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

• Published in: IEEE transactions on cybernetics Vol. 52; no. 3; pp. 1661 - 1670
• Main Authors: Long, Mingkang, Su, Housheng, Zeng, Zhigang
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.03.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">Q -learning (QL) algorithm; Algorithms; Directed graphs; Discrete time; Discrete time systems; Eigenvalues; Eigenvalues and eigenfunctions; Formulas (mathematics); global consensus; Heuristic algorithms; input saturation; Lower bounds; Machine learning; Multi-agent systems; Multiagent systems; Network topologies; Network topology; Output feedback; Protocols; Riccati equation; Saturation; System dynamics
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2020.2987385

This article proposes a <inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula>-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 <inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula>-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.