Almost sure exponential stability of stochastic fluid networks with nonlinear control

Due to the objective of controlling fluid flows, fluid networks are high-order nonlinear stochastic systems in essential. Taking the nonlinearities in pressure drop of fan branch, measurement error of inertia coefficients, and random factors into consideration, this paper presents a stochastic fluid networks model described by Ito stochastic differential equations. As drift term of the stochastic fluid networks does not satisfy the linear growth condition, the almost sure exponential stability cannot get from the moment exponential stability. We directly investigate the almost sure exponential stability of the tracking and regulation problems for fluid networks under decentralised and adaptive control. It shows that the fluid flows in all branches can reach their reference values if we set controller only in links of the networks. We illustrate the results with two examples.