2022/01/31 by Mohamed Maghenem, Maghenem, Mohamed, Alessandro Melis +3
Computer Science · Decision Sciences · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Probabilistic and Robust Engineering Design #math.OC
paper · pdf · doi:10.48550/arxiv.2201.13110
arxiv created 2022/01/31 · openalex publication_date 2022/01/31 · arxiv updated 2022/02/01 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
In this paper, we propose necessary and sufficient conditions for a scalar function to be nonincreasing along solutions to general differential inclusions with state constraints. The problem of determining if a function is nonincreasing appears in the study of stability and safety, typically using Lyapunov and barrier functions, respectively. The results in this paper present infinitesimal conditions that do not require any knowledge about the solutions to the system. Results under different regularity properties of the considered scalar function are provided. This includes when the scalar function is lower semicontinuous, locally Lipschitz and regular, or continuously differentiable.