Optimal Control
Learning objectives and acquired competences:
The module provides an introduction to the formulation, theory, solution, and application of optimal control theory for dynamic systems subject to constraints. The students are enabled to mathematically formulate, analyse and solve optimal control problems appearing in many applications spanning from medicine, process control up to systems biology. Besides an understanding of the theoretical basis the students are enabled to derive numerical solutions for optimal control problems using different numerical solution algorithms. The acquired methods are deepened in the exercises considering small example systems. In the frame of a mini-projects the students derive numerical solutions of small, practical relevant optimal control problems and compare them to analytic solutions.
Content:
- Static optimization
- Numerical algorithms
- Dynamic programming, principle of optimality, Hamilton-Jacobi-Bellman equation
- Variational calculus
- Pontryagin maximum principle
- Numerical solution of optimal control problems
- Infinite and finite horizon optimal control, LQ optimal control
- Model predictive control
- Game theory
- Application examples from various fields such as chemical engineering, economics, aeronautics, robotics, biomedicine, and systems biology