Cooperative linear quadratic differential games for uncertain systems with conservative players

Abstract

This paper investigates cooperative linear quadratic differential games for uncertain dynamic systems with conservative players, who attempt to optimize the worst‐case outcomes with limited a priori knowledge about the uncertainties. Without properly designed control strategies, the uncertainties could cause significant impacts on the performance indexes of players and spoil the cooperation among players. In this paper, compensation‐based robust control techniques are applied to handle the uncertainties, including parameter perturbations and external disturbances, by transforming the impacts of the uncertainties into a more tractable form. Subsequently, using Vickrey–Clarke–Groves principles, an auction‐based control allocation mechanism is designed to incentivize the players to cooperatively implement the compensation. With the methods proposed, the worst‐case performance indexes of players can be improved, and the cooperation among players is maintained in the uncertain system. Numerical examples demonstrate the effectiveness of the proposed methods.