Sufficient conditions for forward invariance and contractivity in hybrid inclusions using barrier functions

由极大单调算子控制的微分包含的定位定理

Locating Theorems of Differential Inclusions Governed by Maximally Monotone Operators

针对极大单调算子控制的微分包含的渐近行为研究中LaSalle不变性原理失效的问题，提出改进版不变性原理与扩展方法，借助非光滑Lyapunov对型函数实现ω-极限集的更精确定位。

Wasserstein空间中连续包含下真集的生存性与不变性

On the Viability and Invariance of Proper Sets under Continuity Inclusions in Wasserstein Spaces

本文研究Wasserstein空间中右端项可能时变不连续的状态约束连续包含，通过分析可达集的无穷小行为，建立约束集生存性与不变性的充要几何条件。

On the Strong Invariance Property for Non-Lipschitz Dynamics

We provide a new sufficient condition for strong invariance for differential inclusions, under very general conditions on the dynamics, in terms of a Hamiltonian inequality. In lieu of the usual Lipschitzness assumption on the multifunction, we assume a feedback realization condition that can in particular be satisfied for measurable dynamics that are neither upper nor lower semicontinuous.

Nagumo型特征的受约束系统的前向不变性

Nagumo Theorem For Constrained Differential Inclusions: Transversal Intersection and Set-Map Regularity

本文提出了一种Nagumo型条件，用于受约束系统的前向不变性分析，并通过示例说明其重要性。

Strong Invariance Using Control Barrier Functions: A Clarke Tangent Cone Approach

Many control applications require that a system be constrained to a particular set of states, often termed as safe set. A practical and flexible method for rendering safe sets forward-invariant involves computing control input using Control Barrier Functions and Quadratic Programming methods. Many prior results however require the resulting control input to be continuous, which requires strong assumptions or can be difficult to demonstrate theoretically. In this paper we use differential inclusion methods to show that simultaneously rendering multiple sets invariant can be accomplished using a…

神经网络控制系统中的前向不变性

Forward Invariance in Neural Network Controlled Systems

本文提出一种结合区间分析与单调系统理论的框架，用于验证和搜索神经网络控制器下非线性系统的前向不变集，并在8维领导者-跟随者系统上验证了其有效性。