Distributed optimization of multi-agent systems with unknown frequency disturbances

The paper studies the dynamic optimization problem for continuous-time multi-agent systems in the presence of external disturbances. These disturbances consist of unknown constant signals and finite many sinusoidal signals with unknown frequencies, magnitudes and phases. Based on adaptive internal model, a distributed design is proposed to achieve the one-dimensional optimization along with the disturbance rejection under a connected interaction topology. A Lyapunov-based technique is utilized to prove the convergence of the multi-agent systems to the optimization point of the overall optimization problem.