Adaptive distributed optimization algorithms for Euler–Lagrange systems

• Published in: Automatica (Oxford) Vol. 119; p. 109060
• Main Authors: Zou, Yao, Meng, Ziyang, Hong, Yiguang
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2020
• Subjects: Distributed algorithm; Distributed optimization; Euler–Lagrange system; Gain adaptation; Distributed optimization; Gain adaptation; Euler–Lagrange system; Distributed algorithm
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2020.109060

This paper investigates the distributed optimization problem of a group of Euler–Lagrange (EL) systems subject to unavailable inertial parameters. A local cost function is assigned to each agent and the sum of all the local cost functions is considered as the global one. Under widely used assumptions, an adaptive distributed algorithm is proposed such that all the agent states converge to the specified point minimizing the global cost function in a cooperative manner. In particular, by introducing a novel auxiliary system with adaptive gains, the proposed optimization algorithm is privacy-preserving such that no actual state of any agent is necessary for other agents. Moreover, the proposed optimization algorithm is fully distributed in the sense that the optimization objective is achieved without knowledge of global graph information, explicit global cost function as well as strongly convex and Lipschitz constants associated with all local cost functions. Numerical simulations are illustrated to validate the theoretical results.