TY - JOUR

T1 - Moment propagation of discrete-time stochastic polynomial systems using truncated carleman linearization

AU - Pruekprasert, Sasinee

AU - Takisaka, Toru

AU - Eberhart, Clovis

AU - Cetinkaya, Ahmet

AU - Dubut, Jérémy

N1 - Funding Information:
The authors are supported by ERATO HASUO Metamathematics for Systems Design Project No. JPMJER1603, JST; J. Dubut is also supported by Grant-in-aid No. 19K20215, JSPS.
Publisher Copyright:
Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND license

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Carleman linearization

KW - Moment computation

KW - Nonlinear systems

KW - Probabilistic safety analysis

KW - Stochastic systems

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U2 - 10.1016/j.ifacol.2020.12.1447

DO - 10.1016/j.ifacol.2020.12.1447

M3 - Conference article

AN - SCOPUS:85105026867

VL - 53

SP - 14462

EP - 14469

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 2

T2 - 21st IFAC World Congress 2020

Y2 - 12 July 2020 through 17 July 2020

ER -