Methods for solving optimal control problems for continuous-discrete systems and their relationship with the hybrid maximum principle

The particular class of continuous-discrete systems is considered in this paper, for this systems the law of switching between continuous subsystems is specified in the form of controlled differential equations, and points of “jumps” are not fixed. In this case we can consider discrete variable as a control (then discrete sequence is a mixed constraint) and a state variable. We consider the transition to other formulation of the problem and communications between algorithms and known necessary optimality conditions.