METHOD OF DISCONTINUOUS TIME CHANGE IN PROBLEMS OF CONTROL FOR IMPULSE AND DISCRETE-CONTINUOUS SYSTEMS

Optimization problems for dynamic systems with impulse and discrete-continuous properties are considered. The main feature of this class of systems is the discontinuous character of the trajectories. This makes the classical methods of analysis of optimal control and the calculus-of-variations problems developed for systems described by an ordinary differential equation nonapplicable. The transformation method developed in recent years and based on the use of a special time change permits one to reduce the initial problem with discontinuous trajectories to the traditional problem of optimal control for a system described by ordinary differential equations with bounded controls. In this paper, aspects of the application of the discontinuous-time-change method are considered: the representations for discontinuous solutions, the proof of solution existence theorems for optimal control problems, and the derivation of optimality conditions.