Distributed Continuous-Time Optimization of Second-Order Multiagent Systems With Nonconvex Input Constraints

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 51; no. 10; pp. 6404 - 6413
• Main Authors: Mo, Lipo, Yu, Yongguang, Zhao, Lin, Cao, Xianbing
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Agreement; Algorithms; continuous-time algorithm; Convergence; Distributed algorithms; distributed optimization; Force; Liapunov functions; Linear programming; Lyapunov methods; Multi-agent systems; Multiagent systems; nonconvex constraints; Nonlinear systems; nonuniform gains; Operators (mathematics); Optimization; Scaling factors; second-order systems
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2019.2961421

This article discusses the distributed continuous-time optimization problem (DCTOP) of second-order multiagent systems (SOMASs). It is assumed that the inputs are required to be in some nonconvex sets, the team objective function (TOF) is a combination of general differentiable convex functions, and each agent can only obtain the information of one local objective function. Based on the neighbors' information, a new distributed continuous-time optimization algorithm (DCTOA) is first proposed for each agent, where its gradient gains are nonuniform. By introducing a scaling factor and a model transformation, the corresponding system is changed into a time-varying nonlinear system which does not contain constraint operator in form. Then, it is proven that all agents' states could reach an agreement and the TOF could be minimized by constructing some new Lyapunov functions. Finally, the effectiveness of the algorithm is shown by simulation results.