Differential graphical games for H∞ control of linear heterogeneous multiagent systems

• Published in: International journal of robust and nonlinear control Vol. 29; no. 10; pp. 2995 - 3013
• Main Authors: Adib Yaghmaie, Farnaz, Hengster Movric, Kristian, Lewis, Frank L., Su, Rong
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10-07-2019
• Subjects: Algorithms; Computer simulation; differential graphical games; Games; H-infinity control; H∞ control; linear heterogeneous multiagent systems; Mathematical analysis; Multiagent systems; Synchronism; Upper bounds
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.4538

Summary
Differential graphical games have been introduced in the literature to solve state synchronization problem for linear homogeneous agents. When the agents are heterogeneous, the previous notion of graphical games cannot be used anymore and a new definition is required. In this paper, we define a novel concept of differential graphical games for linear heterogeneous agents subject to external unmodeled disturbances, which contain the previously introduced graphical game for homogeneous agents as a special case. Using our new formulation, we can solve both the output regulation and H∞ output regulation problems. Our graphical game framework yields coupled Hamilton‐Jacobi‐Bellman equations, which are, in general, impossible to solve analytically. Therefore, we propose a new actor‐critic algorithm to solve these coupled equations numerically in real time. Moreover, we find an explicit upper bound for the overall
L2‐gain of the output synchronization error with respect to disturbance. We demonstrate our developments by a simulation example.