Distributed Predefined-Time Optimization Algorithm: Dynamic Event-Triggered Control

In this article, two types of problems: 1) unconstrained and 2) constrained optimization are solved by developing a class of distributed predefined-time algorithms under dynamic event triggered (DET). First, under the zero-gradient-sum framework and DET-called one-to-one type, the distributed predefined-time algorithm, which contains two time-varying functions, is designed to deal with the unconstrained optimization problem in an initialization-free manner. Furthermore, it is proved in detail that the applied DET function can well exclude Zeno behavior through dynamic threshold variable. Second, the DET-based distributed predefined-time algorithm is applied to the optimization problem with supply–demand balance constraint by introducing an auxiliary variable, in which the algorithm can eliminate the disadvantage that the initial state must meet certain conditions, that is, the initial state can be selected arbitrarily. Different from many existing optimization algorithms, the developed two kinds of algorithms in this work exhibit excellent performance in terms of energy saving, convergence time, and initialization free. Finally, the effectiveness and superiority of the proposed algorithms are verified by three numerical examples.