Modul

The module will be completed by an oral exam (ca. 20 min).

Students can explain the central concepts of the treatment of controlled linear ordinary differential equations (controllability, observability, stabilizability and discoverability) and the associated characterizations and apply them in examples. They are able to describe the basic features of the theory of transfer functions and realization theory. They can discuss the solution of the quadratic optimal control problem and apply it to feedback synthesis. They can describe the basic concepts of control theory including the associated criteria also for non-linear systems and apply them to examples.

none

• controllabilty and observabilty  of systems of linear ordinary differential equations
• stabilizability and detectability
• transfer functions
• realization theory,
• quadratic optimal control, feedback synthesis
• nonlinear controll theory: basic concepts, criteria  via linearization, Lie brackets and Lyapunov functions

The contents of the modules Analysis 1-2 und Lineare Algebra 1-2 are strongly recommended. Further knowledge of ordinary differential equations (as in Analysis 4) is useful.

Total workload: 180 hours

Attendance: 60 h

• lectures, problem classes and examination

Self studies: 120 h

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research on the course content,
• preparation for the module examination