Bipartite Output Formation Tracking Control for Discrete-Time Singular Heterogenous Multi-Agent Systems

Abstract

In this paper, the distributed bipartite output formation control problem of heterogeneous discrete-time singular multi-agent systems (MASs) is studied under the cooperative-competition network. Different from the classical formation control issue, the leader (also called exosystem) is also described by more general discrete-time singular dynamics. Based on the cooperative output regulation theory, the bipartite output formation with two opposing subgroups is realized by reconstructing bipartite tracking error and singular exosystem. To obtain the bipartite state of exosystem, a new exosystem observer associated with discrete-time singular algebraic Riccati equation (ARE) and signed directed topological matrix is designed. The observer coupling gains are introduced to enable the global error system to be included in the stability region of the unit circle. Then under the singular regulator equations and the separation principle, two classes of distributed observed-based controllers via state and output feedbacks are respectively presented for bipartite formation scenarios where the states of followers are known and unknown. Moreover, by redefining the expected relative dynamic positions, the proposed control strategies can be extended to achieve time-varying bipartite output formation. Finally, simulation results are given to verify the feasibility and effectiveness of the proposed algorithms. Note to Practitioners—Formation control of MASs plays a critical role in achieving effective coordination of distributed units, enhancing operational effectiveness, optimizing resource allocation, and improving overall production efficiency. This approach has broad applications across various industries, including transportation, energy, and both military and civilian applications, thereby fostering social and economic development. However, in practical applications such as autonomous aerial vehicle (AAV) clustering cooperative search and intelligent robot symmetrical formation, there exist several challenges: (1) the absence of stability analysis tools in discrete-time singular MASs; (2) the heterogeneity in dynamic characteristics; (3) the complex cooperative-competitive interactions among agents. This paper therefore studies the bipartite output formation control problem for heterogeneous discrete-time singular MASs. Specially, the autonomous exosystem with singular dynamics is seen as a leader and the corresponding new observer is introduced. By proposing distributed state and output feedback control protocols based on regulator equations, the followers maintain both fixed and time-varying relative positions with the exosystem. Furthermore, the proposed bipartite formation control strategies can be extended to address related bipartite consensus and formation problems.