A local-minimization-free zero-gradient-sum algorithm for distributed optimization

• Published in: Automatica (Oxford) Vol. 157; p. 111247
• Main Authors: Guo, Ge, Zhang, Renyongkang, Zhou, Zeng-Di
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2023
• Subjects: Consensus; Distributed convex optimization; Fixed-time convergence; Multi-agent systems; Sliding mode control; Distributed convex optimization; Fixed-time convergence; Consensus; Sliding mode control; Multi-agent systems
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2023.111247

The classical zero-gradient-sum (ZGS) algorithms for distributed optimization require restrictions on the initial conditions or minimization of local cost functions. This paper proposes a sliding mode-based ZGS algorithm that is free of both initial condition restriction and local minimization. Specifically, a sliding manifold is involved to ensure that the sum of local gradients goes to zero within a fixed time under any initial value. Then, a distributed protocol based on the sliding mode is presented to achieve global optimal consensus in a fixed time. The result is also extended to obtain algorithms for accelerated optimization and disturbance rejection. The effectiveness of the results is verified by numerical simulations.