Coalitional Zero-Sum Games for ${H_{\infty}}$ Leader-Following Consensus Control
This addresses robust control for multi-agent systems vulnerable to attacks, offering a distributed solution to a high-dimensional computational challenge, though it appears incremental as it builds on existing game-theoretic and H∞ methods.
The paper tackles the leader-following consensus problem in multi-agent systems under adversarial attacks by formulating it as a coalitional zero-sum game, resulting in a robust H∞ control law with decentralized computation and distributed implementation validated through simulations.
This paper investigates the leader-following consensus problem for a class of multi-agent systems subject to adversarial attack-like external inputs. To address this, we formulate the robust leader-following control problem as a global coalitional min-max zero-sum game using differential game theory. Specifically, the agents' control inputs form a coalition to minimize a global cost function, while the attacks form an opposing coalition to maximize it. Notably, when these external adversarial attacks manifest as disturbances, the designed game-theoretic control policy systematically yields a robust $H_\infty$ control law. Addressing this problem inherently requires solving a high-dimensional generalized algebraic Riccati equation (GARE), which poses significant challenges for distributed computation and controller implementation. To overcome these challenges, we propose a two-fold approach. First, a decentralized computational strategy is devised to decompose the high-dimensional GARE into multiple uniform, lower-dimensional GAREs. Second, a dynamic average consensus-based decoupling algorithm is developed to resolve the inherent coupling structure of the robust control law, thereby facilitating its distributed implementation. Finally, numerical simulations on the formation control of multi-vehicle systems with feedback-linearized dynamics are conducted to validate the effectiveness of the proposed algorithms.