2021/10/13 by Nesir Hüseyin, Huseyin, Nesir, Anar Huseyin +3
Engineering · Mathematics · #93C23 #93C35 #Advanced Differential Equations and Dynamical Systems #Control and Dynamics of Mobile Robots #FOS: Mathematics #Fixed Point Theorems Analysis #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2110.06994
openalex publication_date 2021/10/13 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this paper an approximation of the set of multivariable and L2\nintegrable trajectories of the control system described by Urysohn type\nintegral equation is considered. It is assumed that the system is affine with\nrespect to the control vector. The admissible control functions are chosen from\nthe closed ball of the space L2, centered at the origin with radius \ρ.\nStep by step way, the set of admissible control functions is replaced by the\nset of controls, consisting of a finite number of piecewise-constant control\nfunctions. It is proved that under appropriate choosing of the discretization\nparameters, the set of trajectories generated by a finite number of\npiecewise-constant control functions is an internal approximation of the set of\ntrajectories.\n