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Multi-agent networked control systems (NCSs) are often subject to modeluncertainty and are limited by large communication cost, associated withfeedback of data between the system nodes. To provide robustness against modeluncertainty and to reduce the communication cost, this paper investigates themixed $H_2/H_{\infty}$ control problem for NCS under the sparsity constraint.First, proximal alternating linearized minimization (PALM) is employed to solvethe centralized social optimization where the agents have the same optimizationobjective. Next, we investigate a sparsity-constrained noncooperative game,which accommodates different control-performance criteria of different agents,and propose a best-response dynamics algorithm based on PALM that converges toan approximate Generalized Nash Equilibrium (GNE) of this game. A special caseof this game, where the agents have the same $H_2$ objective, produces apartially-distributed social optimization solution. We validate the proposedalgorithms using a network with unstable node dynamics and demonstrate thesuperiority of the proposed PALM-based method to a previously investigatedsparsity-constrained mixed $H_2/H_{\infty}$ controller.

Game-Theoretic Mixed $H_2/H_{\infty}$ Control with Sparsity Constraint for Multi-agent Networked Control Systems