Moment propagation of discrete-time stochastic polynomial systems using truncated carleman linearization

Sasinee Pruekprasert, Toru Takisaka, Clovis Eberhart, Ahmet Cetinkaya, Jérémy Dubut

Research output: Contribution to journalConference articlepeer-review

1 Citation (Scopus)


We propose a method to compute an approximation of the moments of a discrete-time stochastic polynomial system. We use the Carleman linearization technique to transform this finite-dimensional polynomial system into an infinite-dimensional linear one. After taking expectation and truncating the induced deterministic dynamics, we obtain a finite-dimensional linear deterministic system, which we then use to iteratively compute approximations of the moments of the original polynomial system at different time steps. We provide upper bounds on the approximation error for each moment and show that, for large enough truncation limits, the proposed method precisely computes moments for sufficiently small degrees and numbers of time steps. We use our proposed method for safety analysis to compute bounds on the probability of the system state being outside a given safety region. Finally, we illustrate our results on two concrete examples, a stochastic logistic map and a vehicle dynamics under stochastic disturbance.

Original languageEnglish
Pages (from-to)14462-14469
Number of pages8
Issue number2
Publication statusPublished - 2020
Externally publishedYes
Event21st IFAC World Congress 2020 - Berlin, Germany
Duration: 2020 Jul 122020 Jul 17


  • Carleman linearization
  • Moment computation
  • Nonlinear systems
  • Probabilistic safety analysis
  • Stochastic systems

ASJC Scopus subject areas

  • Control and Systems Engineering


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