Subsystem identification of feedback and feedforward systems with time delay

S. Alireza Seyyed Mousavi, Xingye Zhang, T. M. Seigler, Jesse B. Hoagg

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We present an algorithm for identifying discrete-time feedback-and-feedforward subsystems with time delay that are interconnected in closed loop with a known subsystem. This frequency-domain algorithm uses only measured input and output data from a closed-loop discrete-time system, which is single input and single output. No internal signals are assumed to be measured. The orders of the unknown feedback and feedforward transfer functions are assumed to be known. We use a two-candidate-pool multi-convex-optimization approach to identify not only the feedback and feedforward transfer functions but also the feedback and feedforward time delay. The algorithm guarantees asymptotic stability of the identified closed-loop transfer function. The main analytic result shows that if the data noise is sufficiently small and the cardinality of the feedback-candidate-pool set is sufficiently large, then the identified feedforward and feedback delays are equal to the true delays, and the parameters of the identified feedforward and feedback transfer functions are arbitrarily close to the true parameters. This subsystem identification algorithm has application to modeling human-in-the-loop behavior. To demonstrate this application, we apply the new subsystem identification algorithm to data obtained from a human-in-the-loop control experiment in order to model the humans’ feedback and feedforward (with delay) control behavior.

Original languageEnglish
Article number100002
JournalResults in Control and Optimization
StatePublished - Dec 2020

Bibliographical note

Publisher Copyright:
© 2020 The Author(s)


  • Human motor control
  • Human-in-the-loop modeling
  • Subsystem identification

ASJC Scopus subject areas

  • Control and Optimization
  • Artificial Intelligence
  • Applied Mathematics
  • Control and Systems Engineering
  • Modeling and Simulation


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