Synthesis of Optimal Hybrid Systems for Multipurpose Time-Optimal Operation

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...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2021-06, Vol.255 (5), p.574-586
Main Authors: Bortakovskii, A. S., Evdokimova, E. A.
Format: Article
Language:English
Subjects:
Continuity (mathematics)
Hybrid systems
Mathematics
Mathematics and Statistics
Optimization
Time optimal control
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05394-3