The goal of this course is to highlight important results in nonlinear systems’ and control theory and robotics. The subject of this course will be discussed in weekly consultations on the following topics:

I. Preliminaries and missing topics from the linear systems theory

- Discretization techniques: explicit/implicit Euler approach, the zero-order hold, etc.

- System operator, Gram-matrix, observability, controllability of linear time-varying systems

- Kalman decomposition and its geometric view, Luenberger normal form

- Luenberger observer for MIMO systems

- Unknown-input observability, of linear systems

- Basic control approaches, load estimation, and servo controller

- Optimal control and optimal state observation and the LQG controller loop

- Least mean squares parameter estimation (state-space, ARMAX, static models)

II. Input-affine state-space models [1, Chapter 1]

- Mathematical preliminaries: the “Lie-differential algebra”

- Distributions

- Unobservability, controllability and their geometric view
- State-space transformation, relative degree, normal form of SISO models, zero-dynamics

- I/O linearization, exact linearization

- Model classes and dynamic model extensions

III. Dissipativity theory and special cases [2, Chapter 2]

- Lyapunov theory, Lyapunov functions, domain of attraction

- La Salle’s theorem, advanced stability criteria

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- Induced L2 norm, small gain theory

- Passivity, feedback equivalence to a passive system, minimum phase systems,

- Dynamic invertibility, unknown-input reconstruction, asymptotic output tracking

IV. Applications in robotics [3]

- Feedback linearization of (Port-)Hamiltonian systems

- Inversion-based control vs. feedforward compensation control

- Actuator dynamics, voltage control vs. back-emf compensation control

- Simulation examples on a 4DOF robotic arm

V. Advanced Matlab/Simulink tools and techniques and their usage

- Weekly demonstration and project work

Selected  list of required and recommended literature: