论文标题
使用连续时和混合加速梯度流对开关LTI系统的在线优化。
Online Optimization of Switched LTI Systems Using Continuous-Time and Hybrid Accelerated Gradient Flows
论文作者
论文摘要
本文研究了反馈控制器的设计，以将切换的线性时间不变的动力系统转移到时变凸优化问题的解决方案轨迹。我们提出了两种类型的控制器：（i）受到在线梯度下降方法启发的连续控制器，以及（ii）一种混合控制器，可以将其解释为Nesterov加速梯度方法的在线版本，该方法具有重新启动状态变量。通过设计，控制器将系统不断地转向时变优化器，而无需了解影响系统的外源性干扰。对于光滑且满足Polyak-olojasiewicz不平等的成本函数，我们证明，当系统和控制器的时间尺度足够分离并且系统的开关信号的平均值缓慢而变化时，在线梯度流控制器可确保全局均匀指数稳定性。对于强烈凸的成本函数，我们表明混合加速控制器的表现优于连续梯度下降方法。当成本函数不是强烈凸出时，我们表明混合加速方法可以保证全球实践渐近稳定性。
This paper studies the design of feedback controllers to steer a switching linear time-invariant dynamical system towards 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 towards the time-varying optimizer 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 outperforms the continuous gradient descent method. When the cost function is not strongly convex, we show that the the hybrid accelerated method guarantees global practical asymptotic stability.
