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

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 sufficiently weak. It is then demonstrated in simulation that, by reducing the number of distinct dither signals, the proposed scheme is able to more quickly seek the Nash equilibrium.