Distributed Resilient Time-Varying Affine Formation Optimal Tracking for Multiagent Systems Against Byzantine Attacks

Discrete-time affine formation optimal tracking problems for multi-agent systems with time-varying objective functions and coupled constraints under Byzantine attacks are investigated. The goal of each honest agent at each time step is to track the optimal trajectory by minimizing the sum of all honest agents' local objective functions from the initial time to the present, while adhering to coupled inequality constraints, affine formation constraints and set constraints. A distributed primal-dual protocol is constructed first to address the challenges posed by time variations and coupled constraints on formation trajectories. Further, the proposed protocol is combined with an aggregation rule to ensure resilience against Byzantine attacks. Sufficient conditions are established to guarantee sublinear growth rates of dynamic regrets for both proposed protocols. Numerical simulations reinforce the theoretical analysis.