Dynamic Optimization

Course content

The students understand the of the complex links between their previous mathematical knowledge and the contents of the lecture,
understand the theoretical body of the lecture as a whole and master the corresponding methods, are able to analyze and apply the methods of the lecture, know and understand the problems of optimal control, parameter estimation, optimal experimental design and model discrimination, know and understand the different fundamental approaches in the field of optimal control are are able to apply and analyze them, are able to analyze, interpret, refine and enhance the methods, especially to increase the efficiency of numerical algorithms exemplified for optimal control

Content:

• Modeling dynamic processes via ODE and DAE
• Theory of the initial value problem for ordinary differential equations (ODE) and differential algebraic (DAE) equations
• Marginal value problem, solution via single and multi shooting methods
• Modeling and transformation of optimal control problems
• The Bellmann principal
• Direct, indirect, sequential and simultaneous approaches, including e.g. Pontryagin's Maximum Principal, Single Shot method, collokation methods, multi shooting methods, dynamic optimization, the Hamilton-Jacobi-Bellman-Equality
• Structures and their use in direct multi shooting methods
• Parameter estimation and dynamic problems
• The generalized Gauß-Newton-method, local contraction und convergence
• Statistics of the generalized Gauß-Newton-method
• Optimal experimental design
• Model discrimination