PID-Inspired Continuous-Time Distributed Optimization

This paper proposes two novel distributed continuous-time algorithms inspired by PID control to solve distributed optimization problems. The algorithms are referred to as first-order and second-order, respectively, depend on the intrinsic dynamics of the agents in the network. Sufficient conditions are derived so that both algorithms converge exponentially over undirected connected graphs. Finally, numerical simulations illustrate the effectiveness and efficiency of the proposed algorithms.