Resilient Time-Varying Formation Optimal Tracking for Heterogeneous Multi-Agent Systems With Coupled Constraints

Formation constrained optimal tracking problems for heterogeneous multi-agent systems under Byzantine attacks are studied. The objective of the honest agents, unaffected by Byzantine attacks, is to find optimal trajectories that minimize the cumulative local cost functions of all honest agents, while simultaneously satisfying the cumulative local inequality constraints and maintaining the formation configuration. A distributed resilient formation tracking controller utilizing preview control and primal-dual strategy is proposed without requiring each agent to know which agents are affected by Byzantine attacks. The performance of the proposed algorithm is analyzed in terms of the upper bounds of dynamic regret and constraint violations. Numerical simulations and experiments, involving one uncrewed aerial vehicle and four uncrewed ground vehicles, are performed to verify the effectiveness of the obtained results. Note to Practitioners—This paper is motivated by the formation tracking problem of multi-agent systems, which has potential applications in collaborative reconnaissance, logistics transportation, search and rescue. Existing formation tracking methods typically address the issues under the premise that formation references are known in advance to one or multiple leaders. However, in practical applications, multi-agent systems may be required to converge to a predefined formation configuration while ensuring globally optimal performance even under cyber attacks, given that each agent possesses a local cost function and local constraint functions that may vary in time. Therefore, this paper proposes a distributed resilient formation constrained optimal tracking protocol for heterogeneous multi-agent systems to withstand Byzantine attacks, utilizing neighboring predictable information. The performance is mathematically analyzed, and practical experiments involving one uncrewed aerial vehicle and four uncrewed ground vehicles yield promising results.