Stochastic optimal control for nonlinear damped network dynamics

TL;DR

This paper formulates a stochastic optimal control problem for nonlinear damped network dynamics, providing explicit solutions and simulations to understand the impact of damping on network inflow optimization.

Contribution

It introduces a novel stochastic control framework for nonlinear damped network systems with explicit solutions and numerical analysis.

Findings

Optimal inflow solutions depend on damping characteristics

Numerical simulations demonstrate control effectiveness

Nonlinear damping significantly influences network performance

Abstract

We present a stochastic optimal control problem for a tree network. The dynamics of the network are governed by transport equations with a special emphasis on the non-linear damping function. Demand profiles at the network sinks are modelled by a stochastic differential equations. An explicit optimal inflow into the network is determined and numerical simulations are presented to show the effects for different choices of the non-linear damping.