Finite-time stable tracking control for an underactuated system in SE(3) in discrete time

Reza Hamrah, Amit K. Sanyal

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We consider tracking control of an underactuated system on the tangent bundle of the six-dimensional Lie group of rigid body motions, (Formula presented.). We formulate a finite-time stable (FTS) tracking control scheme for this underactuated system in discrete time. This scheme is based on our recently developed theory for finite-time stability for discrete-time systems using discrete Lyapunov analysis. The proposed scheme here is developed in discrete time as it is more convenient for onboard computer implementation and ensures stability irrespective of the sampling period. This scheme guarantees a stable convergence of translational and rotational tracking errors to the desired trajectory in finite time. Furthermore, the advantages of finite-time stabilisation in discrete-time over finite-time stabilisation of a sampled continuous-time tracking control system is addressed here through a numerical comparison. This comparison is performed using numerical simulations on continuous and discrete FTS tracking control schemes applied to an unmanned aerial vehicle model.

Original languageEnglish (US)
Pages (from-to)1106-1121
Number of pages16
JournalInternational Journal of Control
Issue number4
StatePublished - 2022


  • Geometric control
  • Lie groups
  • Lyapunov stability in discrete time
  • finite-time stability
  • trajectory tracking
  • underactuated system

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications


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