Date: Thu. January 21, 2021
Organized by: Chair in Applied Analysis – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg
Title: Stabilization problem with oscillating inputs under nonlinear controllability conditions

Speaker: Prof. Dr. Alexander Zuyev
Affiliation: Max-Planck-Institut für Dynamik Komplexer Technischer Systeme, Germany

Abstract. This talk is devoted to the development of potential function approach for solving the problems of stabilization and collision avoidance for underactuated nonlinear control systems. In the first part of the talk, we propose a stabilization scheme for driftless control-affine systems whose vector fields satisfy controllability rank condition with iterated Lie brackets. Our control design scheme is based on the use of trigonometric time-varying feedback laws with bounded frequencies. By using the Chen-Fliess series expansion and a modification of Lyapunov’s direct method, we reduce the stabilization problem to a system of algebraic equations and prove its local solvability. Our approach ensures exponential stability of the equilibrium and gives explicit formulas for the coefficients of the control functions. In the second part of this talk, we discuss the problem of generating reference trajectories on the state space with obstacles by using the gradient flow of a navigation function. In general, such gradient flow cannot be implemented for underactuated control systems, and the approximation of non-admissible velocities is required for the control design. We present here approximation results under nonlinear controllability assumptions.


If you like this, you don’t want to miss out our upcoming events!


Don't miss out our posts on Math & Research!

Transition Layers in Elliptic Equations By Maicon Sônego   Stable transition layers in an unbalanced bistable equation Consider the following semi-linear problem where are positive functions in ; is a positive parameter and We assume that the functions satisfy ; for all ; there is a […]
Randomized time-splitting in linear-quadratic optimal control By Daniël Veldman   Introduction Solving an optimal control problem for a large-scale dynamical system can be computationally demanding. This problem appears in numerous applications. One example is Model Predictive Control (MPC), which requires the solution of several optimal control […]
Felix Klein: A Legacy of Innovation in Mathematics and Education By Roberto Rodríguez del Río, Complutense University of Madrid | IES San Mateo, Madrid   Felix Christian Klein lived in a period of history of science in which Mathematics were involved in a process of transformation, […]
Our last Publications
[cris show="publications" persID="223281397,105092142,229344528,239343629,241149469,243434665,105514816,242263337,104776092,236754096,243266999,243266999" year="2020" type="beitrag_fachzeitschrift" sortby="updated" quotation="apa" items="5"]
© 2019-2021 Chair for Dynamics, Control and Numerics - Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg, Germany | Imprint | Contact