Finite-time distributed convex optimization for continuous-time multiagent systems with disturbance rejection

This paper presents continuous distributed algorithms to solve the finite-time distributed convex optimization problems of multiagent systems in the presence of disturbances. The objective is to design distributed algorithms such that a team of agents seeks to minimize the sum of local objective functions in a finite-time and robust manner. Specifically, a distributed optimization algorithm, combined with a continuous integral sliding-mode control scheme, is proposed to solve this finite-time optimization problem, while rejecting local disturbance signals. The developed algorithm is further applied to solve economic dispatch and resource allocation problems, and proven that under proposed schemes, the optimal solution can be achieved in finite time, while satisfying both global equality and local inequality constraints. Examples and numerical simulations are provided to show the effectiveness of the proposed methods.