Matching, linear systems, and the ball and beam

Matching control laws for a ball and beam system

This note describes a method for generating an infinite-dimensional family of nonlinear control laws for underactuated systems. For a ball and beam system, the entire family is found explicitly.

二次函数优化的重球方法渐近最优性的鲁棒控制方法

A Robust Control Approach to Asymptotic Optimality of the Heavy Ball Method for Optimization of Quadratic Functions

本文利用线性不确定反馈控制系统的鲁棒增益裕度，证明了重球方法在有限维二次函数优化中具有可证明的最坏情形渐近最优性。

Acceleration with a Ball Optimization Oracle

Consider an oracle which takes a point $x$ and returns the minimizer of a convex function $f$ in an $\ell_2$ ball of radius $r$ around $x$. It is straightforward to show that roughly $r^{-1}\log\frac{1}ε$ calls to the oracle suffice to find an $ε$-approximate minimizer of $f$ in an $\ell_2$ unit ball. Perhaps surprisingly, this is not optimal: we design an accelerated algorithm which attains an $ε$-approximate minimizer with roughly $r^{-2/3} \log \frac{1}ε$ oracle queries, and give a matching lower bound. Further, we implement ball optimization oracles for functions with locally stable Hessia…