Matthias Gerdts 
Optimal Control of ODEs and DAEs 

1 Introduction
2 Basics from Functional Analysis
2.1 Vector Spaces
2.2 Mappings, Dual Spaces, and Properties
2.3 Function Spaces
2.4 Stieltjes Integral
2.5 Set Arithmetic
2.6 Separation Theorems
2.7 Derivatives
2.8 Variational Equalities and Inequalities
3 Infinite and Finite Dimensional Optimization Problems
3.1 Problem Classes
3.2 Existence of a Solution
3.3 Conical Approximation of Sets
3.4 First Order Necessary Conditions of Fritz-John Type
3.5 Constraint Qualifications
3.6 Necessary and Sufficient Conditions in Finte Dimensions
3.7 Perturbed Nonlinear Optimization Problems
3.8 Numerical Methods
3.9 Duality
3.10 Mixed-Integer Nonlinear Programs and Branch&Bound
4 Local Minimum Principles
4.1 Local Minimum Principles for Index-2 Problems
4.2 Local Minimum Principles for Index-1 Problems
5 Discretization Methods for ODEs and DAEs
5.1 General Discretization Theory
5.2 Backward Differentiation Formulae (BDF)
5.3 Implicit Runge-Kutta Methods
5.4 Linearized Implicit Runge-Kutta Methods
6 Discretization of Optimal Control Problems
6.1 Direct Discretization Methods
6.2 Calculation of Gradients
6.3 Numerical Example
6.4 Discrete Minimum Principle and Approximation of Adjoints
6.5 Convergence
7 Selected Applications and Extensions
7.1 Mixed-Integer Optimal Control
7.2 Open-Loop-Real-Time Control
7.3 Dynamic Parameter Identification