Dynamics and optimal control of multibody systems using fractional generalized divide-and-conquer algorithm

Arman Dabiri, Mohammad Poursina, J. A.Tenreiro Machado

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this paper, a new framework is presented for the dynamic modeling and control of fully actuated multibody systems with open and/or closed chains as well as disturbance in the position, velocity, acceleration, and control input of each joint. This approach benefits from the computed torque control method and embedded fractional algorithms to control the nonlinear behavior of a multibody system. The fractional Brunovsky canonical form of the tracking error is proposed for a generalized divide-and-conquer algorithm (GDCA) customized for having a shortened memory buffer and faster computational time. The suite of a GDCA is highly efficient. It lends itself easily to the parallel computing framework, that is used for the inverse and forward dynamic formulations. This technique can effectively address the issues corresponding to the inverse dynamics of fully actuated closed-chain systems. Eventually, a new stability criterion is proposed to obtain the optimal torque control using the new fractional Brunovsky canonical form. It is shown that fractional controllers can robustly stabilize the system dynamics with a smaller control effort and a better control performance compared to the traditional integer-order control laws.

Original languageEnglish (US)
Pages (from-to)1611-1626
Number of pages16
JournalNonlinear Dynamics
Issue number3
StatePublished - Nov 2020
Externally publishedYes


  • Closed-chain system
  • Computed-torque control
  • Divide and conquer algorithm
  • Fractional control
  • LQR
  • Multibody dynamics
  • Open-chain system
  • Optimal control
  • Parallel computing
  • PID

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Electrical and Electronic Engineering
  • Applied Mathematics


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