Distributed Optimal Output Consensus Control of Heterogeneous Multi-Agent Systems With Safety Constraints

This paper investigates the distributed optimal output consensus control for heterogeneous multi-agent systems (MASs) under the constraint that agents' outputs must remain within a prescribed safe set. A distributed two-layer optimal safe consensus protocol is proposed using the extended projection method, which simultaneously ensures safety requirements and optimal output consensus. Specifically, we construct a distributed projection optimization algorithm with an expanding constraint set in the decision-making layer, while proposing a reference-tracking safety controller to ensure that each agent's output remains within a shrinking safety set in the control layer. We also establish the convergence and safety analysis of the closed-loop system using the small-gain theorem and time-varying control barrier function (CBF) theory, respectively. By these approaches, we reach exactly an optimal solution, where the optimization part may drive the outputs of the system to the boundary of the constraints, and the safety part can avoid approaching the boundary.