Synthesis of Optimal Hybrid Systems for Multipurpose Time-Optimal Operation

Abstract

We consider a time-optimal control problem for a hybrid system of variable dimension. Continuous motion of the system alternates with discrete variations (switchings) at which the dimension of the state space changes. The change of the space of states of the system can occur if the number of control objects changes, which is typical, for example, for the control problems for groups of a variable number of aircrafts. We obtain sufficient conditions for the time-optimal achievement of all purposes by a group of control objects. The application of optimality conditions is demonstrated by academic examples. Bibliography: 18 titles. Illustrations: 3 figures.

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

“…At the switching time, the state space of the system (in particular, its dimension) changes. Such switchings occur, for example, under the change of the number of control objects in control problems for groups of variable [1]. Control systems with variable state spaces were studied, for example, in [2]- [10] under different names.…”