The design of technical processes is often carried out by considering a model of the underlying dynamics, e.g. in the form of ordinary differential equations. This dynamics can often be influenced by actuators for controlling the solution of the differential equation. On the other hand, often one has only partial information on the dynamics of the system but only information by measurements. In this course we will analyze the resulting state-space systems in detail. In particular, we will study controllability and observability notions and discuss optimal control strategies. These tasks often lead to different types of matrix equations whose solution structure and numerical schemes are discussed.
- examples of state-space systems
- analysis of linear systems (controllability, stabilizability, observability, detectability)
- frequency domain analysis (Laplace transformation, Hardy spaces)
- stabilization, pole placement, and Lyapunov equations
- linear-quadratic optimal control and algebraic Riccati equations
- state estimation (Luenberger observer, Kalman filter)
- design of H∞ and robust controllers (optional)
Prerequisites
Required
- basic courses in linear algebra and calculus
Recommended
- basic course in optimization
- numerical analysis/numerical linear algebra
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