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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 9 (1) (2022), 474-486
2023 IEEE Transactions on Control of Network Systems Outstanding Paper Award

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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