Robust Adaptive Control for Discrete-Time Multi-Robot Systems with Actuator and Sensor Attacks

This paper addresses the challenges of achieving robust coordination in discrete-time multi-robot systems subject to uncertainties and Byzantine attacks affecting both actuator and sensor channels. Such adversarial disruptions degrade system performance by corrupting control inputs and state measurements, ultimately threatening stability and consensus in networked robotic systems. To overcome these limitations, a novel discrete-time adaptive control framework is proposed that ensures reliable tracking and stability under both uncoupled and coupled robot dynamics. The approach integrates a modified graph-theoretic structure with node-dependent weighting to capture heterogeneous robot interactions, while explicitly modeling attack effects within the system dynamics. An adaptive control law is developed using a nonlinear basis function approximation to handle unknown system uncertainties, along with a dynamic weight update mechanism that compensates for adversarial disturbances in real time. For the uncoupled case, stability is established through a composite Lyapunov function incorporating logarithmic and quadratic terms, guaranteeing boundedness of all closed-loop signals and asymptotic convergence of the tracking error. This framework is further extended to systems with coupled dynamics by introducing an auxiliary estimation mechanism to reconstruct unmeasurable interactions, leading to a unified adaptive controller capable of mitigating both internal uncertainties and external attacks. Rigorous Lyapunov-based analysis demonstrates that the proposed method ensures asymptotic tracking performance despite the presence of Byzantine disturbances. Numerical simulations validate the theoretical results, showing improved resilience, accurate trajectory tracking, and enhanced robustness compared to existing approaches.