Non-local stability of a Nash equilibrium seeking scheme with dither re-use

Abstract

This paper considers a simple Nash-equilibrium-seeking (NES) scheme acting on a family of plants that can be represented as non-cooperative games. Specifically, the family of plants under investigation have a number of inputs, each of which can be associated with a measured cost. The NES scheme consists of a number of decentralised extremum-seeking (ES) agents which, without requiring knowledge of the underlying plant dynamics, control each input in order to minimise its associated steady-state cost. A non-local stability result for the NES scheme is provided which allows two agents to use the same dither signal if the effect of each agent on the other's steady-state cost function is suffici..