Conditional Cost Function and Necessary Optimality Conditions for Infinite Horizon Optimal Control Problems

An infinite horizon optimal control problem with general endpoint constraints is reduced to a family of standard problems on finite time intervals containing the conditional cost of the phase vector as a terminal term. A new version of the Pontryagin maximum principle containing an explicit characte...

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Bibliographic Details
Published in:Doklady. Mathematics 2023-12, Vol.108 (3), p.425-430
Main Author: Aseev, S. M.
Format: Article
Language:English
Subjects:
Canonical forms
Cost function
Mathematics
Mathematics and Statistics
Maximum principle
Optimal control
Optimization
Phasors
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Summary:An infinite horizon optimal control problem with general endpoint constraints is reduced to a family of standard problems on finite time intervals containing the conditional cost of the phase vector as a terminal term. A new version of the Pontryagin maximum principle containing an explicit characterization of the adjoint variable is obtained for the problem with a general asymptotic endpoint constraint. In the case of the problem with a free final state, this approach leads to a normal form version of the maximum principle formulated completely in the terms of the conditional cost function.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562423600586