Output formation control and energy optimization strategies for singular swarm systems under budget constraint

This paper proposes an energy-optimized output formation control framework for singular swarm systems with dynamic communication topologies, addressing the critical challenge of coordinating energy-constrained multi-agent networks. By integrating constrained equivalent transformation and observability decomposition, we develop a dynamic output feedback protocol featuring a state-dependent formation mapping mechanism. The framework establishes sufficient conditions for leaderless time-varying output formation realization under topology switching, while providing explicit energy feasibility criteria and formation construction constraints. Crucially, a linear matrix inequality-based two-stage optimization method is introduced to determine gain matrices, and the explicit expression of the output formation center function is analytically determined to characterize the swarm’s global motion. Numerical simulation demonstrates the theoretical validity, in which an time-varying regular-octagon output formation along circular trajectories is achieved under the constraint of a given energy budget.