A distributed fixed-time optimization algorithm for multi-agent systems

• Published in: Automatica (Oxford) Vol. 122; p. 109289
• Main Authors: Wang, Xiangyu, Wang, Guodong, Li, Shihua
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.12.2020
• Subjects: Convex optimization; Distributed optimization; Fixed-time stability; Multi-agent systems; Fixed-time stability; Distributed optimization; Convex optimization; Multi-agent systems
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2020.109289

In this paper, the distributed fixed-time optimization problem is investigated for first-order multi-agent systems with strongly convex local cost functions. To solve this problem, a two-piece distributed fixed-time optimization algorithm is proposed. In the first piece, some local optimization controllers are designed for the agents such that each agent converges to its local cost function’s minimizer in the unified fixed time under an arbitrary initial state. In the second piece, based on state information transmissions between neighboring agents and the local cost functions’ Hessian matrices, some distributed optimization controllers are developed for the agents such that they converge to the global cost function’s minimizer together in fixed time. Under the proposed algorithm, all the agents reach the global cost function’s minimizer in fixed time. Moreover, this fixed settling time is independent of the agents’ initial states and it can be predetermined according to the task demands. Numerical simulations demonstrate the effectiveness and advantages of the proposed distributed fixed-time optimization algorithm.