Distributed finite-time optimization of second-order multiagent systems with unknown velocities and disturbances

In this article, the distributed finite-time optimization problem is investigated for second-order multiagent systems with unknown velocities, disturbances, and quadratic local cost functions. To solve this problem, by combining finite-time observers (FTOs), the homogeneous systems theory, and distributed finite-time estimator techniques together, an output feedback-based feedforward-feedback composite distributed control scheme is proposed. Specifically, the control scheme consists of three parts. First, some FTOs are developed for the agents to estimate their unknown velocities and the disturbances together. Second, based on the velocity and disturbance estimates, the homogeneous system theory, and some global information on all the local cost functions' gradients, Hessian matrices, and the velocity estimates, a kind of centralized finite-time optimization controllers is designed. Third, by designing some distributed finite-time estimators and using their estimates to replace the global terms employed in the centralized optimization controllers, the distributed finite-time optimization controllers are derived. These controllers achieve the distributed finite-time optimization goal. Simulations illustrate the effectiveness and superiority of the proposed control scheme.