Online Optimization of Switched LTI Systems Using Continuous-Time and Hybrid Accelerated Gradient Flows
Online Optimization of Switched LTI Systems Using Continuous-Time and Hybrid Accelerated Gradient Flows
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DOI：
10.1016/j.automatica.2022.110579
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发表时间：
2020-08
期刊：
影响因子：
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通讯作者：
G. Bianchin;J. Poveda;E. Dall’Anese
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文献类型：
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作者：
G. Bianchin;J. Poveda;E. Dall’Anese
本文研究了控制线性切换动力系统的反馈控制器设计问题。我们提出了两种类型的控制器：（i）一个连续的控制器的灵感来自在线梯度下降法，和（ii）一个混合控制器，可以被解释为在线版本的Nesterov的加速梯度法与状态变量的重新启动。通过设计，控制器连续地引导系统朝向时变最优平衡点，而不需要影响系统的外部干扰的知识。对于光滑且满足Polyak-Jasojasiewicz不等式的代价函数，我们证明了当系统和控制器的时间尺度充分分离且系统的切换信号平均变化缓慢时，在线梯度流控制器可确保一致全局指数稳定性.对于强凸的成本函数，我们证明了混合加速控制器可以优于连续梯度下降法。当代价函数不是强凸时，我们证明了混合加速方法保证了全局实用渐近稳定性。
This paper studies the design of feedback controllers to steer a switching linear dynamical system to the solution trajectory of a time-varying convex optimization problem. We propose two types of controllers: (i) a continuous controller inspired by the online gradient descent method, and (ii) a hybrid controller that can be interpreted as an online version of Nesterov’s accelerated gradient method with restarts of the state variables. By design, the controllers continuously steer the system toward a time-varying optimal equilibrium point without requiring knowledge of exogenous disturbances affecting the system. For cost functions that are smooth and satisfy the Polyak–Łojasiewicz inequality, we demonstrate that the online gradient-flow controller ensures uniform global exponential stability when the time scales of the system and controller are sufficiently separated and the switching signal of the system varies slowly on average. For cost functions that are strongly convex, we show that the hybrid accelerated controller can outperform the continuous gradient descent method. When the cost function is not strongly convex, we show that the hybrid accelerated method guarantees global practical asymptotic stability.