numerical integration of the adjoint differential equations for small perturbations about the nominal path.

Primary

Paper asmedigitalcollection.asme.org

Standard

DOI 10.1115/1.3640537

Tags

  • Trajectory optimization

  • Optimal control

  • Gradient descent

  • Adjoint equations

  • Numerical methods

  • Variational calculus