Distributed Algorithm Design for Nonsmooth and Nonlinear Resource Allocation Problems of Autonomous High-Order Agents and Its Application to Smart Grids

This article investigates nonsmooth resource allocation problems (RAPs) of autonomous agents, in which the agents have high-order dynamics. Moreover, each agent has a nondifferentiable and private cost function, and the decisions of all agents are restricted by nonlinear network resource constraints and local nonlinear constraints. To the best of our knowledge, there have been no nonsmooth RAPs of high-order agents emerging, much less with nonlinear constraints. Besides, owing to the high-order dynamics, the nonsmooth cost functions and/or the nonlinear constraints, existing distributed algorithms for RAPs are infeasible for our problem. For the purpose of controlling high-order agents to execute nonsmooth resource allocation tasks autonomously, we propose a fully distributed algorithm by means of primal-dual methods and state feedback. In the fully distributed approach, all agents update their control inputs only on the basis of their own and neighbors’ information. Further, we prove the global convergence of the algorithm via nonsmooth analysis and set-valued Lasalle invariance principle. Lastly, we apply the proposed algorithm to the economic dispatch problems (EDPs) of smart grids. By means of our algorithm, the turbine generators can autonomously perform the economic dispatch tasks.