Time-Varying Optimization of LTI Systems Via Projected Primal-Dual Gradient Flows
Time-Varying Optimization of LTI Systems Via Projected Primal-Dual Gradient Flows
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DOI：
10.1109/tcns.2021.3112762
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发表时间：
2021-01
影响因子：
4.2
通讯作者：
G. Bianchin;J. Cortés;J. Poveda;E. Dall’Anese
中科院分区：
文献类型：
--
作者：
G. Bianchin;J. Cortés;J. Poveda;E. Dall’Anese
本文研究了一个时变约束凸优化问题的解轨迹在任意时刻调节线性动力系统的问题。所提出的反馈控制器基于鞍流动力学的自适应，修改以考虑约束集上的投影和来自对象的输出反馈。我们得到了控制器参数可调的充分条件(与被控对象和控制器动态之间的时间尺度分离有关)，以保证闭环系统的指数输入-状态稳定性。该分析是针对时变的强凸代价函数和多面体输出约束的情况而进行的。理论结果在一个交通公路网的匝道控制问题中得到了进一步的验证。
This article investigates the problem of regulating, at every 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 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.