inf340 - Uncertainty Modeling for Control in Digitalised Energy Systems (Complete module description)

The students:

• identify fundamentals of uncertainty modeling in control systems
• characterize problem-specific solution techniques for systems with stochastic and set-based uncertainty
• are aware of software implementations in simulation, control, and state estimation.

Methological competences
The students:

• students identify fundamentals of uncertainty modelling in control systems
• characterise problem-specific solution techniques for systems with stochastic and set-based uncertainty
• are aware of software implementations in simulation, control, and state estimation.

Social competences
The students:

• analyse problems of control-oriented uncertainty modelling
• analyse fundamental solution techniques on a theoretical basis as well as transfer and generalise them independently toward novel research-oriented application scenarios.

Self competences
The students:

• critically reflect the achieved results of their project work
• acknowledge limitations of various approaches for a control-oriented uncertainty modeling.

1. Mathematical modeling of uncertainty in linear and nonlinear dynamic systems
2. Stochastic modeling approaches
   • Probability distributions
   • Bayesian state estimation for discrete-time systems (linear/nonlinear) and for continuous-time systems (linear)
   • Linear estimation techniques in an extended state-space (Carleman linearization for special system classes)
   • Monte-Carlo methods
3. Estimation of states, parameters and simulation of uncertain processes
   • Outlook: Markov models
   • Outlook: Bayesian networks
4. Set-based approaches
   • Set-based algorithms: Forward-backward contractor and bisection techniques
   • Interval methods for a verified solution of ordinary differential equations and for a stability proof of uncertain systems
   • Estimation of states and parameters as well as simulation of uncertain processes
5. Outlook: Synthesis of controllers and state observers under an explicit description of uncertainty

• Jaulin, L., Kieffer, M., Didrit, O., Walter, E., Applied Interval Analysis, Springer- Verlag, 2001.
• Papoulis, A.: Probability, Random Variables, and Stochastic Processes, McGraw- Hill, 4th Ed., 2002.
• Rauh, A. Folien/ Skript zur Vorlesung „Uncertainty Modelling for Control in DES“.