Jorge Cortés

Professor





Time-varying optimization of LTI systems via projected primal-dual gradient flows
G. Bianchin, J. Cortés, J. I. Poveda, E. Dall'Anese
IEEE Transactions on Control of Network Systems, submitted


Abstract

This paper investigates the problem of regulating in real time a linear dynamical system to the solution trajectory of a time-varying constrained convex optimization problem. The proposed feedback controller is based on an adaptation of the saddle-flow dynamics, modified to take into account projections on constraint sets and output-feedback from the plant. We derive sufficient conditions on the tunable parameters of the controller (inherently related to the time-scale separation between plant and controller dynamics) to guarantee exponential and input-to-state stability of the closed-loop system. The analysis is tailored to the case of time-varying strongly convex cost functions and polytopic output constraints. The theoretical results are further validated in a ramp metering control problem in a network of traffic highways.

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Mechanical and Aerospace Engineering, University of California, San Diego
9500 Gilman Dr, La Jolla, California, 92093-0411

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cortes at ucsd.edu
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