4 research outputs found
Online Optimization as a Feedback Controller: Stability and Tracking
This paper develops and analyzes feedback-based online optimization methods
to regulate the output of a linear time-invariant (LTI) dynamical system to the
optimal solution of a time-varying convex optimization problem. The design of
the algorithm is based on continuous-time primal-dual dynamics, properly
modified to incorporate feedback from the LTI dynamical system, applied to a
proximal augmented Lagrangian function. The resultant closed-loop algorithm
tracks the solution of the time-varying optimization problem without requiring
knowledge of (time-varying) disturbances in the dynamical system. The analysis
leverages integral quadratic constraints to provide linear matrix inequality
(LMI) conditions that guarantee global exponential stability and bounded
tracking error. Analytical results show that, under a sufficient time-scale
separation between the dynamics of the LTI dynamical system and the algorithm,
the LMI conditions can be always satisfied. The paper further proposes a
modified algorithm that can track an approximate solution trajectory of the
constrained optimization problem under less restrictive assumptions. As an
illustrative example, the proposed algorithms are showcased for power
transmission systems, to compress the time scales between secondary and
tertiary control, and allow to simultaneously power re-balancing and tracking
of DC optimal power flow points