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SUMMARY:Stabilization problem with oscillating inputs under nonlinear 
 controllability conditions ( A. Zuyev\, MPI für Dynamik Komplexer Tec
 hnischer Systeme\, Germany)
UID:c7947e09-2a2f-4a17-a339-21b886186f44
DESCRIPTION:Stabilization problem with oscillating inputs under nonlin
 ear controllability conditions Speaker: Prof. Dr. Alexander Zuyev Affi
 liation: Max-Planck-Institut für Dynamik Komplexer Technischer System
 e\, Germany Zoom access data: Please contact marius.yamakou@fau.de Abs
 tact: This talk is devoted to the development of potential function ap
 proach for solving the problems of stabilization and collision avoidan
 ce for underactuated nonlinear control systems. In the first part of t
 he talk\, we propose a stabilization scheme for driftless control-affi
 ne 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 frequenci
 es. By using the Chen-Fliess series expansion and a modification of Ly
 apunov&#8217\;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 ex
 plicit formulas for the coefficients of the control functions. In the 
 second part of this talk\, we discuss the problem of generating refere
 nce trajectories on the state space with obstacles by using the gradie
 nt flow of a navigation function. In general\, such gradient flow cann
 ot be implemented for underactuated control systems\, and the approxim
 ation of non-admissible velocities is required for the control design.
  We present here approximation results under nonlinear controllability
  assumptions. Applied Analysis
DTSTART:20210121T093000Z
DTEND:20210121T103000Z
LOCATION:Online
DTSTAMP:20260723T191125Z
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