Output-Feedback Global Consensus of Discrete-Time Multiagent Systems Subject to Input Saturation via Q-Learning Method

This article proposes a $Q$ -learning (QL)-based algorithm for global consensus of saturated discrete-time multiagent systems (DTMASs) via output feedback. According to the low-gain feedback (LGF) theory, control inputs of the saturated DTMASs can avoid the saturation by utilizing the control policies with LGF matrices, which were computed from the modified algebraic Riccati equation (MARE) by requiring the information of system dynamics in most previous works. However, in this article, we first find the lower bound on the real part of Laplacian matrices’ nonzero eigenvalues of directed network topologies. Then, we define a test control input and propose a $Q$ -function to derive a QL Bellman equation, which plays an essential part of the QL algorithm. Subsequently, different from the previous works, the output-feedback gain (OFG) matrix of this article can be obtained by limited iterations of the QL algorithm without requiring the information of agent dynamics and network topologies of the saturated DTMASs. Furthermore, the saturated DTMASs can achieve global consensus rather than the semiglobal consensus of the previous results. Finally, the effectiveness of the QL algorithm is confirmed via two simulations.