Necessary Conditions for the Optimality and Sustainability of Solutions in Infinite-Horizon Optimal Control Problems

The paper deals with an infinite-horizon optimal control problem with general asymptotic endpoint constraints. The fulfillment of constraints of this type can be viewed as the minimal necessary condition for the sustainability of solutions. A new version of the Pontryagin maximum principle with an e...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-09, Vol.11 (18), p.3851
Main Author: Aseev, Sergey M.
Format: Article
Language:English
Subjects:
asymptotic endpoint constraints
Cauchy problems
conditional cost function
Control theory
Cost control
Economic growth
Economics
Growth models
Horizon
infinite horizon
Mathematical functions
Mathematics
Maximum principle
Optimal control
Optimization
Phasors
Pontryagin maximum principle
Sustainability
Sustainable development
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Summary:The paper deals with an infinite-horizon optimal control problem with general asymptotic endpoint constraints. The fulfillment of constraints of this type can be viewed as the minimal necessary condition for the sustainability of solutions. A new version of the Pontryagin maximum principle with an explicitly specified adjoint variable is developed. The proof of the main results is based on the fact that the restriction of the optimal process to any finite time interval is a solution to the corresponding finite-horizon problem containing the conditional cost of the phase vector as a terminal term.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11183851