Passivity-Based Distributed Optimization With Communication Delays Using PI Consensus Algorithm

Abstract

In this paper, we address a class of distributed optimization problems in the presence of inter-agent communication delays based on passivity. We first focus on unconstrained distributed optimization and provide a passivity-based perspective for distributed optimization algorithms. This perspective allows us to handle communication delays while using scattering transformation. Moreover, we extend the results to constrained distributed optimization, where it is shown that the problem is solved by just adding one more feedback loop of a passive system to the solution of the unconstrained ones. We also show that delays can be incorporated in the same way as the unconstrained problems. Finally, the algorithm is applied to a visual human localization problem using a pedestrian detection algorithm.

Distributed continuous‐time algorithm for a general nonsmooth monotropic optimization problem

“…Note that (19) is equivalent to (16), and (21) is the same as (18). Furthermore, it is easy to verify that (20)…”

“…which further amounts to (17), that is, (20) and (17) are equivalent. Summarizing the above analysis gives the above assertion.…”

“…To date, although a wide spectrum of results have been reported for discrete-time networks with various scenarios in the literature, ranging from distributed optimization problems in the absence of constraints to those subject to constraints, [1][2][3][4][5] continuous-time algorithms have attracted an increasing interest in recent years mostly due to the fact that a lot of physical systems operate in a continuum domain, such as the current flow in smart grid. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] For instance, distributed convex optimization problems have been studied in the work of Yang et al 17 subject to local feasible constraints, local inequality and equality constraints, where a proportional-integral continuous-time algorithm has been designed with output information exchange.…”

Smooth Dynamics for Distributed Constrained Optimization With Heterogeneous Delays

“…Distributed optimization in the presence of communication delays has been widely studied in recent years [3], [4], [9]. The work [9] addresses time-varying delays, but it only considers an identical delay known in advance for all communication channels and does not treat inequality constraints, which simplifies convergence analysis.…”

“…The work [9] addresses time-varying delays, but it only considers an identical delay known in advance for all communication channels and does not treat inequality constraints, which simplifies convergence analysis. The problem under unknown and heterogeneous communication delays is addressed via passivity techniques in [3], [4]. However, to ensure optimality in the presence of inequality constraints, delays are assumed to be homogeneous and an additional assumption on the graph is needed in [3], which is not always easy to verify in large scale networks.…”