After successful completion of the course, students are able to

• understand and apply the mathematical principles and methods to describe and analyze nonlinear systems.
• apply Lyapunov theory to analyze stability and devise nonlinear control strategies such as integrator backstepping, PD control and computed torque.
• utilize singular perturbation methods to reduced-order models systematically.
• develop nonlinear control schemes based on differential-geometric and differential-algebraic methods such as differential flatness or exact input-state linearization.

introduction to nonlinear system theory, examples of nonlinear systems (mechanical, electrical, hydraulic), stick-slip effect, basics of dynamical systems, existence and uniqueness of solutions, sensitivity equations, Lyapunov stability, invariance principle of Krasowskii-LaSalle, direct and indirect method of Lyapunov, Lyapunov equation, stability of non-autonomous systems, Lemma of Barbalat, singular perturbation theory, fast and slow manifold, boundary layer model, Theorem of Tikhonov, Lyapunov-based controller design (simple PD-law, computed torque, integrator backstepping, generalized backstepping, recursive backstepping), affine-input systems, exact input-output and input-state linearization of SISO- and MIMO-systems, relative degree, zero dynamics, trajectory tracking, flatness, basics of differential geometry (manifold, tangent and cotangent space, Lie derivatives, Theorem of Frobenius), observer design for linear time-variant systems

lecture, presentation of examples during the lecture

A preliminary discussion is given in the first lecture.

oral exam