Distributed Strategies for Constrained Nonsmooth Resource Allocation Problems With Autonomous Second-Order Agents

• Published in: IEEE transactions on network science and engineering Vol. 11; no. 3; pp. 2927 - 2936
• Main Authors: Deng, Zhenhua, Chen, Tao
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.05.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Constraints; Convergence; Couplings; Cyber-physical systems; distributed strategies; Game theory; Inequality; Manganese; Multi-agent systems; Nonlinear dynamics; nonsmooth optimization; Optimization; Resource allocation; Resource management; Second-order multi-agent systems; State feedback; Wireless networks
• ISSN: 2327-4697; 2334-329X
• DOI: 10.1109/TNSE.2024.3354885

In this paper, constrained nonsmooth resource allocation problems (RAPs) of autonomous agents are investigated. All agents are subject to inequality network resource constraints and local constraints, and each agent has a nonsmooth private payoff function in our problem. Furthermore, in contrast to the well-known RAPs, all agents have second-order linear/nonlinear (SOL/SON) dynamics, which means that there is no way to directly control the actions of agents in our problem. To the best of our knowledge, there are no results on nonsmooth RAPs of autonomous SOL/SON agents, let alone involving inequality constraints. Existing related distributed strategies cannot solve our problem, due to the presence of SOL/SON dynamics, nonsmooth payoff functions, and/or inequality constraints. We put forward two fully distributed subgradient-based strategies on the basis of state feedback and primal-dual methods for SOL and SON agents, respectively. By our strategies, all agents rely only on local information to update their control inputs, compared with existing RAPs with physical systems. We analyze the two strategies using nonsmooth analysis and the set-valued Lasalle invariance principle. Under our strategies, the SOL/SON agents globally converge to the optimal allocation (OA). Finally, numerical simulations demonstrate our strategies.