Abstract
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 The gas dynamics in a single pipeline is modelled in this theoretical framework, and an algorithm withdrawn from the exposed procedure to calculate the equilibrium point is applied to a simple network example.
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Azevedo-Perdicoúlis, TP., Jank, G. Disturbance attenuation of linear quadratic OL-Nash games on repetitive processes with smoothing on the gas dynamics. Multidim Syst Sign Process 23, 131–153 (2012). https://doi.org/10.1007/s11045-010-0109-0
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DOI: https://doi.org/10.1007/s11045-010-0109-0