Distributed Asynchronous Discrete-Time Feedback Optimization

In this article, we present an algorithm that drives the outputs of a network of agents to jointly track the solutions of time-varying optimization problems in a way that is robust to asynchrony in the agents' operations. We consider three operations that can be asynchronous: (1) computations of control inputs, (2) measurements of network outputs, and (3) communications of agents' inputs and outputs. We first show that our algorithm converges to the solution of a time-invariant feedback optimization problem in linear time. Next, we show that our algorithm drives outputs to track the solution of time-varying feedback optimization problems within a bounded error dependent upon the movement of the minimizers and degree of asynchrony in a way that we make precise. These convergence results are extended to quantify agents' asymptotic behavior as the length of their time horizon approaches infinity. Then, to ensure satisfactory network performance, we specify the timing of agents' operations relative to changes in the objective function that ensure a desired error bound. Numerical experiments confirm these developments and show the success of our distributed feedback optimization algorithm under asynchrony.