The course covers control theory for nonlinear dynamic systems, including:
- analysis of input and output stability, for example with the low-gain theorem and the circle criterion
- stability analysis of equilibrium points through linearization and Lyapunov methods
- analysis of stability of passive systems
- design and analysis of closed-loop control for nonlinear systems through linearization, feedback linearization and Lyapunov-based methods
- design and analysis of sliding mode control
- observers for nonlinear systems
- setpoint control and setpoint tracking
- simulation of nonlinear dynamic models, including examples from several scientific applications.
After passing the course, the student should be able to:
1. model and analyze nonlinear dynamic systems that arise in engineering and applied scientific fields, such as mechanics, robotics, biological or epidemiological systems, and network systems, using appropriate mathematical representations and stability concepts
2. apply methods for nonlinear control systems and observer design – including Lyapunov-based methods, feedback linearization, passivity, and high-gain control and sliding mode control – to analyze stability and achieve desired control or management
3. use simulation tools to evaluate the behavior of nonlinear systems and control solutions, and critically reflect on model assumptions and limitations and communicate conclusions.
