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arXiv · 2101.01799

Time-Varying Optimization of LTI Systems via Projected Primal-Dual Gradient Flows

Gianluca Bianchin·Jorge Cortes·Jorge I. Poveda·Emiliano Dall'Anese
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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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Gianluca Bianchin, Jorge Cortes, Jorge I. Poveda, Emiliano Dall'Anese. 2021-01-05. Time-Varying Optimization of LTI Systems via Projected Primal-Dual Gradient Flows. https://arxiv.org/abs/2101.01799

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