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

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

doi:10.48550/arxiv.1911.12683

Cited by 1 publication

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“…To fully describe the moment dynamical system in (22) in terms of the moments, we obtain the update equation of trigonometric moment E[cos(θ(k))] as follows:…”

Section: B Recursive Approachmentioning

confidence: 99%

“…Hence, according to (22), (24), and (25), we can describe the time evolution of the first order moment m x (k) in terms of the slack moment states m c θ and m s θ as follows:…”

Section: B Recursive Approachmentioning

confidence: 99%

“…This approach is limited to short planning horizons since the order and dimension of the polynomial functions increase as the planning horizon increases. In [22], a recursive approach is provided to approximate the moments of discrete-time stochastic polynomial systems. This approach first transforms the polynomial system into an infinite-dimensional linear system using the Carleman linearization technique.…”

Section: Introductionmentioning

confidence: 99%

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Moment-Based Exact Uncertainty Propagation Through Nonlinear Stochastic Autonomous Systems

Jasour¹,

Wang²,

Williams³

2021

Preprint

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In this paper, we address the problem of uncertainty propagation through nonlinear stochastic dynamical systems. More precisely, given a discrete-time continuous-state probabilistic nonlinear dynamical system, we aim at finding the sequence of the moments of the probability distributions of the system states up to any desired order over the given planning horizon. Moments of uncertain states can be used in estimation, planning, control, and safety analysis of stochastic dynamical systems. Existing approaches to address moment propagation problems provide approximate descriptions of the moments and are mainly limited to particular set of uncertainties, e.g., Gaussian disturbances. In this paper, to describe the moments of uncertain states, we introduce trigonometric and also mixed-trigonometric-polynomial moments. Such moments allow us to obtain closed deterministic dynamical systems that describe the exact time evolution of the moments of uncertain states of an important class of autonomous and robotic systems including underwater, ground, and aerial vehicles, robotic arms and walking robots. Such obtained deterministic dynamical systems can be used, in a receding horizon fashion, to propagate the uncertainties over the planning horizon in real-time.To illustrate the performance of the proposed method, we benchmark our method against existing approaches including linear, unscented transformation, and sampling based uncertainty propagation methods that are widely used in estimation, prediction, planning, and control problems.

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“…To fully describe the moment dynamical system in (22) in terms of the moments, we obtain the update equation of trigonometric moment E[cos(θ(k))] as follows:…”

Section: B Recursive Approachmentioning

confidence: 99%

“…Hence, according to (22), (24), and (25), we can describe the time evolution of the first order moment m x (k) in terms of the slack moment states m c θ and m s θ as follows:…”

Section: B Recursive Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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