scholarly journals Anisotropic GPMP2: A Fast Continuous-Time Gaussian Processes Based Motion Planner for Unmanned Surface Vehicles in Environments With Ocean Currents

2022 ◽  
pp. 1-18
Author(s):  
Jiawei Meng ◽  
Yuanchang Liu ◽  
Richard Bucknall ◽  
Weihong Guo ◽  
Ze Ji
Keyword(s):  
Gaussian Processes ◽  
Continuous Time ◽  
Ocean Currents ◽  
Unmanned Surface Vehicles

Maxima and sum for discrete and continuous time Gaussian processes

2015 ◽  
Vol 11 (1) ◽  
pp. 27-46 ◽  
Author(s):  
Yang Chen ◽  
Zhongquan Tan
Keyword(s):  
Gaussian Processes ◽  
Continuous Time

On the supremum distribution of integrated stationary Gaussian processes with negative linear drift

1999 ◽  
Vol 31 (01) ◽  
pp. 135-157 ◽  
Author(s):  
Jinwoo Choe ◽  
Ness B. Shroff
Keyword(s):  
Gaussian Processes ◽  
Extreme Value Theory ◽  
Continuous Time ◽  
Value Theory ◽  
Numerical Examples ◽  
Stationary Increments ◽  
Negative Drift ◽  
Stationary Gaussian Processes ◽  
Continuous Time Processes ◽  
Asymptotic Upper Bound

In this paper we study the supremum distribution of a class of Gaussian processes having stationary increments and negative drift using key results from Extreme Value Theory. We focus on deriving an asymptotic upper bound to the tail of the supremum distribution of such processes. Our bound is valid for both discrete- and continuous-time processes. We discuss the importance of the bound, its applicability to queueing problems, and show numerical examples to illustrate its performance.

scholarly journals Asymptotic distribution of sum and maximum for Gaussian processes

1999 ◽  
Vol 36 (4) ◽  
pp. 1031-1044 ◽  
Author(s):  
Hwai-Chung Ho ◽  
William P. McCormick
Keyword(s):  
Asymptotic Distribution ◽  
Gaussian Processes ◽  
Continuous Time ◽  
Joint Distribution ◽  
Covariance Function ◽  
Random Variables ◽  
Regularity Conditions ◽  
Gaussian Sequence ◽  
Stationary Gaussian Sequence ◽  
Standard Normal

Let {Xn, n ≥ 0} be a stationary Gaussian sequence of standard normal random variables with covariance function r(n) = EX0Xn. Let Under some mild regularity conditions on r(n) and the condition that r(n)lnn = o(1) or (r(n)lnn)−1 = O(1), the asymptotic distribution of is obtained. Continuous-time results are also presented as well as a tube formula tail area approximation to the joint distribution of the sum and maximum.

scholarly journals On Behrens–Fisher problem for continuous time Gaussian processes

2004 ◽  
Vol 389 ◽  
pp. 63-76 ◽  
Author(s):  
Pilar Ibarrola ◽  
Ricardo Vélez
Keyword(s):  
Gaussian Processes ◽  
Continuous Time

scholarly journals Exact overflow asymptotics for queues with many Gaussian inputs

2003 ◽  
Vol 40 (3) ◽  
pp. 704-720 ◽  
Author(s):  
Krzysztof Dębicki ◽  
Michel Mandjes
Keyword(s):  
Brownian Motion ◽  
Gaussian Processes ◽  
Continuous Time ◽  
Time Horizon ◽  
Exact Results ◽  
Service Capacity ◽  
Stationary Increments ◽  
Overflow Probability ◽  
Finite Time Horizon ◽  
Transient Probability

In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the probability that the buffer threshold is exceeded. We consider both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon. We give detailed results for the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.

scholarly journals Policy learning in continuous-time Markov decision processes using Gaussian Processes

2017 ◽  
Vol 116 ◽  
pp. 84-100 ◽  
Author(s):  
Ezio Bartocci ◽  
Luca Bortolussi ◽  
Tomáš Brázdil ◽  
Dimitrios Milios ◽  
Guido Sanguinetti
Keyword(s):  
Markov Decision Processes ◽  
Gaussian Processes ◽  
Continuous Time ◽  
Decision Processes ◽  
Policy Learning ◽  
Markov Decision

scholarly journals Asymptotic distribution of sum and maximum for Gaussian processes

1999 ◽  
Vol 36 (04) ◽  
pp. 1031-1044 ◽  
Author(s):  
Hwai-Chung Ho ◽  
William P. McCormick
Keyword(s):  
Asymptotic Distribution ◽  
Gaussian Processes ◽  
Continuous Time ◽  
Joint Distribution ◽  
Covariance Function ◽  
Random Variables ◽  
Regularity Conditions ◽  
Gaussian Sequence ◽  
Stationary Gaussian Sequence ◽  
Standard Normal

Let {X n , n ≥ 0} be a stationary Gaussian sequence of standard normal random variables with covariance function r(n) = E X 0 X n . Let Under some mild regularity conditions on r(n) and the condition that r(n)lnn = o(1) or (r(n)lnn)−1 = O(1), the asymptotic distribution of is obtained. Continuous-time results are also presented as well as a tube formula tail area approximation to the joint distribution of the sum and maximum.

scholarly journals Extended state observer-based integral line-of-sight guidance law for path following of underactuated unmanned surface vehicles with uncertainties and ocean currents

2021 ◽  
Vol 18 (3) ◽  
pp. 172988142110110
Author(s):  
Mingcong Li ◽  
Chen Guo ◽  
Haomiao Yu
Keyword(s):  
Sliding Mode ◽  
Path Following ◽  
State Observer ◽  
Extended State Observer ◽  
Ocean Currents ◽  
Line Of Sight ◽  
Extended State ◽  
Integral Sliding Mode ◽  
Unmanned Surface Vehicles ◽  
Guidance Law

This article focuses on the problem of path following for underactuated unmanned surface vehicles (USVs) considering model uncertainties and time-varying ocean currents. An extended state observer (ESO)-based integral line-of-sight (ILOS) with an integral sliding mode adaptive fuzzy control scheme is proposed as the main control framework. First, a novel ESO is employed to estimate the surge and sway velocities based on the kinetic model, which are difficult to measure directly. Then, the adaptive ILOS guidance law is proposed, in which the integral vector is incorporated into the adaptive method to estimate the current velocities. Meanwhile, an improved fuzzy algorithm is introduced to optimize the look-ahead distance. Second, the controller is extended to deal with the USV yaw and surge velocity signal tracking using the integral sliding mode technique. The uncertainties of the USV are approximated via the adaptive fuzzy method, and an auxiliary dynamic system is presented to solve the problem of actuator saturation. Then, it is proved that all of the error signals in the closed-loop control system are uniformly ultimately bounded. Finally, a comparative simulation substantiates the availability and superiority of the proposed method for ESO-based ILOS path following of USV.

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