# 376.084 Nonlinear Dynamic Systems and Control This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2025S 2024S 2023S

2024S, VO, 3.0h, 4.5EC

## Properties

• Semester hours: 3.0
• Credits: 4.5
• Type: VO Lecture
• Format: Presence

## Learning outcomes

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.

## Subject of course

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

## Teaching methods

lecture, presentation of examples during the lecture

## Mode of examination

Oral

A preliminary discussion is given in the first lecture.

## Course dates

DayTimeDateLocationDescription
Tue08:00 - 10:0005.03.2024 - 25.06.2024EI 4 Reithoffer HS Vorlesung
Wed09:00 - 11:0006.03.2024 - 26.06.2024EI 4 Reithoffer HS Vorlesung
Tue10:00 - 11:0011.06.2024EI 4 Reithoffer HS Nichtlineare Dynamische Systeme und Regelung
Nonlinear Dynamic Systems and Control - Single appointments
DayDateTimeLocationDescription
Tue05.03.202408:00 - 10:00EI 4 Reithoffer HS Vorlesung
Wed06.03.202409:00 - 11:00EI 4 Reithoffer HS Vorlesung
Tue12.03.202408:00 - 10:00EI 4 Reithoffer HS Vorlesung
Wed13.03.202409:00 - 11:00EI 4 Reithoffer HS Vorlesung
Tue19.03.202408:00 - 10:00EI 4 Reithoffer HS Vorlesung
Wed20.03.202409:00 - 11:00EI 4 Reithoffer HS Vorlesung
Tue09.04.202408:00 - 10:00EI 4 Reithoffer HS Vorlesung
Wed10.04.202409:00 - 11:00EI 4 Reithoffer HS Vorlesung
Tue16.04.202408:00 - 10:00EI 4 Reithoffer HS Vorlesung
Wed17.04.202409:00 - 11:00EI 4 Reithoffer HS Vorlesung
Tue23.04.202408:00 - 10:00EI 4 Reithoffer HS Vorlesung
Wed24.04.202409:00 - 11:00EI 4 Reithoffer HS Vorlesung
Tue30.04.202408:00 - 10:00EI 4 Reithoffer HS Vorlesung
Tue07.05.202408:00 - 10:00EI 4 Reithoffer HS Vorlesung
Wed08.05.202409:00 - 11:00EI 4 Reithoffer HS Vorlesung
Tue14.05.202408:00 - 10:00EI 4 Reithoffer HS Vorlesung
Wed15.05.202409:00 - 11:00EI 4 Reithoffer HS Vorlesung
Wed22.05.202409:00 - 11:00EI 4 Reithoffer HS Vorlesung
Tue28.05.202408:00 - 10:00EI 4 Reithoffer HS Vorlesung
Wed29.05.202409:00 - 11:00EI 4 Reithoffer HS Vorlesung

oral exam

Not necessary

## Curricula

Study CodeObligationSemesterPrecon.Info
066 503 Electrical Power Engineering and Sustainable Energy Systems Mandatory elective
066 507 Telecommunications Mandatory elective
066 515 Automation and Robotic Systems Mandatory elective
066 938 Computer Engineering Mandatory elective

## Literature

Lecture notes (in German language) are provided on the course's webpage.

German