Improved Results on Robust Stability of Multivariable Interval Control Systems

On Robust Stability of Multivariable Interval Control Systems

This paper studies robustness of MIMO control systems with parametric uncertainties, and establishes a lower dimensional robust stability criterion. For control systems with interval transfer matrices, we identify the minimal testing set whose stability can guarantee the stability of the entire uncertain set. Our results improve the results in the literature, and provide a constructive solution to the robustness of a family of MIMO control systems.

事件触发的牛顿极值寻找用于多变量优化

Event-Triggered Newton Extremum Seeking for Multivariable Optimization

本文提出一种事件触发的牛顿极值寻找方法，通过动态估计Hessian逆实现可控收敛速度，提升多变量优化效率。

On the pointwise iteration-complexity of a dynamic regularized ADMM with over-relaxation stepsize

In this paper, we extend the improved pointwise iteration-complexity result of a dynamic regularized alternating direction method of multipliers (ADMM) for a new stepsize domain. In this complexity analysis, the stepsize parameter can even be chosen in the interval $(0,2)$ instead of interval $(0,(1+\sqrt{5})/2)$. As usual, our analysis is established by interpreting this ADMM variant as an instance of a hybrid proximal extragradient framework applied to a specific monotone inclusion problem.

Improved automatic computation of Hessian matrix spectral bounds

This paper presents a fast and powerful method for the computation of eigenvalue bounds for Hessian matrices $\nabla^2 φ(x) $ of nonlinear functions $φ: U \subseteq R^n\rightarrow R$ on hyperrectangles $B \subset U$. The method is based on a recently proposed procedure for an efficient computation of spectral bounds using extended codelists. Both the previous approach and the one presented here substantially differ from established methods in that they do deliberately not use any interval matrices and thus result in a favorable numerical complexity of order $O(n)\,N(φ)$, where $N(φ)$ denotes t…

通过几何均值改进 Bernstein 基下的非负性检验

Improved Nonnegativity Testing in the Bernstein Basis via Geometric Means

本文提出一种基于相邻 Bernstein 系数几何均值的显式下界条件来检验多项式非负性，该方法比传统非负系数检验更宽松，并推广至矩阵值多项式，数值实验验证了其实际优势。