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Chapter 6: Costate Recovery and Nonlinear Programming Implementation

From KKT multipliers to continuous costates and solver-ready LGR implementations

A direct transcription produces primal variables and KKT multipliers, whereas continuous optimal-control theory describes states, controls, and costates. This chapter connects the two descriptions. It derives costate mappings for LG, LGR, and LGL grids, generalizes the transcription to practical Bolza problems, and closes by organizing the resulting arrays, constraints, objective, and initial guess for an NLP solver.

Chapter contents

  1. Costate Estimation Using the Legendre–Gauss Method

  2. Costate Mapping and Recovery of Continuous Costates

  3. Costate Estimation Using the Legendre–Gauss–Radau Method

  4. LGL Costate Estimation and General Pseudospectral Transcription

  5. Practical NLP Implementation of LGR Optimal Control

  6. Exercises

Chapter 5: Orthogonal Collocation and Pseudospectral Foundations
Exercises
Chapter 6: Costate Recovery and Nonlinear Programming Implementation
Costate Estimation Using the Legendre–Gauss Method