Distributed Optimal Fault Estimation and Fault-Tolerant Control for Interconnected Systems: A Stackelberg Differential Graphical Game Approach

This article addresses the distributed optimal fault estimation (FE) and fault-tolerant control (FTC) issues under the bidirectional interaction between a possibly faulty interconnected system and its associated diagnostic interconnected observer. The proposed methodology is based on a framework, named
Stackelberg differential graphical game
, in which the interconnected observer and its corresponding interconnected system are formulated as two graphical games, and they, respectively, play the role of the follower and leader to make
sequential
decisions of the FE and the FTC. Such a framework allows us to fully reveal the property of the bidirectional interaction, based on which a distributed optimal FE and FTC scheme is developed. Moreover, a new concept named
interactive Stackelberg equilibrium
is proposed, where, to reach this equilibrium, an auxiliary controller is suitably designed for each subobserver. In this way, this auxiliary controller can cooperate with other auxiliary controllers of subobservers, and noncooperate with controllers of subsystems, which helps to achieve the distributed optimal FE and FTC goals.