Distributed Privacy-Preserving Time-Varying Output Formation Optimal Tracking for Heterogeneous Multi-Agent Systems With External Disturbances

Privacy-preserving time-varying output formation optimal tracking problems for heterogeneous discrete-time linear multi-agent systems with external disturbances are studied. Agents aim to calculate and track the optimal formation reference that minimizes the sum of local objective functions with a privacy-preserving mechanism while maintaining a predefined time-varying formation. A time-varying output formation optimal tracking protocol over time-varying topologies is constructed by utilizing differential privacy mechanism, stochastic subgradient method and sliding mode idea. Sufficient conditions for multi-agent systems to achieve differential-private output formation optimal tracking are given based on discrete-time Lyapunov theory and convex optimization theory, where the upper bound of the expected regret with respect to the tracking error is also provided. The effectiveness of the theoretical results is verified by a numerical simulation.