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Chapter 2: Hamiltonian Formulation and Necessary Conditions

From dynamic feasibility to Pontryagin’s necessary conditions

The variational machinery becomes useful for control only after the system dynamics are built into the optimization problem. This chapter introduces augmentation, costates, endpoint multipliers, and the Hamiltonian, then carries one continuous derivation through endpoint variation, variation of the Hamiltonian integral, and Pontryagin’s necessary conditions. The four sections are therefore stages of one argument rather than independent lectures.

Chapter contents

  1. Augmentation, Costates, and the Hamiltonian Formulation

  2. First Variation of the Augmented Functional

  3. Variation of the Hamiltonian Integral

  4. Pontryagin’s Necessary Conditions

  5. Exercises

Chapter 1: Optimization Foundations and Variational Methods
Exercises
Chapter 2: Hamiltonian Formulation and Necessary Conditions
Augmentation, Costates, and the Hamiltonian Formulation