Necessary Optimality Conditions for Continuous-Discrete Systems with Instantaneous Switching of the Discrete Part

A continuous-discrete system in which the motion of the continuous part is described by differential equations and the behavior of the discrete part is described by recurrences is considered; instantaneous multiple switchings are allowed. Such systems are called hybrid, and they occupy an intermediate position between continuous-discrete systems with single switchings and logical-dynamical systems. Equations for the variations of functionals defined on the trajectories of such systems are derived. Necessary optimality conditions for the open-loop control are obtained. Application of the optimality conditions is illustrated by examples. DOI: 10.1134/S1064230711040058