1,633 research outputs found
Semi-Global Exponential Stability of Augmented Primal-Dual Gradient Dynamics for Constrained Convex Optimization
Primal-dual gradient dynamics that find saddle points of a Lagrangian have
been widely employed for handling constrained optimization problems. Building
on existing methods, we extend the augmented primal-dual gradient dynamics
(Aug-PDGD) to incorporate general convex and nonlinear inequality constraints,
and we establish its semi-global exponential stability when the objective
function is strongly convex. We also provide an example of a strongly convex
quadratic program of which the Aug-PDGD fails to achieve global exponential
stability. Numerical simulation also suggests that the exponential convergence
rate could depend on the initial distance to the KKT point
Optimal Distributed Feedback Voltage Control under Limited Reactive Power
In this paper, we propose a distributed voltage control in power distribution
networks through reactive power compensation. The proposed control can (i)
operate in a distributed fashion where each bus makes its decision based on
local voltage measurements and communication with neighboring buses, (ii)
always satisfy the reactive power capacity constraint, (iii) drive the voltage
magnitude into an acceptable range, and (iv) minimize an operational cost. We
also perform various numerical case studies to demonstrate the effectiveness
and robustness of the controller using the nonlinear power flow model.Comment: 32 pages, 10 figures; submitted to TP
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