Moment Propagation of Discrete-Time Stochastic Polynomial Systems using Truncated Carleman Linearization

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

doi:10.1016/j.ifacol.2020.12.1447

Cited by 3 publications

(1 citation statement)

References 9 publications

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“…The characterization of the dynamics under truncated Carleman linearization and the truncation error analysis in Section 3 appeared previously in our preliminary conference report (Pruekprasert et al, 2020). Here in this paper, we present new results on tail-probability analysis in Section 5 and provide new techniques to improve the computational efficiency of our methods in Section 6.…”

Section: Related Workmentioning

confidence: 89%

Moment Propagation Through Carleman Linearization with Application to Probabilistic Safety Analysis

Pruekprasert¹,

Dubut²,

Takisaka³

et al. 2022

Preprint

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We develop a method to approximate the moments of a discrete-time stochastic polynomial system. Our method is built upon Carleman linearization with truncation. Specifically, we take a stochastic polynomial system with finitely many states and transform it into an infinitedimensional system with linear deterministic dynamics, which describe the exact evolution of the moments of the original polynomial system. We then truncate this deterministic system to obtain a finite-dimensional linear system, and use it for moment approximation by iteratively propagating the moments along the finite-dimensional linear dynamics across time. We provide efficient online computation methods for this propagation scheme with several error bounds for the approximation. Our result also shows that precise values of certain moments can be obtained when the truncated system is sufficiently large. Furthermore, we investigate techniques to reduce the offline computation load using reduced Kronecker power. Based on the obtained approximate moments and their errors, we also provide probability bounds for the state to be outside of given hyperellipsoidal regions. Those bounds allow us to conduct probabilistic safety analysis online through convex optimization. We demonstrate our results on a logistic map with stochastic dynamics and a vehicle dynamics subject to stochastic disturbance.

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Section: Related Workmentioning

confidence: 89%

Moment Propagation Through Carleman Linearization with Application to Probabilistic Safety Analysis

Pruekprasert¹,

Dubut²,

Takisaka³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Moment propagation of polynomial systems through Carleman linearization for probabilistic safety analysis

Pruekprasert,

Dubut,

Takisaka

et al. 2024

Automatica

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Joint State and Parameter Estimation for Hypersonic Glide Vehicles Based on Moving Horizon Estimation via Carleman Linearization

Gao

Jing

2022

Aerospace

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Aimed at joint state and parameter estimation problems in hypersonic glide vehicle defense, a novel moving horizon estimation algorithm via Carleman linearization is developed in this paper. First, the maneuver characteristic parameters that reflect the target maneuver law are extended into the state vector, and a dynamic tracking model applicable to various hypersonic glide vehicles is constructed. To improve the estimation accuracy, constraints such as path and parameter change amplitude constraints in flight are taken into account, and the estimation problem is transformed into a nonlinear constrained optimal estimation problem. Then, to solve the problem of high time cost for solving a nonlinear constrained optimal estimation problem, in the framework of moving horizon estimation, nonlinear constrained optimization problems are transformed into bilinear constrained optimization problems by linearizing the nonlinear system via Carleman linearization. For ensuring the consistency of the linearized system with the original nonlinear system, the linearized model is continuously updated as the window slides forward. Moreover, a CKF-based arrival cost update algorithm is also provided to improve the estimation accuracy. Simulation results demonstrate that the proposed joint state and parameter estimation algorithm greatly improves the estimation accuracy while reducing the time cost significantly.

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Moment Propagation of Discrete-Time Stochastic Polynomial Systems using Truncated Carleman Linearization

Cited by 3 publications

References 9 publications

Moment Propagation Through Carleman Linearization with Application to Probabilistic Safety Analysis

Moment Propagation Through Carleman Linearization with Application to Probabilistic Safety Analysis

Moment propagation of polynomial systems through Carleman linearization for probabilistic safety analysis

Joint State and Parameter Estimation for Hypersonic Glide Vehicles Based on Moving Horizon Estimation via Carleman Linearization

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