  In this paper, a distributed optimization problem is investigated via input
feedforward passivity. First, an input-feedforward-passivity-based
continuous-time distributed algorithm is proposed. It is shown that the error
system of the proposed algorithm can be decomposed into a group of individual
input feedforward passive (IFP) systems that interact with each other using
output feedback information. Based on this IFP framework, convergence
conditions of a suitable coupling gain are derived over weight-balanced and
uniformly jointly strongly connected (UJSC) topologies. It is also shown that
the IFP-based algorithm converges exponentially when the topology is strongly
connected. Second, a novel distributed derivative feedback algorithm is
proposed based on the passivation of IFP systems. While most works on directed
topologies require knowledge of eigenvalues of the graph Laplacian, the
derivative feedback algorithm is fully distributed, namely, it is robust
against randomly changing weight-balanced digraphs with any positive coupling
gain and without knowing any global information. Finally, numerical examples
are presented to illustrate the proposed distributed algorithms.
