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Chapter 4: Direct Numerical Methods and Collocation

From trajectory parameterization to sparse nonlinear-program transcriptions

Indirect methods optimize through the necessary conditions; direct methods instead discretize the original problem. This chapter develops that alternative from the ground up. Direct shooting motivates finite-dimensional parameterization, numerical integration explains how continuous dynamics become discrete equations, and Euler collocation turns those equations into a sparse nonlinear program on a normalized time domain.

Chapter contents

  1. Direct Numerical Methods and Direct Shooting

  2. Numerical Integration of Ordinary Differential Equations and Collocation

  3. Direct Collocation with Euler Discretization

  4. Sparse NLP Structure and Time Normalization

  5. Exercises

Chapter 3: Linear–Quadratic, Indirect, and Singular Optimal Control
Exercises
Chapter 4: Direct Numerical Methods and Collocation
Direct Numerical Methods and Direct Shooting