Construction of the Reachable Set for a Two-Dimensional Bilinear Impulsive Control System

Abstract

This paper deals with a problem of construction of the reachable set for an impulsive control system with trajectories of bounded variation and impulsive controls (regular vector measures). The considered control system has a bilinear structure relative to the control variable. A method for constructing of the boundary of the reachable set is proposed. This method is based on using of special impulsive optimal control problems and Lyapunov type functions. These functions are strongly monotone relative to the impulsive control system. Presented results are illustrated by a numerical example. An algorithm of numerical approximation of reachable sets for nonlinear impulsive control systems is discussed. This algorithm is realized in the Scientific Python environment.

Keywords

• measure-driven impulsive control system
• trajectories of bounded variation
• reachable set
• monotone of Lyapunov type functions
• numerical methods