论文标题
关于投影轨迹的不同性和非凸反鸣式梯度流的稳健收敛性
On the Differentiability of Projected Trajectories and the Robust Convergence of Non-convex Anti-Windup Gradient Flows
论文作者
论文摘要
本文涉及一类新的不连续的动力系统，以进行约束优化。这些动态特别适合通过物理系统解决闭环中的非线性非凸问题。最近已经提出了使用反馈控制器模拟优化算法的这种方法，用于对电力系统和其他基础架构的自主优化。在本文中，我们考虑了反馈梯度流，这些流动借助反打印机控制来实施限制。我们证明了“投影”轨迹到一阶最佳点的半全球收敛，即从可行的集合上的点投影获得的轨迹的轨迹。在此过程中，我们建立了非凸照，预先定型集的投影图的定向衍生物的属性。
This paper concerns a new class of discontinuous dynamical systems for constrained optimization. These dynamics are particularly suited to solve nonlinear, non-convex problems in closed-loop with a physical system. Such approaches using feedback controllers that emulate optimization algorithms have recently been proposed for the autonomous optimization of power systems and other infrastructures. In this paper, we consider feedback gradient flows that exploit physical input saturation with the help of anti-windup control to enforce constraints. We prove semi-global convergence of "projected" trajectories to first-order optimal points, i.e., of the trajectories obtained from a pointwise projection onto the feasible set. In the process, we establish properties of the directional derivative of the projection map for non-convex, prox-regular sets.
