Control Mechanisms for Mobile Devices

Peter J. Smith

doi:10.1109/TVT.2022.3229515

Control Mechanisms for Mobile Devices

2023-05-01

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Pawel A. Dmochowski *

DOI：10.1109/TVT.2022.3229515

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Abstract

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In this paper we consider control mechanisms for mobile devices in a stochastic environment. In particular, we consider a device in $n$-dimensional space subject to Brownian perturbations where a control mechanism moves the device towards its target location at a speed which is a function of its displacement. For this scenario, we construct stochastic differential equations for the mobility process and solve for the steady state probability density function of displacement. From this we are able to give general solutions to key metrics such as displacement outage (the long term probability of exceeding a given distance from the target), connectivity probability (derived from the SNR distribution in a Rayleigh channel with pathloss), the mean time at which the device first exceeds a given distance from the target, and the mean kinetic energy required by the control mechanism. We evaluate these metrics for important special cases of the control mechanism and also study the optimization problem of minimizing kinetic energy over the parameters of the control function.

Keywords:

Stochastic processes

Steady-state

Mathematical models

Perturbation methods

Adaptation models

Signal to noise ratio

Rayleigh channels

Brownian motion

connectivity

fokker-planck equation

kinetic energy

mobile device

stochastic differential equation

Control Mechanisms for Mobile Devices

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