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