2012/10/16 by M. Soledad Aronna, Maria Soledad Aronna, Aronna, Maria Soledad +2
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis #math.OC
paper · pdf · doi:10.48550/arxiv.1210.4532
arxiv created 2012/10/16 · openalex publication_date 2012/10/16 · arxiv updated 2012/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we study control problems with systems that are governed by ordinary differential equations whose vector fields depend linearly in the time derivatives of some components of the control. The remaining components are considered as classical controls. This kind of system is called `impulsive system'. We assume that the vector fields multiplying the derivatives of each component of the control are commutative. We derive new necessary conditions in terms of the adjoint state and the Lie brackets of the data functions.