Necessary Optimality Conditions for Hybrid System of Variable Dimension with Intermediate Constraints

Abstract

We consider an optimal control problem for a hybrid system. The continuous motion of the system alternates with discrete variations (switchings) at which the dimension of the state space changes. The switching times are found by minimizing a functional taking into account the cost of switchings. We obtain necessary optimality conditions for such systems under additional constraints at the switching times. The application of optimality conditions is illustrated by an academic example. Bibliography: 22 titles.