Q-learning algorithm in solving consensusability problem of discrete-time multi-agent systems

This paper solves the consensusability problem for the single-input discrete-time multi-agent system (MAS) over directed graphs by the linear quadratic regulator (LQR) design method. It is proved that the maximum consensus region is exactly the largest gain margin (GM) of LQR. Based on this, the necessary and sufficient condition on consensusability is derived by solving a standard algebraic Riccati equation (ARE). The developed framework permits that the consensusability problem can be solved when the agents' models are completely unavailable. Q-learning algorithm is employed to compute the maximum consensus region and implement the consensus protocol design. The algorithm runs only on a single agent rather than the intercommunicating MAS hence the unattainable initial admissible protocols are not required. A numerical example is given to illustrate the effectiveness of the developed methods. (c) 2021 Elsevier Ltd. All rights reserved.