Continuous-time distributed convex optimization on time-varying directed networks

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20161402196646
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(1) Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder; CO, United States; (2) Department of Mathematics and Statistics, Queen's University, Kingston; ON, Canada | 1600年 / Cybernet Systems; et al.; Kozo Keikaku Engineering (KKE); MathWorks; Mitsubishi Electric; Springer卷 / Institute of Electrical and Electronics Engineers Inc.期
关键词：
We introduce a general class of continuous-time distributed control systems; where the control input to the dynamics of each agent relies on an observer that estimates the average state. The dynamics of these observers are nonlinear; but the agents only need to have access to local information to implement them. We show that under a general condition on the structure of the underlying time-varying directed graphs; the difference of the agents' estimates and the true average is upper bounded. Using this result; we show that when we have a class P∗ weakly exponentially ergodic flow and the agent's objective functions are differentiable with bounded gradients; any trajectory of the proposed continuous-time dynamics is globally asymptotically convergent to a minimizer. Finally; we demonstrate that the class P∗ weakly exponentially ergodic flow property can be achieved by assuming that the sequence of Laplacians are measurable; cut-balanced; and has a minimum instantaneous flow. As a by-product; we show that the proposed continuous-time dynamics for distributed convex optimization is convergent on any sequence of time-varying strongly connected directed graph. © 2015 IEEE;
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