Disturbance attenuation of linear quadratic OL-Nash games on repetitive processes with smoothing on the gas dynamics

This article presents necessary and sufficient results for existence and uniqueness of an equilibrium of a N -player disturbed Nash game with quadratic performance criteria and an affine repetitive process with smoothing describing the two dimensional 2D-system dynamics, under open loop information pattern. The gas dynamics in a single pipeline is modelled in this theoretical framework, and an algorithm withdrawn from the exposed procedure to calculate the equilibrium point is applied to a simple network example.