Distributed H∞ Time-Varying Formation Tracking of 3-DOF USVs: A Singular Control Approach

This paper investigates distributed $H_\infty$ time-varying formation tracking of three-degree-of-freedom unmanned surface vehicles within a singular control framework under jointly connected switching topologies. A distributed integral sliding-mode protocol is constructed, together with a nonlinear disturbance observer, to handle time-varying external perturbations whose residual is $L_2$-integrable. On the sliding surface, an energy-based $H_\infty$ criterion is imposed to restrict the closed-loop gain from residual disturbances to formation-tracking errors. By employing Laplacian decomposition under joint connectivity and a Cauchy-type convergence argument, sufficient LMI conditions are established to ensure admissibility (regularity, impulse-freeness, and asymptotic stability) and the feasibility of the prescribed time-varying formation tracking task. The resulting distributed gains are explicitly computable and require only local relative-state information. Numerical simulations are provided to demonstrate the effectiveness of the proposed singular control approach.