Seminář Nonlinear Stability and Stabilization with Application to Underactuated Walking


 prof. RNDr. Sergej Čelikovský, CSc. (UTIA AV ČR, Praha)

Datum akce: 
Pátek, 29. Listopad 2013 - 9:00 - 12:30

The course is devoted to the advanced techniques for the stability analysis and stabilizing feedback design in nonlinear systems. To put these advanced techniques into the elementary stability and stabilization knowledge context, the basics from stability theory are repeated. Namely, the definitions of the fundamental types of stability, Lyapunov's methods and other related basics will be recalled in detail. Further, feedback stabilization problem is addressed, this exposition will be clustered around the notion of the so-called Control Lyapunov Function (CLF).

CLF is a useful concept converting the Lyapunov design in many situations into a quite constructive procedure. Typical example here is the so-called adding integrator procedure, or alternatively, the backstepping. Some difficulties for more general classes of systems will be discussed as well. Furthermore,  the additional advanced feedback stabilization techniques will be engaged to stabilize exponentially the tracking error dynamics of certain walking like mechanical systems. To do so in a self-contained manner, some basic information about these mechanical systems will be repeated together with the basics from the exact feedback linearization theory, namely, the notion of the so-called relative degree. The exponentially stable tracking of the mentioned underactuated systems is based on the existence of the auxiliary output having relative degree equal to three. Using this property, the given underactuated mechanical system is transformed into its more simple and equivalent form. Using this form the exponentially stable tracking feedback is designed and thoroughly justified.

  1. Introduction to stability analysis of nonlinear dynamical systems. Lyapunov's methods, La Salle principle, stability of perturbed systems.
  2. Feedback stabilization of nonlinear controlled dynamical systems. Control Lyapunov's function, backstepping and adding integrator problem.
  3. Exact feedback linearization. Relative degree and vector relative degree.
  4. Modeling and control of the underactuated mechanical systems. Design of the reference trajectory and its exponentially stable tracking.


Místo konání: 

Ústav automatizace a měřicí techniky
Technická 12
616 00 Brno
(seminární místnost SD1.48)

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